A fully Bayesian approach for comprehensive mapping of magnitude and phase brain activation in complex-valued fMRI data

Functional magnetic resonance imaging (fMRI) plays a crucial role in neuroimaging, enabling the exploration of brain activity through complex-valued signals. These signals, composed of magnitude and phase, offer a rich source of information for understanding brain functions. Traditional fMRI analyses have largely focused on magnitude information, often overlooking the potential insights offered by phase data. In this paper, we propose a novel fully Bayesian model designed for analyzing single-subject complex-valued fMRI (cv-fMRI) data. Our model, which we refer to as the CV-M&P model, is distinctive in its comprehensive utilization of both magnitude and phase information in fMRI signals, allowing for independent prediction of different types of activation maps. We incorporate Gaussian Markov random fields (GMRFs) to capture spatial correlations within the data, and employ image partitioning and parallel computation to enhance computational efficiency. Our model is rigorously tested through simulation studies, and then applied to a real dataset from a unilateral finger-tapping experiment. The results demonstrate the model's effectiveness in accurately identifying brain regions activated in response to specific tasks, distinguishing between magnitude and phase activation.

Automatic detection of myocardial ischaemia using generalisable spatio-temporal hierarchical Bayesian modelling of DCE-MRI

Dynamic Contrast Enhanced Magnetic Resonance Imaging (DCE-MRI) can be used as a non-invasive method for the assessment of myocardial perfusion. The acquired images can be utilised to analyse the spatial extent and severity of myocardial ischaemia (regions with impaired microvascular blood flow). In the present paper, we propose a novel generalisable spatio-temporal hierarchical Bayesian model (GST-HBM) to automate the detection of ischaemic lesions and improve the in silico prediction accuracy by systematically integrating spatio-temporal context information. We present a computational inference procedure with an adequate trade-off between accuracy and computational efficiency, whereby model parameters are sampled from the posterior distribution with Gibbs sampling, while lower-level hyperparameters are selected using model selection strategies based on the Watanabe Akaike information criterion (WAIC). We have assessed our method on both synthetic (in silico) data with known gold-standard and 12 sets of clinical first-pass myocardial perfusion DCE-MRI datasets. We have also carried out a comparative performance evaluation with four established alternative methods: Gaussian mixture model (GMM), opening and closing operations based on Gaussian mixture model (GMMC&Omax), Markov random field constrained Gaussian mixture model (GMM-MRF) and model-based hierarchical Bayesian model (M-HBM). Our results show that the proposed GST-HBM method achieves much higher in silico prediction accuracy than the established alternative methods. Furthermore, this method appears to provide a more robust delineation of ischaemic lesions in datasets affected by spatially variant noise.

Genetic evaluation of gestation length in Italian Holstein breed

Gestation length (GL) can potentially affect health and performance of both the dam and the newborn calf, and it is controlled by two genetic components, direct and maternal. This means that both the calf (direct effect) and the cow (maternal effect) genotypes contribute to determine GL and its variability. The aims of the present study were to estimate direct and maternal variance components of GL, develop a routine genetic evaluation of GL in Italian Holstein and evaluate potential (un)favourable associations with traits for which selection is undertaken in this population. A multiple-trait repeatability linear animal model was employed for the estimation of variance components considering GL in first and later parities as different traits. The posterior mean (PM) of heritability of the direct effect was 0.43 for first parity and 0.35 for later parities. The PM of heritability of the maternal effect was lower, being 0.08 for primiparae and 0.06 for pluriparae. The posterior standard deviation (PSD) of the heritability estimates was small, ranging from 0.001 to 0.005. The relationship of direct and maternal effects with important traits such as milk yield and fertility indicated that selecting for extreme GL, longer or shorter, may have negative consequences on several traits, suggesting that GL has an intermediate optimum in dairy cattle. In conclusion, this study reveals that selecting an intermediate GL in the Italian Holstein population is advisable. Although scarcely variable compared to other conventional traits for which Italian Holstein is selected, GL is heritable and a deeper knowledge can be useful for decision-making at the farm level.

A Gibbs-INLA algorithm for multidimensional graded response model analysis

In this paper, we propose a novel Gibbs-INLA algorithm for the Bayesian inference of graded response models with ordinal response based on multidimensional item response theory. With the combination of the Gibbs sampling and the integrated nested Laplace approximation (INLA), the new framework avoids the cumbersome tuning which is inevitable in classical Markov chain Monte Carlo (MCMC) algorithm, and has low computing memory, high computational efficiency with much fewer iterations, and still achieve higher estimation accuracy. Therefore, it has the ability to handle large amount of multidimensional response data with different item responses. Simulation studies are conducted to compare with the Metroplis-Hastings Robbins-Monro (MH-RM) algorithm and an application to the study of the IPIP-NEO personality inventory data is given to assess the performance of the new algorithm. Extensions of the proposed algorithm for application on more complicated models and different data types are also discussed.

Genetic analysis of milk and milk composition traits in Murrah buffaloes using Bayesian inference

Accurate and unbiased assessment of genetic parameters of milk and milk composition traits play an important role in formulating breeding program for genetic improvement of Murrah buffaloes. In this study, data spread over 28 years were utilized to estimate genetic parameters of traits viz., 305 d milk yield (305MY), 305 d fat yield (305FY), 305 d solid not fat yield (305SNFY), milk fat percentage (fat%) and solid not fat percentage (SNF) percentage (SNF%) in Murrah buffaloes kept at ICAR-National Dairy Research Institute, Karnal. Bayesian multiple-trait analysis was done using animal model and Gibbs sampling to estimate (co)variance components. Posterior means of heritability and posterior standard deviation for 305MY, 305FY, 305SNFY, fat% and SNF% were 0.18 ± 0.05, 0.17 ± 0.05, 0.18 ± 0.05, 0.07 ± 0.03 and 0.15 ± 0.06 and posterior means of repeatability estimates along with posterior standard deviation for corresponding traits were 0.33 ± 0.04, 0.32 ± 0.04, 0.33 ± 0.04, 0.14 ± 0.02 and 0.30 ± 0.04, respectively. Estimates of genetic correlation varied from -0.080 (305MY and fat %) to 0.999 (305MY and 305SNFY). Permanent environmental correlations varied from -0.060 (305MY and SNF%) to 0.999 (305FY and 305SNFY). This study indicated that all considered traits except fat% have ample genetic variability which can be exploited for selection and genetic improvement of Murrah buffaloes.

A Bayesian latent class extension of naive Bayesian classifier and its application to the classification of gastric cancer patients

BACKGROUND

The Naive Bayes (NB) classifier is a powerful supervised algorithm widely used in Machine Learning (ML). However, its effectiveness relies on a strict assumption of conditional independence, which is often violated in real-world scenarios. To address this limitation, various studies have explored extensions of NB that tackle the issue of non-conditional independence in the data. These approaches can be broadly categorized into two main categories: feature selection and structure expansion. In this particular study, we propose a novel approach to enhancing NB by introducing a latent variable as the parent of the attributes. We define this latent variable using a flexible technique called Bayesian Latent Class Analysis (BLCA). As a result, our final model combines the strengths of NB and BLCA, giving rise to what we refer to as NB-BLCA. By incorporating the latent variable, we aim to capture complex dependencies among the attributes and improve the overall performance of the classifier.

METHODS

Both Expectation-Maximization (EM) algorithm and the Gibbs sampling approach were offered for parameter learning. A simulation study was conducted to evaluate the classification of the model in comparison with the ordinary NB model. In addition, real-world data related to 976 Gastric Cancer (GC) and 1189 Non-ulcer dyspepsia (NUD) patients was used to show the model's performance in an actual application. The validity of models was evaluated using the 10-fold cross-validation.

RESULTS

The presented model was superior to ordinary NB in all the simulation scenarios according to higher classification sensitivity and specificity in test data. The NB-BLCA model using Gibbs sampling accuracy was 87.77 (95% CI: 84.87-90.29). This index was estimated at 77.22 (95% CI: 73.64-80.53) and 74.71 (95% CI: 71.02-78.15) for the NB-BLCA model using the EM algorithm and ordinary NB classifier, respectively.

CONCLUSIONS

When considering the modification of the NB classifier, incorporating a latent component into the model offers numerous advantages, particularly within medical and health-related contexts. By doing so, the researchers can bypass the extensive search algorithm and structure learning required in the local learning and structure extension approach. The inclusion of latent class variables allows for the integration of all attributes during model construction. Consequently, the NB-BLCA model serves as a suitable alternative to conventional NB classifiers when the assumption of independence is violated, especially in domains pertaining to health and medicine.

Does climate change affect the transmission of COVID-19? A Bayesian regression analysis

Aim

Coronavirus is an airborne and infectious disease and it is crucial to check the impact of climatic risk factors on the transmission of COVID-19. The main objective of this study is to determine the effect of climate risk factors using Bayesian regression analysis.

Methods

Coronavirus disease 2019, due to the effect of the SARS-CoV-2 virus, has become a serious global public health issue. This disease was identified in Bangladesh on March 8, 2020, though it was initially identified in Wuhan, China. This disease is rapidly transmitted in Bangladesh due to the high population density and complex health policy setting. To meet our goal, The MCMC with Gibbs sampling is used to draw Bayesian inference, which is implemented in WinBUGS software.

Results

The study revealed that high temperatures reduce confirmed cases and deaths from COVID-19, but low temperatures increase confirmed cases and deaths. High temperatures have decreased the proliferation of COVID-19, reducing the virus's survival and transmission.

Conclusions

Considering only the existing scientific evidence, warm and wet climates seem to reduce the spread of COVID-19. However, more climate variables could account for explaining most of the variability in infectious disease transmission.

A comparison of numerical approaches for statistical inference with stochastic models

Due to our limited knowledge about complex environmental systems, our predictions of their behavior under different scenarios or decision alternatives are subject to considerable uncertainty. As this uncertainty can often be relevant for societal decisions, the consideration, quantification and communication of it is very important. Due to internal stochasticity, often poorly known influence factors, and only partly known mechanisms, in many cases, a stochastic model is needed to get an adequate description of uncertainty. As this implies the need to infer constant parameters, as well as the time-course of stochastic model states, a very high-dimensional inference problem for model calibration has to be solved. This is very challenging from a methodological and a numerical perspective. To illustrate aspects of this problem and show options to successfully tackle it, we compare three numerical approaches: Hamiltonian Monte Carlo, Particle Markov Chain Monte Carlo, and Conditional Ornstein-Uhlenbeck Sampling. As a case study, we select the analysis of hydrological data with a stochastic hydrological model. We conclude that the performance of the investigated techniques is comparable for the analyzed system, and that also generality and practical considerations may be taken into account to guide the choice of which technique is more appropriate for a particular application.

Supplementary Information

The online version contains supplementary material available at 10.1007/s00477-023-02434-z.

Estimation of genetic parameters for important traits using a multi-trait model in late-feathering Qingyuan partridge hens in China

Qingyuan partridge chicken is one of the most well-known Chinese indigenous yellow broilers. In breeding programmes, five traits are usually selected when the chickens are 105 days old, namely body weight (BW), comb height (CH), shank length (SL), shank girth (SG) and feather maturity (FM). The objective of this study was to estimate the genetic parameters of these five traits, especially direct additive genetic correlations, to lay the foundation for balanced selection of Qingyuan partridge chickens. Approximately 9600 records were used for estimation. Variance components for these five traits were estimated using three multi-trait models incorporating different effects via Gibbs sampling. Based on model 1 in which the random effects included direct additive genetic effects and residuals, the estimated direct heritabilities for BW, CH, SL, SG and FM were 0.29 ± 0.04, 0.53 ± 0.04, 0.47 ± 0.04, 0.43 ± 0.05 and 0.18 ± 0.03, respectively. The direct genetic correlations ranged from -0.08 to 0.46. When additionally considering maternal additive genetic effects (model 2), the estimates of direct heritabilities and absolute values of direct additive genetic correlations were smaller. The heritabilities were 0.14 ± 0.04, 0.40 ± 0.02, 0.34 ± 0.05, 0.27 ± 0.05 and 0.12 ± 0.03 for BW, CH, SL, SG and FM, respectively. The direct additive genetic correlations ranged from -0.33 to 0.36. More specifically, the direct additive genetic correlations between BW and CH, SL, SG and FM were 0.19 ± 0.13, 0.15 ± 0.15, 0.36 ± 0.15 and - 0.33 ± 0.21, respectively. The genetic correlations of FM with SL, SG and CH were - 0.15 ± 0.15, -0.08 ± 0.17 and 0.18 ± 0.15, respectively. The direct genetic correlations between CH and SG and SL were - 0.02 ± 0.11 and - 0.20 ± 0.11, respectively, and that between SL and SG was 0.19 ± 0.11. The total heritabilities and maternal additive genetic correlations ranged from 0.16 to 0.44 and from -0.13 to 0.61, respectively. The third model also included the maternal permanent environmental effect for BW. The estimates of direct heritability, direct additive genetic correlation, total heritability and maternal additive genetic correlation were only slightly different from those based on the second model. Therefore, the maternal additive genetic effect has a large effect on the estimation of genetic parameters, and it is better to consider this effect in the genetic evaluation of these five traits. Relatively high direct and maternal additive genetic correlations for most trait pairs suggested that it is better to jointly evaluate these five traits in breeding programmes.

Gene differential co-expression analysis of male infertility patients based on statistical and machine learning methods

Male infertility has always been one of the important factors affecting the infertility of couples of gestational age. The reasons that affect male infertility includes living habits, hereditary factors, etc. Identifying the genetic causes of male infertility can help us understand the biology of male infertility, as well as the diagnosis of genetic testing and the determination of clinical treatment options. While current research has made significant progress in the genes that cause sperm defects in men, genetic studies of sperm content defects are still lacking. This article is based on a dataset of gene expression data on the X chromosome in patients with azoospermia, mild and severe oligospermia. Due to the difference in the degree of disease between patients and the possible difference in genetic causes, common classical clustering methods such as k-means, hierarchical clustering, etc. cannot effectively identify samples (realize simultaneous clustering of samples and features). In this paper, we use machine learning and various statistical methods such as hypergeometric distribution, Gibbs sampling, Fisher test, etc. and genes the interaction network for cluster analysis of gene expression data of male infertility patients has certain advantages compared with existing methods. The cluster results were identified by differential co-expression analysis of gene expression data in male infertility patients, and the model recognition clusters were analyzed by multiple gene enrichment methods, showing different degrees of enrichment in various enzyme activities, cancer, virus-related, ATP and ADP production, and other pathways. At the same time, as this paper is an unsupervised analysis of genetic factors of male infertility patients, we constructed a simulated data set, in which the clustering results have been determined, which can be used to measure the effect of discriminant model recognition. Through comparison, it finds that the proposed model has a better identification effect.

Direct Estimation of Diagnostic Classification Model Attribute Mastery Profiles via a Collapsed Gibbs Sampling Algorithm

This paper proposes a novel collapsed Gibbs sampling algorithm that marginalizes model parameters and directly samples latent attribute mastery patterns in diagnostic classification models. This estimation method makes it possible to avoid boundary problems in the estimation of model item parameters by eliminating the need to estimate such parameters. A simulation study showed the collapsed Gibbs sampling algorithm can accurately recover the true attribute mastery status in various conditions. A second simulation showed the collapsed Gibbs sampling algorithm was computationally more efficient than another MCMC sampling algorithm, implemented by JAGS. In an analysis of real data, the collapsed Gibbs sampling algorithm indicated good classification agreement with results from a previous study.

Bayesian analysis of longitudinal binary responses based on the multivariate probit model: A comparison of five methods

Dichotomous response data observed over multiple time points, especially data that exhibit longitudinal structures, are important in many applied fields. The multivariate probit model has been an attractive tool in such situations for its ability to handle correlations among the outcomes, typically by modeling the covariance (correlation) structure of the latent variables. In addition, a multivariate probit model facilitates controlled imputations for nonignorable dropout, a phenomenon commonly observed in clinical trials of experimental drugs or biologic products. While the model is relatively simple to specify, estimation, particularly from a Bayesian perspective that relies on Markov chain Monte Carlo sampling, is not as straightforward. Here we compare five sampling algorithms for the correlation matrix and discuss their merits: a parameter-expanded Metropolis-Hastings algorithm (Zhang et al., 2006), a parameter-expanded Gibbs sampling algorithm (Talhouk et al., 2012), a parameter-expanded Gibbs sampling algorithm with unit constraints on conditional variances (Tang, 2018), a partial autocorrelation parameterization approach (Gaskins et al., 2014), and a semi-partial correlation parameterization approach (Ghosh et al., 2021). We describe each algorithm, use simulation studies to evaluate their performance, and focus on comparison criteria such as computational cost, convergence time, robustness, and ease of implementations. We find that the parameter-expanded Gibbs sampling algorithm by Talhouk et al. (2012) often has the most efficient convergence with relatively low computational complexity, while the partial autocorrelation parameterization approach is more flexible for estimating the correlation matrix of latent variables for typical late phase longitudinal studies.

Evaluating the effectiveness of a geostatistical approach with groundwater flow modeling for three-dimensional estimation of a contaminant plume

When assessing the risk from an underground environment that is contaminated by radioactive nuclides and hazardous chemicals and planning for remediation, the contaminant plume distribution and the associated uncertainty from measured data should be estimated accurately. While the release history of the contaminant plume may be unknown, the extent of the plume caused by a known source and the associated uncertainty can be calculated inversely from the concentration data using a geostatistical method that accounts for the temporal correlation of its release history and groundwater flow modeling. However, the preceding geostatistical approaches have three drawbacks: (1) no applications of the three-dimensional plume estimation using concentration data from multiple depths in real situations, (2) no constraints for the estimation of the plume distribution, which can yield negative concentration and large uncertainties, and (3) few applications to actual cases with multiple contaminants. To address these problems, the non-negativity constraint using Gibbs sampling was incorporated into the geostatistical method with groundwater flow modeling for contaminant plume estimation. This method was then tested on groundwater contamination in the Gloucester landfill in Ontario, Canada, using three-dimensional contaminant transport model and concentration data from multiple depths. The method was applied to three water soluble organic contaminants: 1,4-dioxane, tetrahydrofuran, and diethyl ether. The effectiveness of the proposed method was verified by the general agreement of the calculated plume distributions of the three contaminants with concentration data from 66 points in 1982 (linear correlation coefficient of about 0.7). In particular, the reproduced peak of 1,4-dioxane corresponding to the large disposal in 1978 was more accurate than the result of preceding minimum relative entropy-based studies. The same peak also appeared in the tetrahydrofuran and diethyl ether distributions approximately within the range of the retardation factor derived from the fraction of organic carbon.

Bayesian dynamic network modelling: an application to metabolic associations in cardiovascular diseases

We propose a novel approach to the estimation of multiple Graphical Models to analyse temporal patterns of association among a set of metabolites over different groups of patients. Our motivating application is the Southall And Brent REvisited (SABRE) study, a tri-ethnic cohort study conducted in the UK. We are interested in identifying potential ethnic differences in metabolite levels and associations as well as their evolution over time, with the aim of gaining a better understanding of different risk of cardio-metabolic disorders across ethnicities. Within a Bayesian framework, we employ a nodewise regression approach to infer the structure of the graphs, borrowing information across time as well as across ethnicities. The response variables of interest are metabolite levels measured at two time points and for two ethnic groups, Europeans and South-Asians. We use nodewise regression to estimate the high-dimensional precision matrices of the metabolites, imposing sparsity on the regression coefficients through the dynamic horseshoe prior, thus favouring sparser graphs. We provide the code to fit the proposed model using the software Stan, which performs posterior inference using Hamiltonian Monte Carlo sampling, as well as a detailed description of a block Gibbs sampling scheme.

Perfect Sampling of the Posterior in the Hierarchical Pitman-Yor Process

The predictive probabilities of the hierarchical Pitman-Yor process are approximated through Monte Carlo algorithms that exploits the Chinese Restaurant Franchise (CRF) representation. However, in order to simulate the posterior distribution of the hierarchical Pitman-Yor process, a set of auxiliary variables representing the arrangement of customers in tables of the CRF must be sampled through Markov chain Monte Carlo. This paper develops a perfect sampler for these latent variables employing ideas from the Propp-Wilson algorithm and evaluates its average running time by extensive simulations. The simulations reveal a significant dependence of running time on the parameters of the model, which exhibits sharp transitions. The algorithm is compared to simpler Gibbs sampling procedures, as well as a procedure for unbiased Monte Carlo estimation proposed by Glynn and Rhee. We illustrate its use with an example in microbial genomics studies.

Multi-trait Bayesian Shrinkage and Variable Selection Models with the BGLR R-package

The BGLR-R package implements various types of single-trait shrinkage/variable selection Bayesian regressions. The package was first released in 2014, since then it has become a software very often used in genomic studies. We recently develop functionality for multitrait models. The implementation allows users to include an arbitrary number of random-effects terms. For each set of predictors, users can choose diffuse, Gaussian, and Gaussian–spike–slab multivariate priors. Unlike other software packages for multitrait genomic regressions, BGLR offers many specifications for (co)variance parameters (unstructured, diagonal, factor analytic, and recursive). Samples from the posterior distribution of the models implemented in the multitrait function are generated using a Gibbs sampler, which is implemented by combining code written in the R and C programming languages. In this article, we provide an overview of the models and methods implemented BGLR’s multitrait function, present examples that illustrate the use of the package, and benchmark the performance of the software.

Approximately counting and sampling knowledge states

Approximately counting and sampling knowledge states from a knowledge space is a problem that is of interest for both applied and theoretical reasons. However, many knowledge spaces used in practice are far too large for standard statistical counting and estimation techniques to be useful. Thus, in this work we use an alternative technique for counting and sampling knowledge states from a knowledge space. This technique is based on a procedure variously known as subset simulation, the Holmes-Diaconis-Ross method, or multilevel splitting. We make extensive use of Markov chain Monte Carlo methods and, in particular, Gibbs sampling, and we analyse and test the accuracy of our results in numerical experiments.

Gibbs Sampling Detection for Large MIMO and MTC Uplinks with Adaptive Modulation

Wireless networks beyond 5G will mostly be serving myriads of sensors and other machine-type communications (MTC), with each device having different requirements in respect to latency, error rate, energy consumption, spectral efficiency or other specifications. Multiple-input multiple-output (MIMO) systems remain a central technology towards 6G, and in cases where massive antenna arrays or cell-free networks are not possible to deploy and only moderately large antenna arrays are allowed, the detection problem at the base-station cannot rely on zero-forcing or matched filters and more complex detection schemes have to be used. The main challenge is to find low complexity, hardware feasible methods that are able to attain near optimal performance. Randomized algorithms based on Gibbs sampling (GS) were proven to perform very close to the optimal detection, even for moderately large antenna arrays, while yielding an acceptable number of operations. However, their performance is highly dependent on the chosen "temperature" parameter (TP). In this paper, we propose and study an optimized variant of the GS method, denoted by triple mixed GS, and where three distinct values for the TP are considered. The method exhibits faster convergence rates than the existing ones in the literature, hence requiring fewer iterations to achieve a target bit error rate. The proposed detector is suitable for symmetric large MIMO systems, however the proposed fixed complexity detector is highly suitable to spectrally efficient adaptively modulated MIMO (AM-MIMO) systems where different types of devices upload information at different bit rates or have different requirements regarding spectral efficiency. The proposed receiver is shown to attain quasi-optimal performance in both scenarios.

Coming Together of Bayesian Inference and Skew Spherical Data

This paper presents Bayesian directional data modeling via the skew-rotationally-symmetric Fisher-von Mises-Langevin (FvML) distribution. The prior distributions for the parameters are a pivotal building block in Bayesian analysis, therefore, the impact of the proposed priors will be quantified using the Wasserstein Impact Measure (WIM) to guide the practitioner in the implementation process. For the computation of the posterior, modifications of Gibbs and slice samplings are applied for generating samples. We demonstrate the applicability of our contribution via synthetic and real data analyses. Our investigation paves the way for Bayesian analysis of skew circular and spherical data.

BML: a versatile web server for bipartite motif discovery

Motif discovery and characterization are important for gene regulation analysis. The lack of intuitive and integrative web servers impedes the effective use of motifs. Most motif discovery web tools are either not designed for non-expert users or lacking optimization steps when using default settings. Here we describe bipartite motifs learning (BML), a parameter-free web server that provides a user-friendly portal for online discovery and analysis of sequence motifs, using high-throughput sequencing data as the input. BML utilizes both position weight matrix and dinucleotide weight matrix, the latter of which enables the expression of the interdependencies of neighboring bases. With input parameters concerning the motifs are given, the BML achieves significantly higher accuracy than other available tools for motif finding. When no parameters are given by non-expert users, unlike other tools, BML employs a learning method to identify motifs automatically and achieve accuracy comparable to the scenario where the parameters are set. The BML web server is freely available at http://motif.t-ridership.com/ (https://github.com/Mohammad-Vahed/BML).

A Gibbs sampler for the multidimensional four-parameter logistic item response model via a data augmentation scheme

The four-parameter logistic (4PL) item response model, which includes an upper asymptote for the correct response probability, has drawn increasing interest due to its suitability for many practical scenarios. This paper proposes a new Gibbs sampling algorithm for estimation of the multidimensional 4PL model based on an efficient data augmentation scheme (DAGS). With the introduction of three continuous latent variables, the full conditional distributions are tractable, allowing easy implementation of a Gibbs sampler. Simulation studies are conducted to evaluate the proposed method and several popular alternatives. An empirical data set was analysed using the 4PL model to show its improved performance over the three-parameter and two-parameter logistic models. The proposed estimation scheme is easily accessible to practitioners through the open-source IRTlogit package.

A spatio-temporal statistical model to analyze COVID-19 spread in the USA

Coronavirus pandemic has affected the whole world extensively and it is of immense importance to understand how the disease is spreading. In this work, we provide evidence of spatial dependence in the pandemic data and accordingly develop a new statistical technique that captures the spatio-temporal dependence pattern of the COVID-19 spread appropriately. The proposed model uses a separable Gaussian spatio-temporal process, in conjunction with an additive mean structure and a random error process. The model is implemented through a Bayesian framework, thereby providing a computational advantage over the classical way. We use state-level data from the United States of America in this study. We show that a quadratic trend pattern is most appropriate in this context. Interestingly, the population is found not to affect the numbers significantly, whereas the number of deaths in the previous week positively affects the spread of the disease. Residual diagnostics establish that the model is adequate enough to understand the spatio-temporal dependence pattern in the data. It is also shown to have superior predictive power than other spatial and temporal models. In fact, we show that the proposed approach can predict well for both short term (1 week) and long term (up to three months).

Hamiltonian Monte Carlo method for estimating variance components

A Hamiltonian Monte Carlo algorithm is a Markov chain Monte Carlo method, and the method has a potential to improve estimating parameters effectively. Hamiltonian Monte Carlo is based on Hamiltonian dynamics, and it follows Hamilton's equations, which are expressed as two differential equations. In the sampling process of Hamiltonian Monte Carlo, a numerical integration method called leapfrog integration is used to approximately solve Hamilton's equations, and the integration is required to set the number of discrete time steps and the integration stepsize. These two parameters require some amount of tuning and calibration for effective sampling. In this study, we applied the Hamiltonian Monte Carlo method to animal breeding data and identified the optimal tunings of leapfrog integration for normal and inverse chi-square distributions. Then, using real pig data, we revealed the properties of the Hamiltonian Monte Carlo method with the optimal tuning by applying models including variance explained by pedigree information or genomic information. Compared with the Gibbs sampling method, the Hamiltonian Monte Carlo method had superior performance in both models. We have provided the source codes of this method written in the Fortran language at https://github.com/A-ARAKAWA/HMC.

Estimation of genetic parameters for production and reproductive traits in Indian Karan-Fries cattle using multi-trait Bayesian approach

Estimates of variance components are needed for implementing genetic selection. This study was conducted to genetic parameters for production and reproductive traits on Indian Karan-Fries cattle using multi-trait repeatability animal model. Data collected from ICAR-National Dairy Research Institute, Karnal, India (from 1988 to 2019) were used. Single-trait and multi-trait repeatability animal models were used for parameter estimation. The posterior mean of Heritability estimates for 305-day milk yield (305-DMY), lactation milk yield (LMY), lactation length (LL) were 0.20 ± 0.03, 0.19 ± 0.03 and 0.06 ± 0.02, respectively. For age at first calving (AFC), calving interval (CI), and days open (DO), the posterior mean of heritability estimates were 0.24 ± 0.08, 0.06 ± 0.01, and 0.07 ± 0.02, respectively. The repeatability estimates for 305-DMY, LMY, LL, CI, and DO were 0.37 ± 0.02, 0.34 ± 0.02, 0.15 ± 0.02, 0.09 ± 0.02, and 0.12 ± 0.02, respectively. Genetic correlation between milk production traits (305-DMY, LMY, and LL) was positive and strong (> 0.80). However, the genetic correlation between milk production trait and AFC ranges from - 0.31 to 0.12. Unfavorable strong genetic correlations were observed between production and reproductive traits (CI and DO) with values ranged from 0.5 to 0.7. Phenotypic correlations among 305-DMY, LMY, and LL were generally positive and high. The moderate heritability estimates and potential genetic variation for 305-DMY, TMY, and AFC suggested that genetic gain can be obtained for these traits through genetic selection. Low heritability estimates found for LL, CI and DO, indicating that the possibility of changing these traits through genetic selection is small. High genetic correlation observed between productive and fertility traits were unfavorable. The existed strong genetic and phenotypic correlation estimates between CI and DO indicates that recording only one of them would be sufficient in the herd. As the multi-trait model showed slight improvements in the h² as well as r estimates for both productive and reproductive traits over univariate analysis, future selection with a multi-trait animal model applying Bayesian approach would be recommended.

Improving pest monitoring networks using a simulation-based approach to contribute to pesticide reduction

Conventional pest management mainly relies on the use of pesticides. However, the negative externalities of pesticides are now well known. More sustainable practices, such as Integrated Pest Management, are necessary to limit crop damage from pathogens, pests and weeds in agroecosystems. Reducing pesticide use requires information to determine whether chemical treatments are really needed. Pest monitoring networks (PMNs) are key contributors to this information. However, the effectiveness of a PMN in delivering relevant information about pests depends on its spatial sampling resolution and its memory length. The trade-off between the monitoring efforts and the usefulness of the information provided is highly dependent on pest ecological traits, the damage they can cause (in terms of crop losses), and economic drivers (production costs, agriculture product prices and incentives). Due to the high complexity of optimising PMNs, we have developed a theoretical model that belongs to the family of Dynamic Bayesian Networks in order to compare several PMNs performances. This model links the characteristics of a PMN to treatment decisions and the resulting pest dynamics. Using simulation and inference tools for graphical models, we derived the proportion of impacted fields, the number of pesticide treatments and the overall gross margins for three types of pest with contrasting levels of endocyclism. The term "endocyclic" refers to an organism whose development is mostly restricted to a field and highly depends on the inoculum present in the considered field. The presence of purely endocyclic pests at a given time increases the probability of reoccurrence. Conversely, slightly endocyclic pests have a low persistence. The simulation analysis considered ten scenarios: an expected margin-based strategy with a spatial resolution of four PMNs and two memory lengths (one year or eight years), as well as two extreme crop protection strategies (systematic treatments on all fields and systematic no treatment). For purely and mainly endocyclic pests (e.g. soil-borne pathogens and most weeds, respectively), we found that increasing the spatial resolution of PMNs made it possible to significantly decrease the number of treatments required for pest control. Taking past observations into account was also effective, but to a lesser extent. PMN information had virtually no influence on the control of non-endocyclic pests (such as flying insects or airborne plant pathogens) which may be due to the spatial coverage addressed in our study. The next step is to extend the analysis of PMNs and to integrate the information generated by PMNs into sustainable pest management strategies, both at the field and the landscape level.

Bayesian Analysis of a Quantile Multilevel Item Response Theory Model

Multilevel item response theory (MLIRT) models are used widely in educational and psychological research. This type of modeling has two or more levels, including an item response theory model as the measurement part and a linear-regression model as the structural part, the aim being to investigate the relation between explanatory variables and latent variables. However, the linear-regression structural model focuses on the relation between explanatory variables and latent variables, which is only from the perspective of the average tendency. When we need to explore the relationship between variables at various locations along the response distribution, quantile regression is more appropriate. To this end, a quantile-regression-type structural model named as the quantile MLIRT (Q-MLIRT) model is introduced under the MLIRT framework. The parameters of the proposed model are estimated using the Gibbs sampling algorithm, and comparison with the original (i.e., linear-regression-type) MLIRT model is conducted via a simulation study. The results show that the parameters of the Q-MLIRT model could be recovered well under different quantiles. Finally, a subset of data from PISA 2018 is analyzed to illustrate the application of the proposed model.

Evaluating uncertainty and variability associated with Toxoplasma gondii survival during cooking and low temperature storage of fresh cut meats

Toxoplasmosis is an infection caused by the protozoan parasite, Toxoplasma gondii. It has been reported as the fourth leading cause of hospitalization and second leading cause of death among 31 major foodborne pathogens in the United States. Humans are infected through consumption of raw or undercooked meat containing T. gondii tissue cysts or ingestion of food, soil, or water contaminated by T. gondii oocysts. People often lack knowledge about how to prevent T. gondii infection, especially the risks associated with eating or handling raw or undercooked meat. Current available data on cooking or low temperature storage for whole cuts of meat are not sufficient to validate inactivation of T. gondii. The objectives of the present study were to estimate the relationship of time and temperature with the survival rate of T. gondii during cooking and low temperature storage of fresh cut meats. We used different statistical sampling techniques such as bootstrap resampling and Gibbs sampling to establish those relationships. Monte Carlo simulation was used to estimate the safe temperature for cooking and storing meats. The results showed no detection of T. gondii in fresh meats when the internal temperature reached above 64 °C (147.2 °F) and below -18 °C (0 °F). The tissue cysts can remain viable at least up to 30 days at 4 °C (39 °F) and about 3.3% cysts survived at 62.8 °C (145 °F). This study can provide helpful information in improving the risk models to further mitigate the public health burden of toxoplasmosis.

Determination of correlations in multivariate longitudinal data with modified Cholesky and hypersphere decomposition using Bayesian variable selection approach

In this article, we present a Bayesian framework for multivariate longitudinal data analysis with a focus on selection of important elements in the generalized autoregressive matrix. An efficient Gibbs sampling algorithm was developed for the proposed model and its implementation in a comprehensive R package called MLModelSelection is available on the comprehensive R archive network. The performance of the proposed approach was studied via a comprehensive simulation study. The effectiveness of the methodology was illustrated using a nonalcoholic fatty liver disease dataset to study correlations in multiple responses over time to explain the joint variability of lung functions and body mass index. Supplementary materials for this article, including a standardized description of the materials needed to reproduce the work, are available as an online supplement.

Robust Bayesian Regression with Synthetic Posterior Distributions

Although linear regression models are fundamental tools in statistical science, the estimation results can be sensitive to outliers. While several robust methods have been proposed in frequentist frameworks, statistical inference is not necessarily straightforward. We here propose a Bayesian approach to robust inference on linear regression models using synthetic posterior distributions based on γ-divergence, which enables us to naturally assess the uncertainty of the estimation through the posterior distribution. We also consider the use of shrinkage priors for the regression coefficients to carry out robust Bayesian variable selection and estimation simultaneously. We develop an efficient posterior computation algorithm by adopting the Bayesian bootstrap within Gibbs sampling. The performance of the proposed method is illustrated through simulation studies and applications to famous datasets.

A Shadow-Test Approach to Adaptive Item Calibration

A shadow-test approach to the calibration of field-test items embedded in adaptive testing is presented. The objective function used in the shadow-test model selects both the operational and field-test items adaptively using a Bayesian version of the criterion of [Formula: see text]-optimality. The constraint set for the model can be used to hide the field-test items completely in the content of the test as well as to deal with such practical issues as random control of their exposure rates. The approach runs on efficient implementations of the Gibbs sampler for the real-time updating of the ability and field-test parameters. Optimal settings for the proposed algorithms were found and used to demonstrate item calibration with smaller than traditional sample sizes in runtimes fully comparable with conventional adaptive testing.

Robosample: A rigid-body molecular simulation program based on robot mechanics

BACKGROUND

Compared with all-atom molecular dynamics (MD), constrained MD methods allow for larger time steps, potentially reducing computational cost. For this reason, there has been continued interest in improving constrained MD algorithms to increase configuration space sampling in molecular simulations.

METHODS

Here, we introduce Robosample, a software package that implements high-performance constrained dynamics algorithms, originally developed for robotics, and applies them to simulations of biomolecular systems. As in the gMolmodel package developed by Spiridon and Minh in 2017, Robosample uses Constrained Dynamics Hamiltonian Monte Carlo (CDHMC) as a Gibbs sampling move - a type of Monte Carlo move where a subset of coordinates is allowed to change. In addition to the previously described Cartesian and torsional dynamics moves, Robosample implements spherical and cylindrical joints that can be distributed along the molecule by the user.

RESULTS

In alanine dipeptide simulations, the free energy surface is recovered by mixing fully flexible with torsional, cylindrical, or spherical dynamics moves. Ramachandran dynamics, where only the two key torsions are mobile, accelerate the slowest transition by an order of magnitude. We also show that simulations of a complex glycan cover significantly larger regions of the configuration space when mixed with constrained dynamics.

MAJOR CONCLUSIONS

Robosample is a tool of choice for efficient conformational sampling of large biomolecules.

GENERAL SIGNIFICANCE

Robosample is intended as a reliable and user-friendly simulation package for fast biomolecular sampling that does not require extensive expertise in mechanical engineering or in the statistical mechanics of reduced coordinates.

Breast Cancer Detection with Low-dimension Ordered Orthogonal Projection in Terahertz Imaging

This paper proposes a new dimension reduction algorithm based on low-dimension ordered orthogonal projection (LOOP), which is used for cancer detection with terahertz (THz) images of freshly excised human breast cancer tissues. A THz image can be represented by a data cube with each pixel containing a high dimension spectrum vector covering several THz frequencies, where each frequency represents a different dimension in the vector. The proposed algorithm projects the high-dimension spectrum vector of each pixel within the THz image into a low-dimension subspace that contains the majority of the unique features embedded in the image. The low-dimension subspace is constructed by sequentially identifying its orthonormal basis vectors, such that each newly chosen basis vector represents the most unique information not contained by existing basis vectors. A multivariate Gaussian mixture model is used to represent the statistical distributions of the low-dimension feature vectors obtained from the proposed dimension reduction algorithm. The model parameters are iteratively learned by using unsupervised learning methods such as Markov chain Monte Carlo or expectation maximization, and the results are used to classify the various regions within a tumor sample. Experiment results demonstrate that the proposed method achieves apparent performance improvement in human breast cancer tissue over existing approaches such as one-dimension Markov chain Monte Carlo. The results confirm that the dimension reduction algorithm presented in this paper is a promising technique for breast cancer detection with THz images, and the classification results present a good correlation with respect to the histopathology results of the analyzed samples.

CHROMATIX: computing the functional landscape of many-body chromatin interactions in transcriptionally active loci from deconvolved single cells

Chromatin interactions are important for gene regulation and cellular specialization. Emerging evidence suggests many-body spatial interactions play important roles in condensing super-enhancer regions into a cohesive transcriptional apparatus. Chromosome conformation studies using Hi-C are limited to pairwise, population-averaged interactions; therefore unsuitable for direct assessment of many-body interactions. We describe a computational model, CHROMATIX, which reconstructs ensembles of single-cell chromatin structures by deconvolving Hi-C data and identifies significant many-body interactions. For a diverse set of highly active transcriptional loci with at least 2 super-enhancers, we detail the many-body functional landscape and show DNase accessibility, POLR2A binding, and decreased H3K27me3 are predictive of interaction-enriched regions.

MultiBUGS: A Parallel Implementation of the BUGS Modelling Framework for Faster Bayesian Inference

MultiBUGS is a new version of the general-purpose Bayesian modelling software BUGS that implements a generic algorithm for parallelising Markov chain Monte Carlo (MCMC) algorithms to speed up posterior inference of Bayesian models. The algorithm parallelises evaluation of the product-form likelihoods formed when a parameter has many children in the directed acyclic graph (DAG) representation; and parallelises sampling of conditionally-independent sets of parameters. A heuristic algorithm is used to decide which approach to use for each parameter and to apportion computation across computational cores. This enables MultiBUGS to automatically parallelise the broad range of statistical models that can be fitted using BUGS-language software, making the dramatic speed-ups of modern multi-core computing accessible to applied statisticians, without requiring any experience of parallel programming. We demonstrate the use of MultiBUGS on simulated data designed to mimic a hierarchical e-health linked-data study of methadone prescriptions including 425,112 observations and 20,426 random effects. Posterior inference for the e-health model takes several hours in existing software, but MultiBUGS can perform inference in only 28 minutes using 48 computational cores.

A Bayesian Latent Class Model to Predict Kidney Obstruction in the Absence of Gold Standard

Kidney obstruction, if untreated in a timely manner, can lead to irreversible loss of renal function. A widely used technology for evaluations of kidneys with suspected obstruction is diuresis renography. However, it is generally very challenging for radiologists who typically interpret renography data in practice to build high level of competency due to the low volume of renography studies and insufficient training. Another challenge is that there is currently no gold standard for detection of kidney obstruction. Seeking to develop a computer-aided diagnostic (CAD) tool that can assist practicing radiologists to reduce errors in the interpretation of kidney obstruction, a recent study collected data from diuresis renography, interpretations on the renography data from highly experienced nuclear medicine experts as well as clinical data. To achieve the objective, we develop a statistical model that can be used as a CAD tool for assisting radiologists in kidney interpretation. We use a Bayesian latent class modeling approach for predicting kidney obstruction through the integrative analysis of time-series renogram data, expert ratings, and clinical variables. A nonparametric Bayesian latent factor regression approach is adopted for modeling renogram curves in which the coefficients of the basis functions are parameterized via the factor loadings dependent on the latent disease status and the extended latent factors that can also adjust for clinical variables. A hierarchical probit model is used for expert ratings, allowing for training with rating data from multiple experts while predicting with at most one expert, which makes the proposed model operable in practice. An efficient MCMC algorithm is developed to train the model and predict kidney obstruction with associated uncertainty. We demonstrate the superiority of the proposed method over several existing methods through extensive simulations. Analysis of the renal study also lends support to the usefulness of our model as a CAD tool to assist less experienced radiologists in the field.

Multi-Target Localization and Tracking Using TDOA and AOA Measurements Based on Gibbs-GLMB Filtering

This paper deals with mobile multi-target detection and tracking. In the traditional method, there are uncertainties such as misdetection and false alarm in the measurement data, and it will be inevitable having to deal with the data association. To solve the target trajectory and state estimation problem under a cluttered environment, this paper proposes a non-concurrent multi-target acoustic localization tracking method based on the Gibbs-generalized labelled multi-Bernoulli (Gibbs-GLMB) filter and considers an acoustic array of a fixed arrangement for the tracking of targets by joint time difference of arrival (TDOA) and angle of arrival (AOA) measurements. Firstly, the TDOAs are calculated by using the generalized cross-correlation algorithm (GCC) and the AOAs are derived from the received signal directions. Secondly, we assume the independence of the targets and fuse the measurements which are used to track the multiple targets via the Gibbs-GLMB filter. Finally, the effectiveness of the method is verified by Monte Carlo simulation experiments.

Modelling for the inheritance of multiple births and fertility in endangered equids: Determining risk factors and genetic parameters in donkeys (Equus asinus)

Multiple births or twinning in equids are dangerous, undesirable situations that compromise the life of the dam and resulting offspring. However, embryo vitrification and freezing techniques take advantage of individuals whose multiple ovulations allow flushing more fertilised embryos from the oviduct to be collected, increasing the productivity and profitability of reproductive techniques. Embryo preservation is especially important in highly endangered populations such as certain donkey (Equus asinus) breeds; for which conventional reproductive techniques have previously been deemed inefficient. For instance, becoming an effective alternative to artificial insemination with frozen semen to preserve the individuals' genetic material. The objective of this study was to examine the historical foaling records of Andalusian donkeys to estimate prevalence, risk factors, phenotypic and genetic parameters for multiple births, assessing the cumulative foal number born per animal, maximum foal number per birth and multiple birth number per animal. We designed a Bayesian General Animal Mixed Model with single records considering the 'fixed' effects of birth year, birth season, birth month, sex, farm, location, and husbandry system. Age was considered and included as a linear and quadratic covariate. Gibbs sampling reported heritability estimates ranging from 0.18 ± 0.101 to 0.24 ± 0.078. Genetic and phenotypic correlations ranged from 0.496 ± 0.298 to 0.846 ± 0.152 and 0.206 ± 0.063 to 0.607 ± 0.054, respectively. Predicted breeding values obtained enable the potential selection against/for these traits, offering a new perspective for donkey breeding and conservation.

Prediction of Structure and Molecular Interaction with DNA of BvrR, a Virulence-Associated Regulatory Protein of Brucella

Brucellosis, also known as "undulant fever" is a zoonotic disease caused by Brucella, which is a facultative intracellular bacterium. Despite efforts to eradicate this disease, infection in uncontrolled domestic animals persists in several countries and therefore transmission to humans is common. Brucella evasion of the innate immune system depends on its ability to evade the mechanisms of intracellular death in phagocytic cells. The BvrR-BvrS two-component system allows the bacterium to detect adverse conditions in the environment. The BvrS protein has been associated with genes of virulence factors, metabolism, and membrane transport. In this study, we predicted the DNA sequence recognized by BvrR with Gibbs Recursive Sampling and identified the three-dimensional structure of BvrR using I-TASSER suite, and the interaction mechanism between BvrR and DNA with Protein-DNA docking and molecular dynamics (MD) simulation. Based on the Gibbs recursive Sampling analysis, we found the motif AAHTGC (H represents A, C, and T nucleotides) as a possible sequence recognized by BvrR. The docking and EMD simulation results showed that C-terminal effector domain of BvrR protein is likely to interact with AAHTGC sequence. In conclusion, we predicted the structure, recognition motif, and interaction of BvrR with DNA.

Multinomial Models with Linear Inequality Constraints: Overview and Improvements of Computational Methods for Bayesian Inference

Many psychological theories can be operationalized as linear inequality constraints on the parameters of multinomial distributions (e.g., discrete choice analysis). These constraints can be described in two equivalent ways: Either as the solution set to a system of linear inequalities or as the convex hull of a set of extremal points (vertices). For both representations, we describe a general Gibbs sampler for drawing posterior samples in order to carry out Bayesian analyses. We also summarize alternative sampling methods for estimating Bayes factors for these model representations using the encompassing Bayes factor method. We introduce the R package multinomineq, which provides an easily-accessible interface to a computationally efficient implementation of these techniques.

Bayesian Hierarchical Model for Protein Identifications

In proteomics, identification of proteins from complex mixtures of proteins extracted from biological samples is an important problem. Among the experimental technologies, Mass-Spectrometry (MS) is the most popular one. Protein identification from MS data typically relies on a "two-step" procedure of identifying the peptide first followed by the separate protein identification procedure next. In this setup, the interdependence of peptides and proteins are neglected resulting in relatively inaccurate protein identification. In this article, we propose a Markov chain Monte Carlo (MCMC) based Bayesian hierarchical model, a first of its kind in protein identification, which integrates the two steps and performs joint analysis of proteins and peptides using posterior probabilities. We remove the assumption of independence of proteins by using clustering group priors to the proteins based on the assumption that proteins sharing the same biological pathway are likely to be present or absent together and are correlated. The complete conditionals of the proposed joint model being tractable, we propose and implement a Gibbs sampling scheme for full posterior inference that provides the estimation and statistical uncertainties of all relevant parameters. The model has better operational characteristics compared to two existing "one-step" procedures on a range of simulation settings as well as on two well-studied datasets.

Bayesian hierarchical model for comparison of different nonlinear function and genetic parameter estimates of meat quails

This study aimed to compare different nonlinear functions to describe the growth curve of European quails and to estimate growth curve parameters, (co)variance components, and genetic and systematic effects that affected the curve using a hierarchical Bayesian model that allows joint estimation. Three different models were fitted in the first stage (Gompertz, Logístic, and von Bertalanffy). The analyzed data set had 45,965 records of 6,838 meat quails selected for higher body weight at 42 d of age for 15 successive generations, weighed at birth, 7, 14, 21, 28, 35, and 42 d of age. Comparisons of the overall goodness of fit were based on deviance information criterion (DIC) and mean square error. Gelfand's check function compared the models at different points of the growth curve. In the second stage, the systematic (sex and generation) and genetic effects were considered in an animal model. Random samples of the a posteriori distributions were obtained by Metropolis-Hastings and Gibbs sampling algorithms. The Gompertz function presented lower DIC and better adjustment at different ages and was defined as the best fit. The heritabilities of A, b, and k parameters were moderate (0.32, 0.29, and 0.18, respectively). The genetics correlations were A and b (0.25), A and k (-0.50), and b and k (0.03). The samples of the posterior marginal distributions for the differences between the estimates of the parameters of the Gompertz model, for generation, A, b, k, age at inflexion point (APOI), and weight at inflexion point (WPOI) showed differences in relation to sex, the females are heavier, A, WPOI, and APOI for females were also higher. In conclusion, 15 generations of selection and changes in the environmental conditions altered the growth curve, leaving the quails heavier and with greater WPOI and APOI, decreased growth rate, and increased the birth weight. The curve parameters could be used in a selection index, despite the difficulty in selecting quails with higher rate of growth and adult body weight.

Bayesian Inference for Mixed Model-Based Genome-Wide Analysis of Expression Quantitative Trait Loci by Gibbs Sampling

The importance of expression quantitative trait locus (eQTL) has been emphasized in understanding the genetic basis of cellular activities and complex phenotypes. Mixed models can be employed to effectively identify eQTLs by explaining polygenic effects. In these mixed models, the polygenic effects are considered as random variables, and their variability is explained by the polygenic variance component. The polygenic and residual variance components are first estimated, and then eQTL effects are estimated depending on the variance component estimates within the frequentist mixed model framework. The Bayesian approach to the mixed model-based genome-wide eQTL analysis can also be applied to estimate the parameters that exhibit various benefits. Bayesian inferences on unknown parameters are based on their marginal posterior distributions, and the marginalization of the joint posterior distribution is a challenging task. This problem can be solved by employing a numerical algorithm of integrals called Gibbs sampling as a Markov chain Monte Carlo. This article reviews the mixed model-based Bayesian eQTL analysis by Gibbs sampling. Theoretical and practical issues of Bayesian inference are discussed using a concise description of Bayesian modeling and the corresponding Gibbs sampling. The strengths of Bayesian inference are also discussed. Posterior probability distribution in the Bayesian inference reflects uncertainty in unknown parameters. This factor is useful in the context of eQTL analysis where a sample size is too small to apply the frequentist approach. Bayesian inference based on the posterior that reflects prior knowledge, will be increasingly preferred with the accumulation of eQTL data. Extensive use of the mixed model-based Bayesian eQTL analysis will accelerate understanding of eQTLs exhibiting various regulatory functions.

Prediction of pivotal pathways and hub genes associated with osteoporosis by Gibbs sampling

Osteoporosis (OP) is a common metabolic bone disease with high incidence, and is recognized as a major public health problem worldwide. It is essential to clarify the pathogenesis of the disease for improving the diagnosis, prevention and treatment of OP. The aim of this study was to clarify the pivotal pathways and hub genes in OP using Gibbs sampling. The gene expression profile datasets were obtained from Gene Expression Omnibus (GEO) database. The pathways were enriched by Kyoto Encyclopedia of Genes and Genomes (KEGG) with genes intersection ≥5 based on gene expression profile data. Then, the acquired pathways were converted into Markov chains (MC). Gibbs sampling was conducted to obtain a new MC. In addition, the average probabilities of each pathway in two states containing human mesenchymal stem cells (hMSC) _middle-aged and hMSC_elderly were calculated through Markov chain Monte Carlo (MCMC) algorithm. Moreover, gene expression variation was taken into account to adjust the probability. Pivotal pathways were identified under adjusted posterior value >0.8. Then, Gibbs sampling was implemented to find hub genes from pathways. There were 280 pathways determined by the gene intersection ≥5. Gibbs sampling identified two disturbed pathways (pathways in cancer and influenza A) and two hub genes (cyclin A1 and WNT2) under the adjusted probability >0.8. Gene expression analysis showed that all the disturbed pathways and hub genes had increased expression levels in hMSC_middle-aged samples compared with hMSC_elderly samples. We identified two pivotal pathways and two hub genes in OP using Gibbs sampling. The results contribute to the understanding of underlying pathogenesis and could be considered as potential biomarkers for the therapy of OP.

Estimation of drug effect in radiographic progression for rheumatoid arthritis and psoriatic arthritis

To demonstrate the treatment effect on structural damage in rheumatoid arthritis (RA) and psoriatic arthritis (PsA), radiographic images of hands and feet are scored according to Sharp scoring systems in randomized clinical trials. However, the quantification of such an effect is challenging because the overall mean progression is lack of clinical interpretation. This article attempts to shed a light on the statistical challenges resulted from its scoring methods and heterogeneity of the study population and proposes a mixture distribution model approach to fit radiographic progression data. With such a model, the drug effect is fully captured by the mean progression of those patients who would progress in the study period under the control treatment. The resulting regression model also lends a tool in examining prognostic factors for radiographic progression. Simulations have been carried out to evaluate the precision of the parameter estimation procedure. Using the data examples from RA and PsA, we will show that the mixture distribution approach provides a better goodness of fit and leads to a casual inference of the study drug, hence a clinically meaningful interpretation.

Identification of hub genes associated with postmenopausal osteoporosis by Gibbs sampling method

Underlying pivotal pathways were identified to reveal potential key genes correlated with postmenopausal osteoporosis (PMOP). The pathways were enriched by Kyoto Encyclopedia of Genes and Genomes (KEGG) with genes intersection greater than 5 based on gene expression profile data, and the acquired pathways were then transformed to Markov chain (MC). Gibbs sampling was conducted to obtain a new MC. Moreover, the average probabilities of each pathway in normal and PMOP were computed via an MC Monte Carlo (MCMC) algorithm, and differential pathways were identified based on probabilities more than 0.7. In addition, frequencies of appearance of pathway genes were counted via MCMC and the hub genes were achieved with the probabilities of gene expression efficiencies in two states. Judging by the gene intersection more than 5, overall 280 pathways were determined. After Gibbs sampling, 2 differential pathways were obtained on the basis of probabilities more than 0.7. Moreover, the hub genes comprising TNNC1, MYL2, and TTN were achieved according to probabilities more than 0.7. The identified pathways and the three hub genes probably are useful for developing approaches for the diagnosis and treatment of PMOP in future preclinical and clinical applications.

Screening pathways and hub genes involved in osteoclastogenesis by gene expression analysis of circulating monocytes based on Gibbs sampling

Differential expression pathways and hub genes in circulating monocytes from healthy Chinese women with high peak bone mass (PBM) vs. low PBM were explored using a Markov chain Monte Carlo (MCMC) algorithm. Human circulating monocytes transcription profiling (containing 14 samples with high PBM and 12 samples with low PBM) and KEGG pathways were all downloaded from the public database. Initial state of all the pathways were constructed and Gibbs sampling was performed to obtain a Markov chain and the posterior values of all the pathways were calculated. The probability (α) of occurrence of each pathway was calculated based on the posterior value and it was adjusted by taking gene expression variation into account. Pathways with α_adj >0.8 were considered as differentially expressed pathways. Then, these steps were performed again on all the genes in the differentially expressed pathways to find the hub genes in the differential pathways. After Gibbs sampling, neuroactive ligand-receptor interaction (hsa04080) with α_adj = 0.986 was screened out as the differentially expressed pathway. Analyzing the genes in this pathway, three genes (neurotensin, tachykinin receptor 3 and follicle-stimulating hormone receptor) with α_adj >0.8 were identified as hub genes in circulating monocytes which may associate with osteoporosis development. One pathway and three genes which may possess close relationship with osteoporosis development were found in this study. These results provide insights into our understanding of the role of circulating monocytes in osteoporosis development.

Searching for perturbed biological pathways and genes through analyzing the expression profile changes in osteoclasts after treatment by bisphosphonates

Criticality pathways and genes related to osteoporosis were identified. We downloaded the expression data of osteoclasts treated with or without bisphosphonates and all human pathways from the public database. Gibbs sampling and Markov chain were performed to identify the disturbed pathways and the hub genes in the disturbed pathways. Pathways and genes with adjusted probability (α_adj ) ≥0.75 were considered as the disturbed pathways and hub genes. We identified four disturbed pathways (Maturity onset diabetes of the young, Olfactory transduction, Cyanoamino acid metabolism, Taurine and hypotaurine metabolism) and two hub genes (OR2A4 and NKX2-2) with α_adj ≥0.75. The expression levels of these disturbed pathways and hub genes were downregulated in bisphosphonates group. In conclusion, four disturbed pathways and two hub genes related to osteoporosis were identified. These results give us a better understanding of the potential mechanism of bisphosphonate treatment and the pathogenesis of osteoporosis.

A De Novo Shape Motif Discovery Algorithm Reveals Preferences of Transcription Factors for DNA Shape Beyond Sequence Motifs

DNA shape adds specificity to sequence motifs but has not been explored systematically outside this context. We hypothesized that DNA-binding proteins (DBPs) preferentially occupy DNA with specific structures ("shape motifs") regardless of whether or not these correspond to high information content sequence motifs. We present ShapeMF, a Gibbs sampling algorithm that identifies de novo shape motifs. Using binding data from hundreds of in vivo and in vitro experiments, we show that most DBPs have shape motifs and can occupy these in the absence of sequence motifs. This "shape-only binding" is common for many DBPs and in regions co-bound by multiple DBPs. When shape and sequence motifs co-occur, they can be overlapping, flanking, or separated by consistent spacing. Finally, DBPs within the same protein family have different shape motifs, explaining their distinct genome-wide occupancy despite having similar sequence motifs. These results suggest that shape motifs not only complement sequence motifs but also facilitate recognition of DNA beyond conventionally defined sequence motifs.

Surveillance of animal diseases through implementation of a Bayesian spatio-temporal model: A simulation example with neurological syndromes in horses and West Nile Virus

A potentially sensitive way to detect disease outbreaks is syndromic surveillance, i.e. monitoring the number of syndromes reported in the population of interest, comparing it to the baseline rate, and drawing conclusions about outbreaks using statistical methods. A decision maker may use the results to take disease control actions or to initiate enhanced epidemiological investigations. In addition to the total count of syndromes there are often additional pieces of information to consider when assessing the probability of an outbreak. This includes clustering of syndromes in space and time as well as historical data on the occurrence of syndromes, seasonality of the disease, etc. In this paper, we show how Bayesian theory for syndromic surveillance applies to the occurrence of neurological syndromes in horses in France. Neurological syndromes in horses may be connected e.g. to West Nile Virus (WNV), a zoonotic disease of growing concern for public health in Europe. A Bayesian method for spatio-temporal cluster detection of syndromes and for determining the probability of an outbreak is presented. It is shown how surveillance can be performed simultaneously for a specific class of diseases (WNV or diseases similar to WNV in terms of the information available to the system) and a non-specific class of diseases (not similar to WNV in terms of the information available to the system). We also discuss some new extensions to the spatio-temporal models and the computational algorithms involved. It is shown step-by-step how data from historical WNV outbreaks and surveillance data for neurological syndromes can be used for model construction. The model is implemented using a Gibbs sampling procedure, and its sensitivity and specificity is evaluated. Finally, it is illustrated how predictive modelling of syndromes can be useful for decision making in animal health surveillance.

Network partitioning algorithms as cooperative games

The paper is devoted to game-theoretic methods for community detection in networks. The traditional methods for detecting community structure are based on selecting dense subgraphs inside the network. Here we propose to use the methods of cooperative game theory that highlight not only the link density but also the mechanisms of cluster formation. Specifically, we suggest two approaches from cooperative game theory: the first approach is based on the Myerson value, whereas the second approach is based on hedonic games. Both approaches allow to detect clusters with various resolutions. However, the tuning of the resolution parameter in the hedonic games approach is particularly intuitive. Furthermore, the modularity-based approach and its generalizations as well as ratio cut and normalized cut methods can be viewed as particular cases of the hedonic games. Finally, for approaches based on potential hedonic games we suggest a very efficient computational scheme using Gibbs sampling.