Practical Bayesian Inference in Neuroscience: Or How I Learned To Stop Worrying and Embrace the Distribution

Typical statistical practices in the biological sciences have been increasingly called into question due to difficulties in replication of an increasing number of studies, many of which are confounded by the relative difficulty of null significance hypothesis testing designs and interpretation of p-values. Bayesian inference, representing a fundamentally different approach to hypothesis testing, is receiving renewed interest as a potential alternative or complement to traditional null significance hypothesis testing due to its ease of interpretation and explicit declarations of prior assumptions. Bayesian models are more mathematically complex than equivalent frequentist approaches, which have historically limited applications to simplified analysis cases. However, the advent of probability distribution sampling tools with exponential increases in computational power now allows for quick and robust inference under any distribution of data. Here we present a practical tutorial on the use of Bayesian inference in the context of neuroscientific studies. We first start with an intuitive discussion of Bayes' rule and inference followed by the formulation of Bayesian-based regression and ANOVA models using data from a variety of neuroscientific studies. We show how Bayesian inference leads to easily interpretable analysis of data while providing an open-source toolbox to facilitate the use of Bayesian tools.

Can Pheromones Contribute to Phylogenetic Hypotheses? A Case Study of Chrysomelidae

Pheromones mediate species-level communication in the search for mates, nesting, and feeding sites. Although the role of pheromones has long been discussed by various authors, their existence was not proven until the mid-twentieth century when the first sex pheromone was identified. From this finding, much has been speculated about whether this communication mechanism has acted as a regulatory agent in the process of speciation, competition, and sexual selection since it acts as an intraspecific barrier. Chrysomelidae is one of the major Phytophaga lineages, with approximately 40,000 species. Due to this immense diversity the internal relationships remain unstable when analyzed only with morphological data, consequently recent efforts have been directed to molecular analyses to establish clarity for the relationships and found their respective monophyly. Therefore, our goals are twofold 1) to synthesize the current literature on Chrysomelidae sex pheromones and 2) to test whether Chrysomelidae sex pheromones and their chemical structures could be used in phylogenetic analysis for the group. The results show that, although this is the first analysis in Chrysomelidae to use pheromones as a phylogenetic character, much can be observed in agreement with previous analyses, thus confirming that pheromones, when known in their entirety within lineages, can be used as characters in phylogenetic analyses, bringing elucidation to the relationships and evolution of organisms.

New insights into phylogenetic relationships of Rhabdocoela (Platyhelminthes) including members of Mariplanellida

BACKGROUND

Previous flatworm phylogenetic research has been carried out analysing 18S and 28S DNA markers. Through this methodology, Mariplanellinae subfamily has been recently re-classified as Mariplanellida status novus. This new classification implied that 3 genera belonged to Mariplanellida: Mariplanella, Lonchoplanella and Poseidoplanella. In this study, we aim to clarify some of the relationships within Rhabdocoela analysing 18S and 28S DNA markers of a total of 91 species through Maximum Likelihood and Bayesian Inference methodologies. A total of 11 species and genera, including Lonchoplanella, from the island of Sylt are included and had not previously been involved in any molecular phylogenetic analyses.

RESULTS

Our phylogenetic results support Mariplanellida as an independent group within Rhabdocoela and its status as an infraorder. Our study suggests that Lonchoplanella axi belongs to Mariplanellida. Within Rhabdocoela, Haloplanella longatuba is nested within Thalassotyphloplanida, instead of Limnotyphloplanida. Within Kalyptorhynchia, the taxon Eukalyptorhynchia turned out to be paraphyletic including members of Schizorhynchia. These results also support the position of the genus Toia separate from Cicerinidae.

CONCLUSIONS

Lonchoplanella axi belongs to Mariplanellida, whose status as infraorder is herein confirmed. The genus Toia belongs separate from Cicerinidae. Further research is needed to clarify the phylogenetic relationships of Hoploplanella. Most of the species, genera and families included in this study with more than one terminal are monophyletic and well supported. Adding gene markers and complementary morphological studies will help to clarify those relationships that remain uncertain.

Bayesian interpolation with deep linear networks

Characterizing how neural network depth, width, and dataset size jointly impact model quality is a central problem in deep learning theory. We give here a complete solution in the special case of linear networks with output dimension one trained using zero noise Bayesian inference with Gaussian weight priors and mean squared error as a negative log-likelihood. For any training dataset, network depth, and hidden layer widths, we find non-asymptotic expressions for the predictive posterior and Bayesian model evidence in terms of Meijer-G functions, a class of meromorphic special functions of a single complex variable. Through novel asymptotic expansions of these Meijer-G functions, a rich new picture of the joint role of depth, width, and dataset size emerges. We show that linear networks make provably optimal predictions at infinite depth: the posterior of infinitely deep linear networks with data-agnostic priors is the same as that of shallow networks with evidence-maximizing data-dependent priors. This yields a principled reason to prefer deeper networks when priors are forced to be data-agnostic. Moreover, we show that with data-agnostic priors, Bayesian model evidence in wide linear networks is maximized at infinite depth, elucidating the salutary role of increased depth for model selection. Underpinning our results is a novel emergent notion of effective depth, given by the number of hidden layers times the number of data points divided by the network width; this determines the structure of the posterior in the large-data limit.

A review of the Bayesian approach with the MCMC and the HMC as a competitor of classical likelihood statistics for pharmacometricians

This article reviews the Bayesian inference with the Monte Carlo Markov Chain (MCMC) and the Hamiltonian Monte Carlo (HMC) samplers as a competitor of the classical likelihood statistical inference for pharmacometricians. The MCMC and the HMC samplers have greatly contributed to realization of the Bayesian methods with minimal requirement of mathematical theory. They do not require any closed form of the posterior density nor linear approximation of complex nonlinear models in high dimension even with non-conjugate priors. The HMC even weakens the dependency of the chain and improves computational efficiency. Pharmacometrics is one of great beneficiaries since they use complex multivariate multilevel nonlinear mixed effects models based on the restricted maximum likelihood estimation. Comprehension of the Bayesian approach will help pharmacometricians to access the data analysis more conveniently.

Influence of the exposure concentration of dissolved cadmium on its organotropism, toxicokinetic and fate in Gammarus fossarum

Information on the relationship between the exposure concentrations of metals and their biodistribution among organs remained scarce in invertebrates. The objective of this study was to investigate the effects of Cd concentration on the organotropism, toxico-kinetic and fate of this metal in different organs of gammarids exposed to dissolved radioisotope ¹⁰⁹Cd. Gammarids male were exposed for 7 days to three environmental Cd concentrations (i.e. 4, 52 and 350 ng.L^-1) before being placed in depuration conditions (i.e. uncontaminated water). At several sampling times, Cd concentrations were determined by ¹⁰⁹Cd γ-counting in water, caeca, cephalon, gills, intestine and remaining tissues. Bioconcentration Factors (BCF) and Cd relative proportions in organs were calculated to assess the exposure concentration effect on the bioaccumulation capacities. The dependance of the organ-specific kinetic parameters to Cd water concentrations were estimated by fitting nested one-compartment toxico-kinetic (TK) models to both the accumulation and depuration data, by Bayesian inference. Then, for each Cd concentrations, the metal exchanges among organs over time were formalized by a multi-compartments TK model fitted to all organ data simultaneously. Our results highlighted that, at the end of the exposure phase, BCF and Cd relative proportions, in each organ, were not significantly modulated by water concentrations. Kinetically, Cd accumulation rates in all organs (except intestines) were depended on the exposure concentration, but not the elimination rates. The in vivo management of Cd (i.e. metal exchanges among organs) remained qualitatively unchanged according to exposure concentration. All these results also highlighted key role of that organs in the management of Cd: bioconcentration by caeca, storage by gills and main entry pathway by intestine. This study shows the interest of implementing TK approaches to test the effect of environmental factors on bioaccumulation, inter-organ exchanges and fate of contaminants in invertebrate body to enhance the understanding of the toxicity risk.

Safety analytics at a granular level using a Gaussian process modulated renewal model: A case study of the COVID-19 pandemic

With the advance of intelligent transportation system technologies, contributing factors to crashes can be obtained in real time. Analyzing these factors can be critical in improving traffic safety. Despite many crash models having been successfully developed for safety analytics, most models associate crash observations and contributing factors at the aggregate level, resulting in potential information loss. This study proposes an efficient Gaussian process modulated renewal process model for safety analytics that does not suffer from information loss due to data aggregations. The proposed model can infer crash intensities in the continuous-time dimension so that they can be better associated with contributing factors that change over time. Moreover, the model can infer non-homogeneous intensities by relaxing the independent and identically distributed (i.i.d.) exponential assumption of the crash intervals. To demonstrate the validity and advantages of this proposed model, an empirical study examining the impacts of the COVID-19 pandemic on traffic safety at six interstate highway sections is performed. The accuracy of our proposed renewal model is verified by comparing the areas under the curve (AUC) of the inferred crash intensity function with the actual crash counts. Residual box plot shows that our proposed models have lower biases and variances compared with Poisson and Negative binomial models. Counterfactual crash intensities are then predicted conditioned on exogenous variables at the crash time. Time-varying safety impacts such as bimodal, unimodal, and parabolic patterns are observed at the selected highways. The case study shows the proposed model enables safety analytics at a granular level and provides a more detailed insight into the time-varying safety risk in a changing environment.

Application of the Bayesian spline method to analyze real-time measurements of ultrafine particle concentration in the Parisian subway

BACKGROUND

Air pollution in subway environments is a growing concern as it often exceeds WHO recommendations for indoor air quality. Ultrafine particles (UFP), for which there is still no regulation nor a standardized exposure monitoring method, are the strongest contributor to this pollution when the number concentration is used as exposure metric.

OBJECTIVES

We aimed to assess the real-time UFP number concentration in the personal breathing zone (PBZ) of three types of underground Parisian subway professionals and analyze it using a novel Bayesian spline approach. Consecutively, we investigated the effect of job, week day, subway station, worker location, and some further events on UFP number concentrations.

METHODS

The data collection procedure originated from a longitudinal study and lasted for a total duration of 6 weeks (from October 7 to November 15, 2019, i.e. two weeks per type of subway professionals). Time-series were built from the real-time particle number concentration (PNC) measured in the PBZ of professionals during their work-shifts. Complementarily, contextual information expressed as Station, Environment, and Event variables were extracted from activity logbooks completed for every work-shift. A Bayesian spline approach was applied to model the PNC within a Bayesian framework as a function of the mentioned contextual information.

RESULTS

Overall, the Bayesian spline method suited a real-time personal PNC data modeling approach. The model enabled estimating the differences in UFP exposure between subway professionals, stations, and various locations. Our results suggest a higher PNC closer to the subway tracks, with the highest PNC on subway station platforms. Studied event and week day variables had a lesser influence.

CONCLUSION

It was shown that the Bayesian spline method is suitable to investigate individual exposure to UFP in underground subway settings. This method is informative for better documenting the magnitude and variability of UFP exposure, and for understanding the determinants in view of further regulation and control of this exposure.

One and multi-compartments toxico-kinetic modeling to understand metals' organotropism and fate in Gammarus fossarum

The use of freshwater invertebrates for biomonitoring has been increasing for several decades, but little is known about relations between external exposure concentration of metals and their biodistribution among different tissues. One and multi-compartments toxicokinetic (TK) models are powerful tools to formalize and predict how a contaminant is bioaccumulated. The aim of this study is to develop modeling approaches to improve knowledge on dynamic of accumulation and fate of Cd and Hg in gammarid's organs. Gammarids were exposed to dissolved metals (11.1 ± 1.2 µg.L^-1 of Cd or 0.27 ± 0.13 µg.L^-1 of Hg) before a depuration phase. At each sampling days, their organs (caeca, cephalon, intestine and remaining tissues) were separated by dissection before analyses. Results allowed us to determine that i) G.fossarum takes up Cd as efficiently as the mussel M.galloprovincialis, but eliminates it more rapidly, ii) organs which accumulate and depurate the most, in terms of concentrations, are caeca and intestine for both metals; iii) the one-compartment TK models is the most relevant for Hg, while the multi-compartments TK model allows a better fit to Cd data, demonstrating dynamic transfer of Cd among organs.

Are There Reliable Qualitative Individual Difference in Cognition?

In this paper we propose a new set of questions that focus on the direction of effects. In almost all studies the direction is important. For example, in a Stroop task we expect responses to incongruent items to be slower than those to congruent ones, and this direction implies one theoretical explanation. Yet, if congruent words are slowed down relative to incongruent words we would have a completely different theoretical explanation. We ask a ‘does everybody’ question, such as, ‘does every individual show a Stroop effect in the same direction?’ Or, ‘does every individual respond faster to loud tones than soft tones?’ If all individuals truly have effects in the same direction that implicate a common theory, we term the differences among them as quantitative individual differences. Conversely, if all individuals truly have effects in different directions that implicate different theories, we term the differences among them as qualitative individual differences. Here, we provide a users guide to the question of whether individual differences are qualitative or quantitative. We discuss theoretical issues, methodological advances, new software for assessment, and, most importantly, how the question impacts theory development in cognitive science. Our hope is that this mode of analysis is a productive tool in researchers’ toolkits.

Towards robust statistical inference for complex computer models

Ecologists increasingly rely on complex computer simulations to forecast ecological systems. To make such forecasts precise, uncertainties in model parameters and structure must be reduced and correctly propagated to model outputs. Naively using standard statistical techniques for this task, however, can lead to bias and underestimation of uncertainties in parameters and predictions. Here, we explain why these problems occur and propose a framework for robust inference with complex computer simulations. After having identified that model error is more consequential in complex computer simulations, due to their more pronounced nonlinearity and interconnectedness, we discuss as possible solutions data rebalancing and adding bias corrections on model outputs or processes during or after the calibration procedure. We illustrate the methods in a case study, using a dynamic vegetation model. We conclude that developing better methods for robust inference of complex computer simulations is vital for generating reliable predictions of ecosystem responses.

Poroelasticity as a Model of Soft Tissue Structure: Hydraulic Permeability Reconstruction for Magnetic Resonance Elastography in Silico

Magnetic Resonance Elastography allows noninvasive visualization of tissue mechanical properties by measuring the displacements resulting from applied stresses, and fitting a mechanical model. Poroelasticity naturally lends itself to describing tissue - a biphasic medium, consisting of both solid and fluid components. This article reviews the theory of poroelasticity, and shows that the spatial distribution of hydraulic permeability, the ease with which the solid matrix permits the flow of fluid under a pressure gradient, can be faithfully reconstructed without spatial priors in simulated environments. The paper describes an in-house MRE computational platform - a multi-mesh, finite element poroelastic solver coupled to an artificial epistemic agent capable of running Bayesian inference to reconstruct inhomogenous model mechanical property images from measured displacement fields. Building on prior work, the domain of convergence for inference is explored, showing that hydraulic permeabilities over several orders of magnitude can be reconstructed given very little prior knowledge of the true spatial distribution.

Phylogenetic comparison between Type IX Secretion System (T9SS) protein components suggests evidence of horizontal gene transfer

Porphyromonas gingivalis is one of the major bacteria that causes periodontitis. Chronic periodontitis is a severe form of periodontal disease that ultimately leads to tooth loss. Virulence factors that contribute to periodontitis are secreted by Type IX Secretion System (T9SS). There are aspects of T9SS protein components that have yet to be characterised. Thus, the aim of this study is to investigate the phylogenetic relationship between members of 20 T9SS component protein families. The Bayesian Inference (BI) trees for 19 T9SS protein components exhibit monophyletic clades for all major classes under Bacteroidetes with strong support for the monophyletic clades or its subclades that is consistent with phylogeny exhibited by the constructed BI tree of 16S rRNA. The BI tree of PorR is different from the 19 BI trees of T9SS protein components as it does not exhibit monophyletic clades for all major classes under Bacteroidetes. There is strong support for the phylogeny exhibited by the BI tree of PorR which deviates from the phylogeny based on 16S rRNA. Hence, it is possible that the porR gene is subjected to horizontal transfer as it is known that virulence factor genes could be horizontally transferred. Seven genes (porR included) that are involved in the biosynthesis of A-LPS are found to be flanked by insertion sequences (IS5 family transposons). Therefore, the intervening DNA segment that contains the porR gene might be transposed and subjected to conjugative transfer. Thus, the seven genes can be co-transferred via horizontal gene transfer. The BI tree of UgdA does not exhibit monophyletic clades for all major classes under Bacteroidetes which is similar to the BI tree of PorR (both are a part of the seven genes). Both BI trees also exhibit similar topology as the four identified clusters with strong support and have similar relative positions to each other in both BI trees. This reinforces the possibility that porR and the other six genes might be horizontally transferred. Other than the BI tree of PorR, the 19 other BI trees of T9SS protein components also exhibit evidence of horizontal gene transfer. However, their genes might undergo horizontal gene transfer less frequently compared to porR because the intervening DNA segment that contains porR is easily exchanged between bacteria under Bacteroidetes due to the presence of insertion sequences (IS5 family transposons) that flank it. In conclusion, this study can provide a better understanding about the phylogeny of T9SS protein components.

A Review of Electrical Impedance Tomography in Lung Applications: Theory and Algorithms for Absolute Images

Electrical Impedance Tomography (EIT) is under fast development, the present paper is a review of some procedures that are contributing to improve spatial resolution and material properties accuracy, admitivitty or impeditivity accuracy. A review of EIT medical applications is presented and they were classified into three broad categories: ARDS patients, obstructive lung diseases and perioperative patients. The use of absolute EIT image may enable the assessment of absolute lung volume, which may significantly improve the clinical acceptance of EIT. The Control Theory, the State Observers more specifically, have a developed theory that can be used for the design and operation of EIT devices. Electrode placement, current injection strategy and electrode electric potential measurements strategy should maximize the number of observable and controllable directions of the state vector space. A non-linear stochastic state observer, the Unscented Kalman Filter, is used directly for the reconstruction of absolute EIT images. Historically, difference images were explored first since they are more stable in the presence of modelling errors. Absolute images require more detailed models of contact impedance, stray capacitance and properly refined finite element mesh where the electric potential gradient is high. Parallelization of the forward program computation is necessary since the solution of the inverse problem often requires frequent solutions of the forward problem. Several reconstruction algorithms benefit by the Bayesian inverse problem approach and the concept of prior information. Anatomic and physiologic information are used to form the prior information. An already tested methodology is presented to build the prior probability density function using an ensemble of CT scans and in vivo impedance measurements. Eight absolute EIT image algorithms are presented.

Bayesian High-Dimensional Regression for Change Point Analysis

In many econometrics applications, the dataset under investigation spans heterogeneous regimes that are more appropriately modeled using piece-wise components for each of the data segments separated by change-points. We consider using Bayesian high-dimensional shrinkage priors in a change point setting to understand segment-specific relationship between the response and the covariates. Covariate selection before and after each change point can identify possibly different sets of relevant covariates, while the fully Bayesian approach ensures posterior inference for the change points is also available. We demonstrate the flexibility of the approach for imposing different variable selection constraints like grouping or partial selection and discuss strategies to detect an unknown number of change points. Simulation experiments reveal that this simple approach delivers accurate variable selection, and inference on location of the change points, and substantially outperforms a frequentist lasso-based approach, uniformly across a wide range of scenarios. Application of our model to Minnesota house price dataset reveals change in the relationship between house and stock prices around the sub-prime mortgage crisis.

The effects of nonignorable missing data on label-free mass spectrometry proteomics experiments

An idealized version of a label-free discovery mass spectrometry proteomics experiment would provide absolute abundance measurements for a whole proteome, across varying conditions. Unfortunately, this ideal is not realized. Measurements are made on peptides requiring an inferential step to obtain protein level estimates. The inference is complicated by experimental factors that necessitate relative abundance estimation and result in widespread non-ignorable missing data. Relative abundance on the log scale takes the form of parameter contrasts. In a complete-case analysis, contrast estimates may be biased by missing data and a substantial amount of useful information will often go unused. To avoid problems with missing data, many analysts have turned to single imputation solutions. Unfortunately, these methods often create further difficulties by hiding inestimable contrasts, preventing the recovery of interblock information and failing to account for imputation uncertainty. To mitigate many of the problems caused by missing values, we propose the use of a Bayesian selection model. Our model is tested on simulated data, real data with simulated missing values, and on a ground truth dilution experiment where all of the true relative changes are known. The analysis suggests that our model, compared with various imputation strategies and complete-case analyses, can increase accuracy and provide substantial improvements to interval coverage.

Genetic parameters for marbling and body score in Anglonubian goats using Bayesian inference via threshold and linear models

Objective

The aim of this study was to estimate (co) variance components and genetic parameters for categorical carcass traits using Bayesian inference via mixed linear and threshold animal models in Anglonubian goats.

Methods

Data were obtained from Anglonubian goats reared in the Brazilian Mid-North region. The traits in study were body condition score, marbling in the rib eye, ribeye area, fat thickness of the sternum, hip height, leg perimeter, and body weight. The numerator relationship matrix contained information from 793 animals. The single- and two-trait analyses were performed to estimate (co) variance components and genetic parameters via linear and threshold animal models. For estimation of genetic parameters, chains with 2 and 4 million cycles were tested. An 1,000,000-cycle initial burn-in was considered with values taken every 250 cycles, in a total of 4,000 samples. Convergence was monitored by Geweke criteria and Monte Carlo error chain.

Results

Threshold model best fits categorical data since it is more efficient to detect genetic variability. In two-trait analysis the contribution of the increase in information and the correlations between traits contributed to increase the estimated values for (co) variance components and heritability, in comparison to single-trait analysis. Heritability estimates for the study traits were from low to moderate magnitude.

Conclusion

Direct selection of the continuous distribution of traits such as thickness sternal fat and hip height allows obtaining the indirect selection for marbling of ribeye.

Slow climate mode reconciles historical and model-based estimates of climate sensitivity

The latest Intergovernmental Panel on Climate Change Assessment Report widened the equilibrium climate sensitivity (ECS) range from 2° to 4.5°C to an updated range of 1.5° to 4.5°C in order to account for the lack of consensus between estimates based on models and historical observations. The historical ECS estimates range from 1.5° to 3°C and are derived assuming a linear radiative response to warming. A Bayesian methodology applied to 24 models, however, documents curvature in the radiative response to warming from an evolving contribution of interannual to centennial modes of radiative response. Centennial modes display stronger amplifying feedbacks and ultimately contribute 28 to 68% (90% credible interval) of equilibrium warming, yet they comprise only 1 to 7% of current warming. Accounting for these unresolved centennial contributions brings historical records into agreement with model-derived ECS estimates.

A BAYESIAN HIERARCHICAL SPATIAL MODEL FOR DENTAL CARIES ASSESSMENT USING NON-GAUSSIAN MARKOV RANDOM FIELDS

Research in dental caries generates data with two levels of hierarchy: that of a tooth overall and that of the different surfaces of the tooth. The outcomes often exhibit spatial referencing among neighboring teeth and surfaces, i.e., the disease status of a tooth or surface might be influenced by the status of a set of proximal teeth/surfaces. Assessments of dental caries (tooth decay) at the tooth level yield binary outcomes indicating the presence/absence of teeth, and trinary outcomes at the surface level indicating healthy, decayed, or filled surfaces. The presence of these mixed discrete responses complicates the data analysis under a unified framework. To mitigate complications, we develop a Bayesian two-level hierarchical model under suitable (spatial) Markov random field assumptions that accommodates the natural hierarchy within the mixed responses. At the first level, we utilize an autologistic model to accommodate the spatial dependence for the tooth-level binary outcomes. For the second level and conditioned on a tooth being non-missing, we utilize a Potts model to accommodate the spatial referencing for the surface-level trinary outcomes. The regression models at both levels were controlled for plausible covariates (risk factors) of caries, and remain connected through shared parameters. To tackle the computational challenges in our Bayesian estimation scheme caused due to the doubly-intractable normalizing constant, we employ a double Metropolis-Hastings sampler. We compare and contrast our model performances to the standard non-spatial (naive) model using a small simulation study, and illustrate via an application to a clinical dataset on dental caries.

Morphological and molecular characterisation, and phylogenetic position of X. browni sp. n., X. penevi sp. n. and two known species of Xiphinema americanum-group (Nematoda, Longidoridae)

Using ribosomal (18S, ITS1, ITS2, D2-D3 expansion segments of 28S rDNA) and mitochondrial (partial cox1 and nad4) DNA markers in a study of several populations of Xiphinemaamericanum-group from Europe and Morocco, two cryptic species Xiphinemabrownisp. n. (formerly reported as Xiphinemapachtaicum) and Xiphinemapenevisp. n. were revealed. The species are described, illustrated and their phylogenetic relationships discussed. The first species is most similar to Xiphinemaparasimile and is a member of Xiphinemasimile species complex. The phylogenetic reconstructions inferred from three molecular markers (18S, D2-D3 28S rDNA and cox1) showed that Xiphinemapenevisp. n. is part of Xiphinemapachtaicum-subgroup and is closely related to Xiphinemaincertum, Xiphinemapachtaicum, Xiphinemaparapachydermum, Xiphinemaplesiopachtaicum, Xiphinemaastaregiense and Xiphinemapachydermum. Also, a separate “Xiphinemasimile-subgroup”, outside the Xiphinemapachtaicum-subgroup and so far consisting only of the parthenogenetic species Xiphinemasimile, Xiphinemaparasimile, Xiphinemabrownisp. n. and probably Xiphinemavallense was formed. New primers for amplification and sequencing of part of the nad4 mitochondrial gene were designed and used.

de Finetti Priors using Markov chain Monte Carlo computations

Recent advances in Monte Carlo methods allow us to revisit work by de Finetti who suggested the use of approximate exchangeability in the analyses of contingency tables. This paper gives examples of computational implementations using Metropolis Hastings, Langevin and Hamiltonian Monte Carlo to compute posterior distributions for test statistics relevant for testing independence, reversible or three way models for discrete exponential families using polynomial priors and Gröbner bases.

A Bayesian hierarchical model for maximizing the vascular adhesion of nanoparticles

The complex vascular dynamics and wall deposition of systemically injected nanoparticles is regulated by their geometrical properties (size, shape) and biophysical parameters (ligand-receptor bond type and surface density, local shear rates). Although sophisticated computational models have been developed to capture the vascular behavior of nanoparticles, it is increasingly recognized that purely deterministic approaches, where the governing parameters are known a priori and conclusively describe behaviors based on physical characteristics, may be too restrictive to accurately reflect natural processes. Here, a novel computational framework is proposed by coupling the physics dictating the vascular adhesion of nanoparticles with a stochastic model. In particular, two governing parameters (i.e. the ligand-receptor bond length and the ligand surface density on the nanoparticle) are treated as two stochastic quantities, whose values are not fixed a priori but would rather range in defined intervals with a certain probability. This approach is used to predict the deposition of spherical nanoparticles with different radii, ranging from 750 to 6,000 nm, in a parallel plate flow chamber under different flow conditions, with a shear rate ranging from 50 to 90 sec^-1. It is demonstrated that the resulting stochastic model can predict the experimental data more accurately than the original deterministic model. This approach allows one to increase the predictive power of mathematical models of any natural process by accounting for the experimental and intrinsic biological uncertainties.

The Age Pattern of Increases in Mortality Affected by HIV: Bayesian Fit of the Heligman-Pollard Model to Data from the Agincourt HDSS Field Site in Rural Northeast South Africa

BACKGROUND

We investigate the sex-age-specific changes in the mortality of a prospectively monitored rural population in South Africa. We quantify changes in the age pattern of mortality in a parsimonious way by estimating the eight parameters of the Heligman-Pollard (HP) model of age-specific mortality. In its traditional form this model is difficult to fit and does not account for uncertainty.

OBJECTIVE

1. To quantify changes in the sex-age pattern of mortality experienced by a population with endemic HIV. 2. To develop and demonstrate a robust Bayesian estimation method for the HP model that accounts for uncertainty.

METHODS

Bayesian estimation methods are adapted to work with the HP model. Temporal changes in parameter values are related to changes in HIV prevalence.

RESULTS

Over the period when the HIV epidemic in South Africa was growing, mortality in the population described by our data increased profoundly with losses of life expectancy of ~15 years for both males and females. The temporal changes in the HP parameters reflect in a parsimonious way the changes in the age pattern of mortality. We develop a robust Bayesian method to estimate the eight parameters of the HP model and thoroughly demonstrate it.

CONCLUSIONS

Changes in mortality in South Africa over the past fifteen years have been profound. The HP model can be fit well using Bayesian methods, and the results can be useful in developing a parsimonious description of changes in the age pattern of mortality.

COMMENTS

The motivating aim of this work is to develop new methods that can be useful in applying the HP eight-parameter model of age-specific mortality. We have done this and chosen an interesting application to demonstrate the new methods.

Estimating population parameters using the structured serial coalescent with Bayesian MCMC inference when some demes are hidden

Using the structured serial coalescent with Bayesian MCMC and serial samples, we estimate population size when some demes are not sampled or are hidden, ie ghost demes. It is found that even with the presence of a ghost deme, accurate inference was possible if the parameters are estimated with the true model. However with an incorrect model, estimates were biased and can be positively misleading. We extend these results to the case where there are sequences from the ghost at the last time sample. This case can arise in HIV patients, when some tissue samples and viral sequences only become available after death. When some sequences from the ghost deme are available at the last sampling time, estimation bias is reduced and accurate estimation of parameters associated with the ghost deme is possible despite sampling bias. Migration rates for this case are also shown to be good estimates when migration values are low.