Adjusting Incidence Estimates with Laboratory Test Performances: A Pragmatic Maximum Likelihood Estimation-Based Approach

Understanding the incidence of disease is often crucial for public policy decision-making, as observed during the COVID-19 pandemic. Estimating incidence is challenging, however, when the definition of incidence relies on tests that imperfectly measure disease, as in the case when assays with variable performance are used to detect the SARS-CoV-2 virus. To our knowledge, there are no pragmatic methods to address the bias introduced by the performance of labs in testing for the virus. In the setting of a longitudinal study, we developed a maximum likelihood estimation-based approach to estimate laboratory performance-adjusted incidence using the expectation-maximization algorithm. We constructed confidence intervals (CIs) using both bootstrapped-based and large-sample interval estimator approaches. We evaluated our methods through extensive simulation and applied them to a real-world study (TrackCOVID), where the primary goal was to determine the incidence of and risk factors for SARS-CoV-2 infection in the San Francisco Bay Area from July 2020 to March 2021. Our simulations demonstrated that our method converged rapidly with accurate estimates under a variety of scenarios. Bootstrapped-based CIs were comparable to the large-sample estimator CIs with a reasonable number of incident cases, shown via a simulation scenario based on the real TrackCOVID study. In more extreme simulated scenarios, the coverage of large-sample interval estimation outperformed the bootstrapped-based approach. Results from the application to the TrackCOVID study suggested that assuming perfect laboratory test performance can lead to an inaccurate inference of the incidence. Our flexible, pragmatic method can be extended to a variety of disease and study settings.

BayesAge: A maximum likelihood algorithm to predict epigenetic age

Introduction: DNA methylation, specifically the formation of 5-methylcytosine at the C5 position of cytosine, undergoes reproducible changes as organisms age, establishing it as a significant biomarker in aging studies. Epigenetic clocks, which integrate methylation patterns to predict age, often employ linear models based on penalized regression, yet they encounter challenges in handling missing data, count-based bisulfite sequence data, and interpretation. Methods: To address these limitations, we introduce BayesAge, an extension of the scAge methodology originally designed for single-cell DNA methylation analysis. BayesAge employs maximum likelihood estimation (MLE) for age inference, models count data using binomial distributions, and incorporates LOWESS smoothing to capture non-linear methylation-age dynamics. This approach is tailored for bulk bisulfite sequencing datasets. Results: BayesAge demonstrates superior performance compared to scAge. Notably, its age residuals exhibit no age association, offering a less biased representation of epigenetic age variation across populations. Furthermore, BayesAge facilitates the estimation of error bounds on age inference. When applied to down-sampled data, BayesAge achieves a higher coefficient of determination between predicted and actual ages compared to both scAge and penalized regression. Discussion: BayesAge presents a promising advancement in epigenetic age prediction, addressing key challenges encountered by existing models. By integrating robust statistical techniques and tailored methodologies for count-based data, BayesAge offers improved accuracy and interpretability in predicting age from bulk bisulfite sequencing datasets. Its ability to estimate error bounds enhances the reliability of age inference, thereby contributing to a more comprehensive understanding of epigenetic aging processes.

Frequentist and Bayesian tolerance intervals for setting specification limits for left-censored gamma distributed drug quality attributes

Tolerance intervals from quality attribute measurements are used to establish specification limits for drug products. Some attribute measurements may be below the reporting limits, that is, left-censored data. When data has a long, right-skew tail, a gamma distribution may be applicable. This paper compares maximum likelihood estimation (MLE) and Bayesian methods to estimate shape and scale parameters of censored gamma distributions and to calculate tolerance intervals under varying sample sizes and extents of censoring. The noninformative reference prior and the maximal data information prior (MDIP) are used to compare the impact of prior choice. Metrics used are bias and root mean square error for the parameter estimation and average length and confidence coefficient for the tolerance interval evaluation. It will be shown that Bayesian method using a reference prior overall performs better than MLE for the scenarios evaluated. When sample size is small, the Bayesian method using MDIP yields conservatively too wide tolerance intervals that are unsuitable basis for specification setting. The metrics for all methods worsened with increasing extent of censoring but improved with increasing sample size, as expected. This study demonstrates that although MLE is relatively simple and available in user-friendly statistical software, it falls short in accurately and precisely producing tolerance limits that maintain the stated confidence depending on the scenario. The Bayesian method using noninformative prior, even though computationally intensive and requires considerable statistical programming, produces tolerance limits which are practically useful for specification setting. Real-world examples are provided to illustrate the findings from the simulation study.

Quantifying the HIV reservoir with dilution assays and deep viral sequencing

People living with HIV on antiretroviral therapy often have undetectable virus levels by standard assays, but "latent" HIV still persists in viral reservoirs. Eliminating these reservoirs is the goal of HIV cure research. The quantitative viral outgrowth assay (QVOA) is commonly used to estimate the reservoir size, that is, the infectious units per million (IUPM) of HIV-persistent resting CD4+ T cells. A new variation of the QVOA, the ultra deep sequencing assay of the outgrowth virus (UDSA), was recently developed that further quantifies the number of viral lineages within a subset of infected wells. Performing the UDSA on a subset of wells provides additional information that can improve IUPM estimation. This paper considers statistical inference about the IUPM from combined dilution assay (QVOA) and deep viral sequencing (UDSA) data, even when some deep sequencing data are missing. Methods are proposed to accommodate assays with wells sequenced at multiple dilution levels and with imperfect sensitivity and specificity, and a novel bias-corrected estimator is included for small samples. The proposed methods are evaluated in a simulation study, applied to data from the University of North Carolina HIV Cure Center, and implemented in the open-source R package SLDeepAssay.

Maximum Augmented Empirical Likelihood Estimation of Categorical Marginal Models for Large Sparse Contingency Tables

Categorical marginal models (CMMs) are flexible tools for modelling dependent or clustered categorical data, when the dependencies themselves are not of interest. A major limitation of maximum likelihood (ML) estimation of CMMs is that the size of the contingency table increases exponentially with the number of variables, so even for a moderate number of variables, say between 10 and 20, ML estimation can become computationally infeasible. An alternative method, which retains the optimal asymptotic efficiency of ML, is maximum empirical likelihood (MEL) estimation. However, we show that MEL tends to break down for large, sparse contingency tables. As a solution, we propose a new method, which we call maximum augmented empirical likelihood (MAEL) estimation and which involves augmentation of the empirical likelihood support with a number of well-chosen cells. Simulation results show good finite sample performance for very large contingency tables.

Semiparametric probit regression model with misclassified current status data

Current status data arise when each subject under study is examined only once at an observation time, and one only knows the failure status of the event of interest at the observation time rather than the exact failure time. Moreover, the obtained failure status is frequently subject to misclassification due to imperfect tests, yielding misclassified current status data. This article conducts regression analysis of such data with the semiparametric probit model, which serves as an important alternative to existing semiparametric models and has recently received considerable attention in failure time data analysis. We consider the nonparametric maximum likelihood estimation and develop an expectation-maximization (EM) algorithm by incorporating the generalized pool-adjacent-violators (PAV) algorithm to maximize the intractable likelihood function. The resulting estimators of regression parameters are shown to be consistent, asymptotically normal, and semiparametrically efficient. Furthermore, the numerical results in simulation studies indicate that the proposed method performs satisfactorily in finite samples and outperforms the naive method that ignores misclassification. We then apply the proposed method to a real dataset on chlamydia infection.

Optimal Estimation of Quantum Coherence by Bell State Measurement: A Case Study

Quantum coherence is the most distinguished feature of quantum mechanics. As an important resource, it is widely applied to quantum information technologies, including quantum algorithms, quantum computation, quantum key distribution, and quantum metrology, so it is important to develop tools for efficient estimation of the coherence. Bell state measurement plays an important role in quantum information processing. In particular, it can also, as a two-copy collective measurement, directly measure the quantum coherence of an unknown quantum state in the experiment, and does not need any optimization procedures, feedback, or complex mathematical calculations. In this paper, we analyze the performance of estimating quantum coherence with Bell state measurement for a qubit case from the perspective of semiparametric estimation and single-parameter estimation. The numerical results show that Bell state measurement is the optimal measurement for estimating several frequently-used coherence quantifiers, and it has been demonstrated in the perspective of the quantum limit of semiparametric estimation and Fisher information.

Super-resolution biomedical imaging via reference-free statistical implicit neural representation

Objective.Supervised deep learning for image super-resolution (SR) has limitations in biomedical imaging due to the lack of large amounts of low- and high-resolution image pairs for model training. In this work, we propose a reference-free statistical implicit neural representation (INR) framework, which needs only a single or a few observed low-resolution (LR) image(s), to generate high-quality SR images.Approach.The framework models the statistics of the observed LR images via maximum likelihood estimation and trains the INR network to represent the latent high-resolution (HR) image as a continuous function in the spatial domain. The INR network is constructed as a coordinate-based multi-layer perceptron, whose inputs are image spatial coordinates and outputs are corresponding pixel intensities. The trained INR not only constrains functional smoothness but also allows an arbitrary scale in SR imaging.Main results.We demonstrate the efficacy of the proposed framework on various biomedical images, including computed tomography (CT), magnetic resonance imaging (MRI), fluorescence microscopy, and ultrasound images, across different SR magnification scales of 2×, 4×, and 8×. A limited number of LR images were used for each of the SR imaging tasks to show the potential of the proposed statistical INR framework.Significance.The proposed method provides an urgently needed unsupervised deep learning framework for numerous biomedical SR applications that lack HR reference images.

Efficient Localization Method Based on RSSI for AP Clusters

The localization accuracy is susceptible to the received signal strength indication (RSSI) fluctuations for RSSI-based wireless localization methods. Moreover, the maximum likelihood estimation (MLE) of the target location is nonconvex, and locating target presents a significant computational complexity. In this paper, an RSSI-based access point cluster localization (APCL) method is proposed for locating a moving target. Multiple location-constrained access points (APs) are used in the APCL method to form an AP cluster as an anchor node (AN) in the wireless sensor network (WSN), and the RSSI of the target is estimated with several RSSI samples obtained by the AN. With the estimated RSSI for each AN, the solution for the target location can be obtained quickly and accurately due to the fact that the MLE localization problem is transformed into an eigenvalue problem by constructing an eigenvalue equation. Simulation and experimental results show that the APCL method can meet the requirement of high-precision real-time localization of moving targets in WSN with higher localization accuracy and lower computational effort compared to the existing classical RSSI-based localization methods.

Random Effects Multinomial Processing Tree Models: A Maximum Likelihood Approach

The present article proposes and evaluates marginal maximum likelihood (ML) estimation methods for hierarchical multinomial processing tree (MPT) models with random and fixed effects. We assume that an identifiable MPT model with S parameters holds for each participant. Of these S parameters, R parameters are assumed to vary randomly between participants, and the remaining [Formula: see text] parameters are assumed to be fixed. We also propose an extended version of the model that includes effects of covariates on MPT model parameters. Because the likelihood functions of both versions of the model are too complex to be tractable, we propose three numerical methods to approximate the integrals that occur in the likelihood function, namely, the Laplace approximation (LA), adaptive Gauss-Hermite quadrature (AGHQ), and Quasi Monte Carlo (QMC) integration. We compare these three methods in a simulation study and show that AGHQ performs well in terms of both bias and coverage rate. QMC also performs well but the number of responses per participant must be sufficiently large. In contrast, LA fails quite often due to undefined standard errors. We also suggest ML-based methods to test the goodness of fit and to compare models taking model complexity into account. The article closes with an illustrative empirical application and an outlook on possible extensions and future applications of the proposed ML approach.

Statistical methods for handling nondetected results in food chemical monitoring data to improve food risk assessments

Chemical risk assessment is important for risk management, and estimates of chemical exposure must be as accurate as possible. Chemical concentrations in food below the limit of detection are known as nondetects and result in left-censored data. During statistical analysis, the method used for handling values below the limit of detection is important. Many risk assessors employ widely used substitution methods to treat left-censored data, as recommended by international organizations. The National Institute of Food and Drug Safety Evaluation of South Korea also recommends these methods, which are currently used for chemical exposure assessments. However, these methods have statistical limitations, and international organizations recommend more advanced alternative statistical approaches. In this study, we assessed the validity of currently used statistical methods for handling nondetects. To identify the most suitable statistical method for handling nondetection, we created virtual data and conducted simulation studies. Based on both simulation and case studies, the Maximum Likelihood Estimation (MLE) and Robust Regression on Order Statistics (ROS) methods were found to be the best options. The statistical values obtained from these methods were similar to those obtained from the commonly used 1/2 Limit of Detection (LOD) substitution method for nondetection treatment. In three case studies, we compared the various methods based on the root mean squared error. The data for all case studies were from the same source, to avoid heterogeneity. Across various sample sizes and nondetection rates, the mean and 95th percentile values for all treatment methods were similar. However, "lognormal maximum likelihood estimation" method was not suitable for estimating the mean. Risk assessors should consider statistical processing of monitoring data to reduce uncertainty. Currently used substitution methods are effective and easy to apply to large datasets with nondetection rates <80%. However, advanced statistical methods are required in some circumstances, and national guidelines are needed regarding their use in risk assessments.

CBIR-SAR System Using Stochastic Distance

This article proposes a system for Content-Based Image Retrieval (CBIR) using stochastic distance for Synthetic-Aperture Radar (SAR) images. The methodology consists of three essential steps for image retrieval. First, it estimates the roughness (α^) and scale (γ^) parameters of the GI0 distribution that models SAR data in intensity. The parameters of the model were estimated using the Maximum Likelihood Estimation and the fast approach of the Log-Cumulants method. Second, using the triangular distance, CBIR-SAR evaluates the similarity between a query image and images in the database. The stochastic distance can identify the most similar regions according to the image features, which are the estimated parameters of the data model. Third, the performance of our proposal was evaluated by applying the Mean Average Precision (MAP) measure and considering clippings from three radar sensors, i.e., UAVSAR, OrbiSaR-2, and ALOS PALSAR. The CBIR-SAR results for synthetic images achieved the highest MAP value, retrieving extremely heterogeneous regions. Regarding the real SAR images, CBIR-SAR achieved MAP values above 0.833 for all polarization channels for image samples of forest (UAVSAR) and urban areas (ORBISAR). Our results confirmed that the proposed method is sensitive to the degree of texture, and hence, it relies on good estimates. They are inputs to the stochastic distance for effective image retrieval.

Statistical inference of the rates of cell proliferation and phenotypic switching in cancer

Recent evidence suggests that nongenetic (epigenetic) mechanisms play an important role at all stages of cancer evolution. In many cancers, these mechanisms have been observed to induce dynamic switching between two or more cell states, which commonly show differential responses to drug treatments. To understand how these cancers evolve over time, and how they respond to treatment, we need to understand the state-dependent rates of cell proliferation and phenotypic switching. In this work, we propose a rigorous statistical framework for estimating these parameters, using data from commonly performed cell line experiments, where phenotypes are sorted and expanded in culture. The framework explicitly models the stochastic dynamics of cell division, cell death and phenotypic switching, and it provides likelihood-based confidence intervals for the model parameters. The input data can be either the fraction of cells or the number of cells in each state at one or more time points. Through a combination of theoretical analysis and numerical simulations, we show that when cell fraction data is used, the rates of switching may be the only parameters that can be estimated accurately. On the other hand, using cell number data enables accurate estimation of the net division rate for each phenotype, and it can even enable estimation of the state-dependent rates of cell division and cell death. We conclude by applying our framework to a publicly available dataset.

SFBC Recognition over Orthogonal Frequency Division Multiplexing Schemes in the Presence of Inphase and Quadrature Phase Discrepancies for Cognitive Radio Applications

A radio is adaptive if it can autonomously analyze the communications environment and instantly modify its settings to achieve the best possible efficiency. In orthogonal frequency division multiplexing (OFDM) transmissions, identifying the space frequency block coding (SFBC) category utilized is one of the most important tasks of an adaptive receiver. Previous approaches to this problem did not take into consideration the fact that real systems typically suffer from transmission defects. This study offers a novel maximum likelihood recognizer capable of distinguishing between SFBC OFDM waveforms in the context of inphase and quadrature phase differences (IQDs). The theoretical findings show that IQDs arising from the transmitter and recipient can be combined with channel paths to generate so-called effective channel paths. The conceptual examination demonstrates that the outlined maximum likelihood strategy of the SFBC recognition and effective channel estimation processes is implemented by an expectation maximization tool utilizing the error control decoders' soft outputs. The simulations results reveal that the suggested strategy delivers a much greater recognition accuracy than the typical approaches outlined in the comparable literature. At a signal-to-noise ratio (SNR) of 14 dB, for example, the proposed approach achieves a bit error rate (BER) of 0.00002, which is very close to the case of perfect estimation and compensation for IQDs, outperforming the previous reported works which achieved BERs of 0.01 and 0.02.

The Impact of Sample Size and Various Other Factors on Estimation of Dichotomous Mixture IRT Models

The purpose of this study was to examine the effects of different data conditions on item parameter recovery and classification accuracy of three dichotomous mixture item response theory (IRT) models: the Mix1PL, Mix2PL, and Mix3PL. Manipulated factors in the simulation included the sample size (11 different sample sizes from 100 to 5000), test length (10, 30, and 50), number of classes (2 and 3), the degree of latent class separation (normal/no separation, small, medium, and large), and class sizes (equal vs. nonequal). Effects were assessed using root mean square error (RMSE) and classification accuracy percentage computed between true parameters and estimated parameters. The results of this simulation study showed that more precise estimates of item parameters were obtained with larger sample sizes and longer test lengths. Recovery of item parameters decreased as the number of classes increased with the decrease in sample size. Recovery of classification accuracy for the conditions with two-class solutions was also better than that of three-class solutions. Results of both item parameter estimates and classification accuracy differed by model type. More complex models and models with larger class separations produced less accurate results. The effect of the mixture proportions also differentially affected RMSE and classification accuracy results. Groups of equal size produced more precise item parameter estimates, but the reverse was the case for classification accuracy results. Results suggested that dichotomous mixture IRT models required more than 2,000 examinees to be able to obtain stable results as even shorter tests required such large sample sizes for more precise estimates. This number increased as the number of latent classes, the degree of separation, and model complexity increased.

EM and SAGE Algorithms for DOA Estimation in the Presence of Unknown Uniform Noise

The existing expectation maximization (EM) and space-alternating generalized EM (SAGE) algorithms are only applied to direction of arrival (DOA) estimation in known noise. In this paper, the two algorithms are designed for DOA estimation in unknown uniform noise. Both the deterministic and random signal models are considered. In addition, a new modified EM (MEM) algorithm applicable to the noise assumption is also proposed. Next, these EM-type algorithms are improved to ensure the stability when the powers of sources are not equal. After being improved, simulation results illustrate that the EM algorithm has similar convergence with the MEM algorithm, the SAGE algorithm outperforms the EM and MEM algorithms for the deterministic signal model, and the SAGE algorithm cannot always outperform the EM and MEM algorithms for the random signal model. Furthermore, simulation results show that processing the same snapshots from the random signal model, the SAGE algorithm for the deterministic signal model can require the fewest computations.

Bio-Inspired Swarm Intelligence Optimization Algorithm-Aided Hybrid TDOA/AOA-Based Localization

A TDOA/AOA hybrid location algorithm based on the crow search algorithm optimized by particle swarm optimization is proposed to address the challenge of solving the nonlinear equation of time of arrival (TDOA/AOA) location in the non-line-of-sight (NLoS) environment. This algorithm keeps its optimization mechanism on the basis of enhancing the performance of the original algorithm. To obtain a better fitness value throughout the optimization process and increase the algorithm's optimization accuracy, the fitness function based on maximum likelihood estimation is modified. In order to speed up algorithm convergence and decrease needless global search without compromising population diversity, an initial solution is simultaneously added to the starting population location. Simulation findings demonstrate that the suggested method outperforms the TDOA/AOA algorithm and other comparable algorithms, including Taylor, Chan, PSO, CPSO, and basic CSA algorithms. The approach performs well in terms of robustness, convergence speed, and node positioning accuracy.

Accelerated failure time modeling via nonparametric mixtures

An accelerated failure time (AFT) model assuming a log-linear relationship between failure time and a set of covariates can be either parametric or semiparametric, depending on the distributional assumption for the error term. Both classes of AFT models have been popular in the analysis of censored failure time data. The semiparametric AFT model is more flexible and robust to departures from the distributional assumption than its parametric counterpart. However, the semiparametric AFT model is subject to producing biased results for estimating any quantities involving an intercept. Estimating an intercept requires a separate procedure. Moreover, a consistent estimation of the intercept requires stringent conditions. Thus, essential quantities such as mean failure times might not be reliably estimated using semiparametric AFT models, which can be naturally done in the framework of parametric AFT models. Meanwhile, parametric AFT models can be severely impaired by misspecifications. To overcome this, we propose a new type of the AFT model using a nonparametric Gaussian-scale mixture distribution. We also provide feasible algorithms to estimate the parameters and mixing distribution. The finite sample properties of the proposed estimators are investigated via an extensive stimulation study. The proposed estimators are illustrated using a real dataset.

Lensless Three-Dimensional Imaging under Photon-Starved Conditions

In this paper, we propose a lensless three-dimensional (3D) imaging under photon-starved conditions using diffraction grating and computational photon counting method. In conventional 3D imaging with and without the lens, 3D visualization of objects under photon-starved conditions may be difficult due to lack of photons. To solve this problem, our proposed method uses diffraction grating imaging as lensless 3D imaging and computational photon counting method for 3D visualization of objects under these conditions. In addition, to improve the visual quality of 3D images under severely photon-starved conditions, in this paper, multiple observation photon counting method with advanced statistical estimation such as Bayesian estimation is proposed. Multiple observation photon counting method can estimate the more accurate 3D images by remedying the random errors of photon occurrence because it can increase the samples of photons. To prove the ability of our proposed method, we implement the optical experiments and calculate the peak sidelobe ratio as the performance metric.

Inferential properties with a novel two parameter Poisson generalized Lindley distribution with regression and application to INAR(1) process

Based on the well-known Poisson (P) distribution and the new generalized Lindley distribution (NGLD) developed by using gamma (α,θ) and gamma (α-1,θ) distributions, a new compound two-parameter Poisson generalized Lindley (TPPGL) distribution is proposed in this paper and thereon systematically explores the mathematical properties. Closed form expressions are assembled for such properties including the probability generating function, moments, skewness, kurtosis, etc. The likelihood-based method is used for estimating the parameters followed by a broad Monte Carlo simulation study. To further motivate the proposed model, a count regression model and a first order integer valued autoregressive process are constructed based on the novel TPPGL distribution. The empirical importance of the proposed models is confirmed through application to four real datasets.

[The Validity of the Poisson Distribution to Analyze Microbial Colony Counts on Agar Plates for Food Samples]

Microbial colony counts of food samples in microbiological examinations are one of the most important items. The probability distributions for the colony counts per agar plate at the dilution of counting had not been intensively studied so far. Recently we analyzed the colony counts of food samples with several probability distributions using the Pearson's chi-square value by the "traditional" statistics as the index of fit [Fujikawa and Tsubaki, Food Hyg.Saf.Sc., 60, 88-95 (2019)]. As a result, the selected probability distributions depended on the samples. In this study we newly selected a probability distribution, namely a statistical model, suitable for the above data with the method of maximum likelihood from the probabilistic point of view. The Akaike's Information Criterion (AIC) was used as the index of fit. Consequently, the Poisson model were better than the negative binomial model for all of four food samples. The Poisson model was also better than the binomial for three of four microbial culture samples. With Baysian Information Criterion (BIC), the Poisson model was also better than these two models for all the samples. These results suggested that the Poisson distribution would be the best model to estimate the colony counts of food samples. The present study would be the first report on the statistical model selection for the colony counts of food samples with AIC and BIC.

The Geometry of Generalized Likelihood Ratio Test

The generalized likelihood ratio test (GLRT) for composite hypothesis testing problems is studied from a geometric perspective. An information-geometrical interpretation of the GLRT is proposed based on the geometry of curved exponential families. Two geometric pictures of the GLRT are presented for the cases where unknown parameters are and are not the same under the null and alternative hypotheses, respectively. A demonstration of one-dimensional curved Gaussian distribution is introduced to elucidate the geometric realization of the GLRT. The asymptotic performance of the GLRT is discussed based on the proposed geometric representation of the GLRT. The study provides an alternative perspective for understanding the problems of statistical inference in the theoretical sense.

A superior extension for the Lomax distribution with application to Covid-19 infections real data

We present a new continuous lifetime model with four parameters by combining the Lomax and the Weibull distributions. The extended odd Weibull Lomax (EOWL) distribution is what we’ll call it. This new distribution possesses several desirable properties thanks to the simple linear representation of its hazard rate function, moments, and moment -generating function, with stress-strength reliability that are provided in a simple closed forms. The parameters of the EOWL model are estimated using classical methods such as the maximum likelihood (MLE) and the maximum product of spacing (MPS) and estimated also but using a non-classical method such as Bayesian analytical approaches. Bayesian estimation is performed using the Monte Carlo Markov Chain method. Monte Carlo simulation are used to assess the effectiveness of the estimation methods throughout the Metropolis Hasting (MH) algorithm. To illustrate the suggested distribution’s effectiveness and suitability for simulating real-world pandemics, we used three existing COVID-19 data sets from the United Kingdom, the United States of America, and Italy which are studied to serve as illustrative examples. We graphed the P-P plots and TTT plots for the proposed distribution proving its superiority in a graphical manner for modelling the three data sets in the paper.

A semiparametric isotonic regression model for skewed distributions with application to DNA-RNA-protein analysis

In this paper, we propose a semiparametric regression model that is built upon an isotonic regression model with the assumption that the random error follows a skewed distribution. We develop an expectation-maximization algorithm for obtaining the maximum likelihood estimates of the model parameters, examine the asymptotic properties of the estimators, conduct simulation studies to explore the performance of the proposed model, and apply the method to evaluate the DNA-RNA-protein relationship and identify genes that are key factors in tumor progression.

Low-Complexity Hyperbolic Embedding Schemes for Temporal Complex Networks

Hyperbolic embedding can effectively preserve the property of complex networks. Though some state-of-the-art hyperbolic node embedding approaches are proposed, most of them are still not well suited for the dynamic evolution process of temporal complex networks. The complexities of the adaptability and embedding update to the scale of complex networks with moderate variation are still challenging problems. To tackle the challenges, we propose hyperbolic embedding schemes for the temporal complex network within two dynamic evolution processes. First, we propose a low-complexity hyperbolic embedding scheme by using matrix perturbation, which is well-suitable for medium-scale complex networks with evolving temporal characteristics. Next, we construct the geometric initialization by merging nodes within the hyperbolic circular domain. To realize fast initialization for a large-scale network, an R tree is used to search the nodes to narrow down the search range. Our evaluations are implemented for both synthetic networks and realistic networks within different downstream applications. The results show that our hyperbolic embedding schemes have low complexity and are adaptable to networks with different scales for different downstream tasks.

A gentle tutorial on accelerated parameter and confidence interval estimation for hidden Markov models using Template Model Builder

A very common way to estimate the parameters of a hidden Markov model (HMM) is the relatively straightforward computation of maximum likelihood (ML) estimates. For this task, most users rely on user-friendly implementation of the estimation routines via an interpreted programming language such as the statistical software environment R. Such an approach can easily require time-consuming computations, in particular for longer sequences of observations. In addition, selecting a suitable approach for deriving confidence intervals for the estimated parameters is not entirely obvious, and often the computationally intensive bootstrap methods have to be applied. In this tutorial, we illustrate how to speed up the computation of ML estimates significantly via the R package TMB. Moreover, this approach permits simple retrieval of standard errors at the same time. We illustrate the performance of our routines using different data sets: first, two smaller samples from a mobile application for tinnitus patients and a well-known data set of fetal lamb movements with 87 and 240 data points, respectively. Second, we rely on larger data sets of simulated data of sizes 2000 and 5000 for further analysis. This tutorial is accompanied by a collection of scripts, which are all available in the Supporting Information. These scripts allow any user with moderate programming experience to benefit quickly from the computational advantages of TMB.

Modeling Overdispersed Dengue Data via Poisson Inverse Gaussian Regression Model: A Case Study in the City of Campo Grande, MS, Brazil

Dengue fever is a tropical disease transmitted mainly by the female Aedes aegypti mosquito that affects millions of people every year. As there is still no safe and effective vaccine, currently the best way to prevent the disease is to control the proliferation of the transmitting mosquito. Since the proliferation and life cycle of the mosquito depend on environmental variables such as temperature and water availability, among others, statistical models are needed to understand the existing relationships between environmental variables and the recorded number of dengue cases and predict the number of cases for some future time interval. This prediction is of paramount importance for the establishment of control policies. In general, dengue-fever datasets contain the number of cases recorded periodically (in days, weeks, months or years). Since many dengue-fever datasets tend to be of the overdispersed, long-tail type, some common models like the Poisson regression model or negative binomial regression model are not adequate to model it. For this reason, in this paper we propose modeling a dengue-fever dataset by using a Poisson-inverse-Gaussian regression model. The main advantage of this model is that it adequately models overdispersed long-tailed data because it has a wider skewness range than the negative binomial distribution. We illustrate the application of this model in a real dataset and compare its performance to that of a negative binomial regression model.

Precision of attenuation coefficient measurements by optical coherence tomography

SIGNIFICANCE

Optical coherence tomography (OCT) is an interferometric imaging modality, which provides tomographic information on the microscopic scale. Furthermore, OCT signal analysis facilitates quantification of tissue optical properties (e.g., the attenuation coefficient), which provides information regarding the structure and organization of tissue. However, a rigorous and standardized measure of the precision of the OCT-derived optical properties, to date, is missing.

AIM

We present a robust theoretical framework, which provides the Cramér -Rao lower bound σμOCT for the precision of OCT-derived optical attenuation coefficients.

APPROACH

Using a maximum likelihood approach and Fisher information, we derive an analytical solution for σμOCT when the position and depth of focus are known. We validate this solution, using simulated OCT signals, for which attenuation coefficients are extracted using a least-squares fitting procedure.

RESULTS

Our analytical solution is in perfect agreement with simulated data without shot noise. When shot noise is present, we show that the analytical solution still holds for signal-to-noise ratios (SNRs) in the fitting window being above 20 dB. For other cases (SNR&lt;20 dB, focus position not precisely known), we show that the numerical calculation of the precision agrees with the σμOCT derived from simulated signals.

CONCLUSIONS

Our analytical solution provides a fast, rigorous, and easy-to-use measure for OCT-derived attenuation coefficients for signals above 20 dB. The effect of uncertainties in the focal point position on the precision in the attenuation coefficient, the second assumption underlying our analytical solution, is also investigated by numerical calculation of the lower bounds. This method can be straightforwardly extended to uncertainty in other system parameters.

On parameter estimation of the standard omega distribution

The standard omega distribution is defined on the unit interval so that it is a probabilistic model for observations in rates and percentages. It is, in fact, the unit form of the exponentiated half logistic distribution. In this work, we first give a detailed shape analysis from which we observe that it is another flexible beta-like distribution. We observe that it can be J-shaped, reverse J-shaped, U-shaped, unimodal and show left and right skewness according to the values of its shape parameters. Contrary to the ordinary beta, it has the advantage of having a clear distribution function. We then discuss the existence and uniqueness of the maximum likelihood estimators and the Bayesian estimate of the parameters. The existence and uniqueness of the maximum likelihood estimators of the parameters will give a great advantage to the possible practitioners of this model since the possibility of finding a spurious solution to the likelihood equations disappears then. The comparison of these estimators with the existing ones for the general omega distribution is made with the help of a simulation study. Two real data fitting demonstrations prove its usefulness among other beta-like distributions such as Kumaraswamy, log-Lindley and Topp-Leone.

An Improved Parameter Estimator of the Homodyned K Distribution Based on the Maximum Likelihood Method for Ultrasound Tissue Characterization

The homodyned K distribution (HK) can generally describe the ultrasound backscatter envelope statistics distribution with parameters that have specific physical meaning. However, creating robust and reliable HK parameter estimates remains a crucial concern. The maximum likelihood estimator (MLE) usually yields a small variance and bias in parameter estimation. Thus, two recent studies have attempted to use MLE for parameter estimation of HK distribution. However, some of the statements in these studies are not fully justified and they may hinder the application of parameter estimation of HK distribution based on MLE. In this study, we propose a new parameter estimator for the HK distribution based on the MLE (i.e., MLE1), which overcomes the disadvantages of conventional MLE of HK distribution. The MLE1 was compared with other estimators, such as XU estimator (an estimation method based on the first moment of the intensity and tow log-moments) and ANN estimator (an estimation method based on artificial neural networks). We showed that the estimations of parameters α and k are the best overall (in terms of the relative bias, normalized standard deviation, and relative root mean squared errors) using the proposed MLE1 compared with the others based on the simulated data when the sample size was N = 1000. Moreover, we assessed the usefulness of the proposed MLE1 when the number of scatterers per resolution cell was high (i.e., α up to 80) and when the sample size was small (i.e., N = 100), and we found a satisfactory result. Tests on simulated ultrasound images based on Field II were performed and the results confirmed that the proposed MLE1 is feasible and reliable for the parameter estimation from the ultrasonic envelope signal. Therefore, the proposed MLE1 can accurately estimate the HK parameters with lower uncertainty, which presents a potential practical value for further ultrasonic applications.

A New Coarse Gating Strategy Driven Multidimensional Assignment for Two-Stage MHT of Bearings-Only Multisensor-Multitarget Tracking

The problem of two-dimensional bearings-only multisensor-multitarget tracking is addressed in this work. For this type of target tracking problem, the multidimensional assignment (MDA) is crucial for identifying measurements originating from the same targets. However, the computation of the assignment cost of all possible associations is extremely high. To reduce the computational complexity of MDA, a new coarse gating strategy is proposed. This is realized by comparing the Mahalanobis distance between the current estimate and initial estimate in an iterative process for the maximum likelihood estimation of the target position with a certain threshold to eliminate potential infeasible associations. When the Mahalanobis distance is less than the threshold, the iteration will exit in advance so as to avoid the expensive computational costs caused by invalid iteration. Furthermore, the proposed strategy is combined with the two-stage multiple hypothesis tracking framework for bearings-only multisensor-multitarget tracking. Numerical experimental results verify its effectiveness.

Toward accurate diagnosis and surveillance of bacterial infections using enhanced strain-level metagenomic next-generation sequencing of infected body fluids

Metagenomic next-generation sequencing (mNGS) enables comprehensive pathogen detection and has become increasingly popular in clinical diagnosis. The distinct pathogenic traits between strains require mNGS to achieve a strain-level resolution, but an equivocal concept of 'strain' as well as the low pathogen loads in most clinical specimens hinders such strain awareness. Here we introduce a metagenomic intra-species typing (MIST) tool (https://github.com/pandafengye/MIST), which hierarchically organizes reference genomes based on average nucleotide identity (ANI) and performs maximum likelihood estimation to infer the strain-level compositional abundance. In silico analysis using synthetic datasets showed that MIST accurately predicted the strain composition at a 99.9% average nucleotide identity (ANI) resolution with a merely 0.001× sequencing depth. When applying MIST on 359 culture-positive and 359 culture-negative real-world specimens of infected body fluids, we found the presence of multiple-strain reached considerable frequencies (30.39%-93.22%), which were otherwise underestimated by current diagnostic techniques due to their limited resolution. Several high-risk clones were identified to be prevalent across samples, including Acinetobacter baumannii sequence type (ST)208/ST195, Staphylococcus aureus ST22/ST398 and Klebsiella pneumoniae ST11/ST15, indicating potential outbreak events occurring in the clinical settings. Interestingly, contaminations caused by the engineered Escherichia coli strain K-12 and BL21 throughout the mNGS datasets were also identified by MIST instead of the statistical decontamination approach. Our study systemically characterized the infected body fluids at the strain level for the first time. Extension of mNGS testing to the strain level can greatly benefit clinical diagnosis of bacterial infections, including the identification of multi-strain infection, decontamination and infection control surveillance.

Target Localization in Wireless Sensor Networks Based on Received Signal Strength and Convex Relaxation

A new positioning algorithm based on RSS measurement is proposed. The algorithm adopts maximum likelihood estimation and semi-definite programming. The received signal strength model is transformed to a non-convex estimator for the positioning of the target using the maximum likelihood estimation. The non-convex estimator is then transformed into a convex estimator by semi-definite programming, and the global minimum of the target location estimation is obtained. This algorithm aims at the L0 known problem and then extends its application to the case of L0 unknown. The simulations and experimental results show that the proposed algorithm has better accuracy than the existing positioning algorithms.

Inference of regulatory networks through temporally sparse data

A major goal in genomics is to properly capture the complex dynamical behaviors of gene regulatory networks (GRNs). This includes inferring the complex interactions between genes, which can be used for a wide range of genomics analyses, including diagnosis or prognosis of diseases and finding effective treatments for chronic diseases such as cancer. Boolean networks have emerged as a successful class of models for capturing the behavior of GRNs. In most practical settings, inference of GRNs should be achieved through limited and temporally sparse genomics data. A large number of genes in GRNs leads to a large possible topology candidate space, which often cannot be exhaustively searched due to the limitation in computational resources. This paper develops a scalable and efficient topology inference for GRNs using Bayesian optimization and kernel-based methods. Rather than an exhaustive search over possible topologies, the proposed method constructs a Gaussian Process (GP) with a topology-inspired kernel function to account for correlation in the likelihood function. Then, using the posterior distribution of the GP model, the Bayesian optimization efficiently searches for the topology with the highest likelihood value by optimally balancing between exploration and exploitation. The performance of the proposed method is demonstrated through comprehensive numerical experiments using a well-known mammalian cell-cycle network.

Distribution Theory Following Blinded and Unblinded Sample Size Re-estimation under Parametric Models

Asymptotic distribution theory for maximum likelihood estimators under fixed alternative hypotheses is reported in the literature even though the power of any realistic test converges to one under fixed alternatives. Under fixed alternatives, authors have established that nuisance parameter estimates are inconsistent when sample size re-estimation (SSR) follows blinded randomization. These results have helped to inhibit the use of SSR. In this paper, we argue for local alternatives to be used instead of fixed alternatives. Motivated by Gould and Shih (1998), we treat unavailable treatment assignments in blinded experiments as missing data and rely on single imputation from marginal distributions to fill in for missing data. With local alternatives, it is sufficient to proceed only with the first step of the EM algorithm mimicking imputation under the null hypothesis. Then, we show that blinded and unblinded estimates of the nuisance parameter σ θ 2 are consistent, and re-estimated sample sizes converge to their locally asymptotically optimal values. This theoretical finding is confirmed through Monte-Carlo simulation studies. Practical utility is illustrated through a multiple logistic regression example. We conclude that, for hypothesis testing with a predetermined minimally clinically relevant local effect size, both blinded and unblinded SSR procedures lead to similar sample sizes and power.

Bayesian and Classical Inference under Type-II Censored Samples of the Extended Inverse Gompertz Distribution with Engineering Applications

In this article, we introduce a new three-parameter distribution called the extended inverse-Gompertz (EIGo) distribution. The implementation of three parameters provides a good reconstruction for some applications. The EIGo distribution can be seen as an extension of the inverted exponential, inverse Gompertz, and generalized inverted exponential distributions. Its failure rate function has an upside-down bathtub shape. Various statistical and reliability properties of the EIGo distribution are discussed. The model parameters are estimated by the maximum-likelihood and Bayesian methods under Type-II censored samples, where the parameters are explained using gamma priors. The performance of the proposed approaches is examined using simulation results. Finally, two real-life engineering data sets are analyzed to illustrate the applicability of the EIGo distribution, showing that it provides better fits than competing inverted models such as inverse-Gompertz, inverse-Weibull, inverse-gamma, generalized inverse-Weibull, exponentiated inverted-Weibull, generalized inverted half-logistic, inverted-Kumaraswamy, inverted Nadarajah-Haghighi, and alpha-power inverse-Weibull distributions.

Classical and Bayesian Inference of an Exponentiated Half-Logistic Distribution under Adaptive Type II Progressive Censoring

The point and interval estimations for the unknown parameters of an exponentiated half-logistic distribution based on adaptive type II progressive censoring are obtained in this article. At the beginning, the maximum likelihood estimators are derived. Afterward, the observed and expected Fisher’s information matrix are obtained to construct the asymptotic confidence intervals. Meanwhile, the percentile bootstrap method and the bootstrap-t method are put forward for the establishment of confidence intervals. With respect to Bayesian estimation, the Lindley method is used under three different loss functions. The importance sampling method is also applied to calculate Bayesian estimates and construct corresponding highest posterior density (HPD) credible intervals. Finally, numerous simulation studies are conducted on the basis of Markov Chain Monte Carlo (MCMC) samples to contrast the performance of the estimations, and an authentic data set is analyzed for exemplifying intention.

An Accurate Method for Studying Individual Microbial Lag: Experiments and Computations

Variability in the behavior of microbial foodborne pathogens and spoilers causes difficulties in predicting the safety and quality of food products during their shelf life. Therefore, the quantification of the individual microbial lag phase distribution is of high relevance to the field of quantitative microbial risk assessment. To construct models that predict the effect of changes in environmental conditions on the individual lag, an accurate determination of these distributions is required. Therefore, the current research focuses on the development of an experimental and computational method for accurate determination of individual lag phase distribution. The experimental method is unique in the sense that full liquid volumes are sampled without using dilutions to detect the final population, thereby minimizing experimental errors. Moreover, the method does not aim at the isolation of single cells but at a low number of cells. The fact that several cells can be present in the initial samples instead of having a single cell is considered by the computational method. This method relies on Monte Carlo simulation to predict the individual lag phase distribution for a given set of distribution parameters and maximum likelihood estimation to find the parameters that describe the experimental data best. The method was validated both through simulation and experiments and was found to deliver a desired accuracy.

A first-order binomial-mixed Poisson integer-valued autoregressive model with serially dependent innovations

Motivated by the extended Poisson INAR(1), which allows innovations to be serially dependent, we develop a new family of binomial-mixed Poisson INAR(1) (BMP INAR(1)) processes by adding a mixed Poisson component to the innovations of the classical Poisson INAR(1) process. Due to the flexibility of the mixed Poisson component, the model includes a large class of INAR(1) processes with different transition probabilities. Moreover, it can capture some overdispersion features coming from the data while keeping the innovations serially dependent. We discuss its statistical properties, stationarity conditions and transition probabilities for different mixing densities (Exponential, Lindley). Then, we derive the maximum likelihood estimation method and its asymptotic properties for this model. Finally, we demonstrate our approach using a real data example of iceberg count data from a financial system.

Estimating the sample mean and standard deviation from order statistics and sample size in meta-analysis

In recent years, a growing number of researchers have attempted to overcome the constraints of size and scope in different medical studies to find out the overall treatment effects. As a widespread technique to combine results of multiple studies, commonly used meta-analytic approaches for continuous outcomes demand sample means and standard deviations of primary studies, which are absent sometimes, especially when the outcome is skewed. Instead, the median, the extrema, and/or the quartiles are reported. One feasible solution is to convert the preceding order statistics to demanded statistics to keep effect measures consistent. In this article, we propose new methods based on maximum likelihood estimation for known distributions with unknown parameters. For unknown underlying distributions, the Box-Cox transformation is applied to the reported order statistics so that the techniques for normal distribution can be utilized. Two approaches for estimating the power parameter in Box-Cox transformation are provided. Both simulation studies and real data analysis indicate that in most cases, the proposed methods outperform the existing methods in estimation accuracy.

A High-Speed Demodulation Technology of Fiber Optic Extrinsic Fabry-Perot Interferometric Sensor Based on Coarse Spectrum

A fast real-time demodulation method based on the coarsely sampled spectrum is proposed for transient signals of fiber optic extrinsic Fabry-Perot interferometers (EFPI) sensors. The feasibility of phase demodulation using a coarse spectrum is theoretically analyzed. Based on the coarse spectrum, fast Fourier transform (FFT) algorithm is used to roughly estimate the cavity length. According to the rough estimation, the maximum likelihood estimation (MLE) algorithm is applied to calculate the cavity length accurately. The dense wavelength division multiplexer (DWDM) is used to split the broadband spectrum into the coarse spectrum, and the high-speed synchronous ADC collects the spectrum. The experimental results show that the system can achieve a real-time dynamic demodulation speed of 50 kHz, a static measurement root mean square error (RMSE) of 0.184 nm, and a maximum absolute and relative error distribution of 15 nm and 0.005% of the measurement cavity length compared with optical spectrum analyzers (OSA).

A Novel Statistical Optimization Algorithm for Estimating Perfusion Curves in Susceptibility Contrast-Enhanced MRI

Dynamic susceptibility contrast-enhanced magnetic resonance imaging is an important tool for evaluating intravascular indicator dynamics, which in turn is valuable for understanding brain physiology and pathophysiology. This procedure usually involves fitting a gamma-variate function to observed concentration-time curves in order to eliminate undesired effects of recirculation and the leakage of contrast agents. Several conventional curve-fitting approaches are routinely applied. The nonlinear optimization methods typically are computationally expensive and require reliable initial values to guarantee success, whereas a logarithmic linear least-squares (LL-LS) method is more stable and efficient, and does not suffer from the initial-value problem, but it can show degraded performance, especially when a few data or outliers are present. In this paper, we demonstrate, that the original perfusion curve-fitting problem can be transformed into a gamma-distribution-fitting problem by treating the concentration-time curves as a random sample from a gamma distribution with time as the random variable. A robust maximum-likelihood estimation (MLE) algorithm can then be readily adopted to solve this problem. The performance of the proposed method is compared with the nonlinear Levenberg-Marquardt (L-M) method and the LL-LS method using both synthetic and real data. The results show that the performance of the proposed approach is far superior to those of the other two methods, while keeping the advantages of the LL-LS method, such as easy implementation, low computational load, and dispensing with the need to guess the initial values. We argue that the proposed method represents an attractive alternative option for assessing intravascular indicator dynamics in clinical applications. Moreover, we also provide valuable suggestions on how to select valid data points and set the initial values in the two traditional approaches (LL-LS and nonlinear L-M methods) to achieve more reliable estimations.

Inference for Inverse Power Lomax Distribution with Progressive First-Failure Censoring

This paper investigates the statistical inference of inverse power Lomax distribution parameters under progressive first-failure censored samples. The maximum likelihood estimates (MLEs) and the asymptotic confidence intervals are derived based on the iterative procedure and asymptotic normality theory of MLEs, respectively. Bayesian estimates of the parameters under squared error loss and generalized entropy loss function are obtained using independent gamma priors. For Bayesian computation, Tierney–Kadane’s approximation method is used. In addition, the highest posterior credible intervals of the parameters are constructed based on the importance sampling procedure. A Monte Carlo simulation study is carried out to compare the behavior of various estimates developed in this paper. Finally, a real data set is analyzed for illustration purposes.

A semiparametric mixture model approach for regression analysis of partly interval-censored data with a cured subgroup

Failure time data with a cured subgroup are frequently confronted in various scientific fields and many methods have been proposed for their analysis under right or interval censoring. However, a cure model approach does not seem to exist in the analysis of partly interval-censored data, which consist of both exactly observed and interval-censored observations on the failure time of interest. In this article, we propose a two-component mixture cure model approach for analyzing such type of data. We employ a logistic model to describe the cured probability and a proportional hazards model to model the latent failure time distribution for uncured subjects. We consider maximum likelihood estimation and develop a new expectation-maximization algorithm for its implementation. The asymptotic properties of the resulting estimators are established and the finite sample performance of the proposed method is examined through simulation studies. An application to a set of real data on childhood mortality in Nigeria is provided.

COVID-19 Vaccine Priority Strategy Using a Heterogenous Transmission Model Based on Maximum Likelihood Estimation in the Republic of Korea

(1) Background: The vaccine supply is likely to be limited in 2021 due to constraints in manufacturing. To maximize the benefit from the rollout phase, an optimal strategy of vaccine allocation is necessary based on each country's epidemic status. (2) Methods: We first developed a heterogeneous population model considering the transmission matrix using maximum likelihood estimation based on the epidemiological records of individual COVID-19 cases in the Republic of Korea. Using this model, the vaccine priorities for minimizing mortality or incidence were investigated. (3) Results: The simulation results showed that the optimal vaccine allocation strategy to minimize the mortality (or incidence) was to prioritize elderly and healthcare workers (or adults) as long as the reproductive number was below 1.2 (or over 0.9). (4) Conclusion: Our simulation results support the current Korean government vaccination priority strategy, which prioritizes healthcare workers and senior groups to minimize mortality, under the condition that the reproductive number remains below 1.2. This study revealed that, in order to maintain the current vaccine priority policy, it is important to ensure that the reproductive number does not exceed the threshold by concurrently implementing nonpharmaceutical interventions.

Efficient Likelihood Estimation of Generalized Structural Equation Models with a Mix of Normal and Nonnormal Responses

A maximum likelihood estimation routine is presented for a generalized structural equation model that permits a combination of response variables from various distributions (e.g., normal, Poisson, binomial, etc.). The likelihood function does not have a closed-form solution and so must be numerically approximated, which can be computationally demanding for models with several latent variables. However, the dimension of numerical integration can be reduced if one or more of the latent variables do not directly affect any nonnormal endogenous variables. The method is demonstrated using an empirical example, and the full estimation details, including first-order derivatives of the likelihood function, are provided.

Estimating the proportion of resistance alleles from bulk Sanger sequencing, circumventing the variability of individual DNA

Specimens should be examined as much as possible to obtain a precise estimate of the proportion of resistance alleles in agricultural fields. Monitoring traps that use semiochemicals on sticky sheets are helpful in this regard. However, insects captured by such traps are ordinarily left in the field until collection. Owing to DNA degradation, the amount of DNA greatly varies among insects, causing serious problems in obtaining maximum likelihood estimates and confidence intervals of the proportion of the resistance alleles. We propose a statistical procedure that can circumvent this degradation issue. R scripts for the calculation are provided for readers. We also propose the utilization of a Sanger sequencer. We demonstrate these procedures using field samples of diamide-resistant strains of the diamondback moth, Plutella xylostella (Lepidoptera: Plutellidae). The validity of the assumptions used in the statistical analysis is examined using the same data.

A family of Gamma-generated distributions: Statistical properties and applications

In this paper, we concentrate on the statistical properties of Gamma-X family of distributions. A special case of this family is the Gamma-Weibull distribution. Therefore, the statistical properties of Gamma-Weibull distribution as a sub-model of Gamma-X family are discussed such as moments, variance, skewness, kurtosis and Rényi entropy. Also, the parameters of the Gamma-Weibull distribution are estimated by the method of maximum likelihood. Some sub-models of the Gamma-X are investigated, including the cumulative distribution, probability density, survival and hazard functions. The Monte Carlo simulation study is conducted to assess the performances of these estimators. Finally, the adequacy of Gamma-Weibull distribution in data modeling is verified by the two clinical real data sets.Mathematics Subject Classification: 62E99; 62E15.

Robotic integration enables autonomous operation of laboratory scale stirred tank bioreactors with model-driven process analysis

Given its geometric similarity to large-scale production plants and the excellent possibilities for precise process control and monitoring, the classic stirred tank bioreactor (STR) still represents the gold standard for bioprocess development at a laboratory scale. However, compared to microbioreactor technologies, bioreactors often suffer from a low degree of process automation and deriving key performance indicators (KPIs) such as specific rates or yields often requires manual sampling and sample processing. A widely used parallelized STR setup was automated by connecting it to a liquid handling system and controlling it with a custom-made process control system. This allowed for the setup of a flexible modular platform enabling autonomous operation of the bioreactors without any operator present. Multiple unit operations like automated inoculation, sampling, sample processing and analysis, and decision making, for example for automated induction of protein production were implemented to achieve such functionality. The data gained during application studies was used for fitting of bioprocess models to derive relevant KPIs being in good agreement with literature. By combining the capabilities of STRs with the flexibility of liquid handling systems, this platform technology can be applied to a multitude of different bioprocess development pipelines at laboratory scale.

Hypothesis Testing Methods for Multivariate Multi-Occasion Intra-Individual Change

In psychological and educational measurement, it is often of interest to assess change in an individual. The current study expanded on previous research by introducing methods that can evaluate individual change on multiple latent traits measured on multiple occasions. The four methods considered are the likelihood ratio test (LRT), the multivariate Wald test (MWT), the modified multivariate Wald test (MMWT), and the score test (ST). Simulation studies were conducted to examine the true positive rate (TPR) and the false positive rate (FPR) of the new methods under a conventional fixed-form test and a computerized adaptive test (CAT). Manipulated variables included the number of occasions, change magnitudes, patterns of change, and correlations between latent traits. Results revealed that, in terms of FPR, all methods except MWT had close adherence to the nominal significance level. Among the three methods, the LRT is recommended as it provided a balance between FPR and TPR. Larger change magnitude yielded higher TPR, regardless of the remaining factors. With the same test length, a CAT yielded higher TPR than a conventional test. Real-data examples are provided of identifying psychometrically significant change across two to four occasions using a multivariate adaptive self-report medical outcomes measure from hospitalized patients. The detection of significant change among the three methods agreed highly, and those patients identified as having significant change exhibited large profile differences, which provided support for the valid performance of the proposed methods.