Study on Bayesian Skew-Normal Linear Mixed Model and Its Application in Fire Insurance.

Fire insurance is a crucial component of property insurance, and its rating depends on the forecast of insurance loss claim data. Fire insurance loss claim data have complicated characteristics such as skewness and heavy tail. The traditional linear mixed model is commonly difficult to accurately describe the distribution of loss. Therefore, it is crucial to establish a scientific and reasonable distribution model of fire insurance loss claim data. In this study, the random effects and random errors in the linear mixed model are firstly assumed to obey the skew-normal distribution. Then, a skew-normal linear mixed model is established using the Bayesian MCMC method based on a set of U.S. property insurance loss claims data. Comparative analysis is conducted with the linear mixed model of logarithmic transformation. Afterward, a Bayesian skew-normal linear mixed model for Chinese fire insurance loss claims data is designed. The posterior distribution of claim data parameters and related parameter estimation are employed with the R language JAGS package to obtain the predicted and simulated loss claim values. Finally, the optimization model in this study is used to determine the insurance rate. The results demonstrate that the model established by the Bayesian MCMC method can overcome data skewness, and the fitting and correlation with the sample data are better than the log-normal linear mixed model. Hence, it can be concluded that the distribution model proposed in this paper is reasonable for describing insurance claims. This study innovates a new approach for calculating the insurance premium rate and expands the application of the Bayesian method in the fire insurance field.

Phylogenetic Analysis That Models Compositional Heterogeneity over the Tree.

Molecular sequences in a phylogenetic analysis can differ in composition, and that shows that the process of evolution can change over time. However, models of evolution in common use are homogeneous over the tree, and if used in a phylogenetic analysis with compositionally tree-heterogeneous datasets these models can recover incorrect trees. The NDCH or Node-Discrete Compositional Heterogeneity model is able to model such data by accommodating differences in composition over the tree. Usage, problems, and limitations of this model are discussed, and a modification, the NDCH2 model, is described that can ameliorate some of these problems and limitations. Using these models can greatly increase the fit of the model to the data and can find better tree topologies. These models and various statistical tests are illustrated using a bacterial SSU rRNA dataset. These models are implemented in the software P4, and files for the analyses described here are made available.

Identifying immunity gaps for measles using Belgian serial serology data.

Vaccine-preventable diseases, such as measles, have been re-emerging in countries with moderate to high vaccine uptake. It is increasingly important to identify and close immunity gaps and increase coverage of routine childhood vaccinations, including two doses of the measles-mumps-rubella vaccine (MMR). Here, we present a simple cohort model relying on a Bayesian approach to evaluate the evolution of measles seroprevalence in Belgium using the three most recent cross-sectional serological survey data collections (2002, 2006 and 2013) and information regarding vaccine properties. We find measles seroprevalence profiles to be similar for the different regions in Belgium. These profiles exhibit a drop in seroprevalence in birth cohorts that were offered vaccination at suboptimal coverages in the first years after routine vaccination has been started up. This immunity gap is observed across all cross-sectional survey years, although it is more pronounced in survey year 2013. At present, the COVID-19 pandemic could negatively impact the immunization coverage worldwide, thereby increasing the need for additional immunization programs in groups of children that are impacted by this. Therefore, it is now even more important to identify existing immunity gaps and to sustain and reach vaccine-derived measles immunity goals.

Highly pathogenic avian influenza virus of the A/H5N8 subtype, clade 2.3.4.4b, caused outbreaks in Kazakhstan in 2020.

Background: Large poultry die-offs happened in Kazakhstan during autumn of 2020. The birds' disease appeared to be avian influenza. Northern Kazakhstan was hit first and then the disease propagated across the country affecting eleven provinces. This study reports the results of full-genome sequencing of viruses collected during the outbreaks and investigation of their relationship to avian influenza virus isolates in the contemporary circulation in Eurasia. Methods: Samples were collected from diseased birds during the 2020 outbreaks in Kazakhstan. Initial virus detection and subtyping was done using RT-PCR. Ten samples collected during expeditions to Northern and Southern Kazakhstan were used for full-genome sequencing of avian influenza viruses. Phylogenetic analysis was used to compare viruses from Kazakhstan to viral isolates from other world regions. Results: Phylogenetic trees for hemagglutinin and neuraminidase show that viruses from Kazakhstan belong to the A/H5N8 subtype and to the hemagglutinin H5 clade 2.3.4.4b. Deduced hemagglutinin amino acid sequences in all Kazakhstan's viruses in this study contain the polybasic cleavage site (KRRKR-G) indicative of the highly pathogenic phenotype. Building phylogenetic trees with the Bayesian phylogenetics results in higher statistical support for clusters than using distance methods. The Kazakhstan's viruses cluster with isolates from Southern Russia, the Russian Caucasus, the Ural region, and southwestern Siberia. Other closely related prototypes are from Eastern Europe. The Central Asia Migratory Flyway passes over Kazakhstan and birds have intermediate stops in Northern Kazakhstan. It is postulated that the A/H5N8 subtype was introduced with migrating birds. Conclusion: The findings confirm the introduction of the highly pathogenic avian influenza viruses of the A/Goose/Guangdong/96 (Gs/GD) H5 lineage in Kazakhstan. This virus poses a tangible threat to public health. Considering the results of this study, it looks justifiable to undertake measures in preparation, such as install sentinel surveillance for human cases of avian influenza in the largest pulmonary units, develop a human A/H5N8 vaccine and human diagnostics capable of HPAI discrimination.

The influence of the correlation-covariance structure of measurement errors over uncertainties propagation in online monitoring: application to environmental indicators in SUDS.

This paper presents a methodology to assess the influence of the correlation-covariance structure of measurement errors in online monitoring over the propagation of uncertainties, applied to wet-weather environmental indicators in sustainable urban drainage systems (SUDSs). The effect of auto-correlated and heteroskedastic errors in measured time-series over the estimated probability density function (PDF) of different environmental indicators is analyzed for a wide variety of possible error structures in the data. For this purpose, multiple correlation-covariance structures are randomly generated from exploring the parametric space of a linear exponent autoregressive (LEAR) model, employing a Bayesian-based Markov Chain Monte Carlo sampling technique. Significant differences tests are proposed to identify the most correlated parameters of the correlation-covariance error model with statistics of the environmental indicator PDFs. The method is applied to total suspended solids (TSS) and chemical oxygen demand (COD) time-series recorded during 13 rainfall events at the inlet and outlet of a SUDS train (stormwater settling tank-horizontal constructed wetland). In this case, results showed that the total error in the estimation of the analyzed environmental indicators is mostly explained by standard uncertainties (flattening of the PDFs) rather than bias contributions (displacement of the PDFs). The correlation-covariance model parameters related to the temporal delimitation of hydrographs/pollutographs and the intensity of the autocorrelation showed to have the strongest influence in the propagation of measurement errors (flattening/displacement of the PDFs).

Changes in spatiotemporal drought characteristics over northeast China from 1960 to 2018 based on the modified nested Copula model.

Drought forecasting is helpful for understanding the inherent mechanism of hydrological extremes and taking corresponding measures to mitigate drought impacts. Northeast China, which is an important, major grain-producing area in China, has been challenged by substantial losses due to frequent drought. In this study, to predict the spatiotemporal variation in drought events over Northeast China, a model-based simulation framework is proposed based on precipitation data at 70 meteorological stations from 1960 to 2018. The core of the model framework is run theory, modified Copula model- based Bayesian-MCMC, Gibbs sampling, and a new definition of drought intensity center and drought intensity accumulation area. The results showed that a total of 6408 drought events occurred at the 70 meteorological stations in Northeast China over the past 59 years. The empirical distribution functions of longitude, latitude, and time can be used to fit the edge distribution of the original variable. In comparison to the traditional maximum likelihood method, the Bayesian-MCMC method is more accurate for parameter estimation of the Copula model. The Frank Copula is the optimum joint function of longitude and latitude, while the Gaussian Copula is the optimum joint function of location and time. Gibbs sampling can provide a relatively larger sample size for predicting future drought conditions. The spatiotemporal variation in drought in Northeast China changes similarly throughout the year. Drought is mainly concentrated in southwestern Liaoning from February to April. The drought intensity center moves to the northeast from May to September. Western Heilongjiang is the main drought-stricken area from October to November. The drought intensity center moves southwest from December to January of the following year. This study provides a method for effectively predicting drought events and is of great significance to the protection, development, and utilization of water resources.

Improving the performance of Bayesian phylogenetic inference under relaxed clock models.

BACKGROUND: Bayesian MCMC has become a common approach for phylogenetic inference. But the growing size of molecular sequence data sets has created a pressing need to improve the computational efficiency of Bayesian phylogenetic inference algorithms. RESULTS: This paper develops a new algorithm to improve the efficiency of Bayesian phylogenetic inference for models that include a per-branch rate parameter. In a Markov chain Monte Carlo algorithm, the presented proposal kernel changes evolutionary rates and divergence times at the same time, under the constraint that the implied genetic distances remain constant. Specifically, the proposal operates on the divergence time of an internal node and the three adjacent branch rates. For the root of a phylogenetic tree, there are three strategies discussed, named Simple Distance, Small Pulley and Big Pulley. Note that Big Pulley is able to change the tree topology, which enables the operator to sample all the possible rooted trees consistent with the implied unrooted tree. To validate its effectiveness, a series of experiments have been performed by implementing the proposed operator in the BEAST2 software. CONCLUSIONS: The results demonstrate that the proposed operator is able to improve the performance by giving better estimates for a given chain length and by using less running time for a given level of accuracy. Measured by effective samples per hour, use of the proposed operator results in overall mixing more efficient than the current operators in BEAST2. Especially for large data sets, the improvement is up to half an order of magnitude.

Practical Speedup of Bayesian Inference of Species Phylogenies by Restricting the Space of Gene Trees.

Species tree inference from multilocus data has emerged as a powerful paradigm in the postgenomic era, both in terms of the accuracy of the species tree it produces as well as in terms of elucidating the processes that shaped the evolutionary history. Bayesian methods for species tree inference are desirable in this area as they have been shown not only to yield accurate estimates, but also to naturally provide measures of confidence in those estimates. However, the heavy computational requirements of Bayesian inference have limited the applicability of such methods to very small data sets. In this article, we show that the computational efficiency of Bayesian inference under the multispecies coalescent can be improved in practice by restricting the space of the gene trees explored during the random walk, without sacrificing accuracy as measured by various metrics. The idea is to first infer constraints on the trees of the individual loci in the form of unresolved gene trees, and then to restrict the sampler to consider only resolutions of the constrained trees. We demonstrate the improvements gained by such an approach on both simulated and biological data.

The popularity spectrum applied to a cross-cultural question.

We investigate a new approach for identifying the contribution of horizontal transmission between groups to cross-cultural similarity. This method can be applied to datasets that record the presence or absence of artefacts, or attributes thereof, in archaeological and ethnographic assemblages, from which popularity spectra can be constructed. Based on analytical and simulation models, we show that the form of such spectra is sensitive to horizontal transmission between groups. We then fit the analytical model to existing datasets by Bayesian MCMC and obtain evidence for strong horizontal transmission in oceanic as opposed to continental datasets. We check the validity of our statistical method by using individual-based models, and show that the vertical transmission rate tends to be underestimated if the datasets are obtained from lattice-structured rather than island-structured meta-populations. We also suggest that there may be more borrowing of functional than stylistic traits, although the evidence for this is currently ambiguous.

A Population Dynamic Model to Assess the Diabetes Screening and Reporting Programs and Project the Burden of Undiagnosed Diabetes in Thailand.

Diabetes mellitus (DM) is rising worldwide, exacerbated by aging populations. We estimated and predicted the diabetes burden and mortality due to undiagnosed diabetes together with screening program efficacy and reporting completeness in Thailand, in the context of demographic changes. An age and sex structured dynamic model including demographic and diagnostic processes was constructed. The model was validated using a Bayesian Markov Chain Monte Carlo (MCMC) approach. The prevalence of DM was predicted to increase from 6.5% (95% credible interval: 6.3-6.7%) in 2015 to 10.69% (10.4-11.0%) in 2035, with the largest increase (72%) among 60 years or older. Out of the total DM cases in 2015, the percentage of undiagnosed DM cases was 18.2% (17.4-18.9%), with males higher than females (p-value < 0.01). The highest group with undiagnosed DM was those aged less than 39 years old, 74.2% (73.7-74.7%). The mortality of undiagnosed DM was ten-fold greater than the mortality of those with diagnosed DM. The estimated coverage of diabetes positive screening programs was ten-fold greater for elderly compared to young. The positive screening rate among females was estimated to be significantly higher than those in males. Of the diagnoses, 87.4% (87.0-87.8%) were reported. Targeting screening programs and good reporting systems will be essential to reduce the burden of disease.

Disentangling the drivers of invasion spread in a vector-borne tree disease.

Pine wilt disease (PWD) invaded southern Japan in the early 1900s and has gradually expanded its range to northern Honshu (Japanese mainland). The disease is caused by a pathogenic North American nematode, which is transmitted by native pine sawyer beetles. Recently, the disease has invaded other portions of East Asia and Europe where extensive mortality of host pines is anticipated to resemble historical patterns seen in Japan. There is a critical need to identify the main drivers of PWD invasion spread so as to predict the future spread and evaluate containment strategies in newly invaded world regions. But the coupling of pathogen and vector population dynamics introduces considerable complexity that is important for understanding this and other plant disease invasions. In this study, we analysed historical (1980-2011) records of PWD infection and vector abundance, which were spatially extensive but recorded at coarse categorical levels (none, low and high) across 403 municipalities in northern Honshu. We employed a multistate occupancy model that accounted both for demographic stochasticity and observation errors in categorical data. Analysis revealed that sparse sawyer populations had lower probabilities of transition to high abundance than did more abundant populations even when regional abundance stayed the same, suggesting the existence of positive density dependence, that is an Allee effect, in sawyer dynamics. Climatic conditions (average accumulated degree days) substantially limited invasion spread in northern regions, but this climatic influence on sawyer dynamics was generally weaker than the Allee effect. Our results suggest that tactics (eg sanitation logging of infected pines) which strengthen Allee effects in sawyer dynamics may be effective strategies for slowing the spread of PWD.

Causality test of ambient fine particles and human influenza in Taiwan: Age group-specific disparity and geographic heterogeneity.

Influenza is a major global public health problem, with serious outcomes that can result in hospitalization or even death. We investigate the causal relationship between human influenza cases and air pollution, quantified by ambient fine particles <2.5µm in aerodynamic diameter (PM2.5). A modified Granger causality test is proposed to ascertain age group-specific causal relationship between weekly influenza cases and weekly adjusted accumulative PM2.5 from 2009 to 2015 in 11 cities and counties in Taiwan. We examine the causal relationship based on posterior probabilities of the log-linear integer-valued GARCH (generalized autoregressive conditional heteroscedastic) model with covariates, which enable us to handle characteristics of influenza data such as integer-value, lagged dependence, and over-dispersion. The resulting posterior probabilities show that the adult age group (25-64) and the elderly group in New Taipei in the north and cities in southwestern part of Taiwan are strongly affected by ambient fine particles. Moreover, the elderly group is clearly affected in all study sites. Globalization and economic growth have resulted in increased ambient air pollution (including PM2.5) and subsequently substantial public health concerns in the West Pacific region. Minimizing exposure to air pollutants is particularly important for the elderly and susceptible individuals with respiratory diseases.

Single-virion sequencing of lamivudine-treated HBV populations reveal population evolution dynamics and demographic history.

BACKGROUND: Viral populations are complex, dynamic, and fast evolving. The evolution of groups of closely related viruses in a competitive environment is termed quasispecies. To fully understand the role that quasispecies play in viral evolution, characterizing the trajectories of viral genotypes in an evolving population is the key. In particular, long-range haplotype information for thousands of individual viruses is critical; yet generating this information is non-trivial. Popular deep sequencing methods generate relatively short reads that do not preserve linkage information, while third generation sequencing methods have higher error rates that make detection of low frequency mutations a bioinformatics challenge. Here we applied BAsE-Seq, an Illumina-based single-virion sequencing technology, to eight samples from four chronic hepatitis B (CHB) patients - once before antiviral treatment and once after viral rebound due to resistance. RESULTS: With single-virion sequencing, we obtained 248-8796 single-virion sequences per sample, which allowed us to find evidence for both hard and soft selective sweeps. We were able to reconstruct population demographic history that was independently verified by clinically collected data. We further verified four of the samples independently through PacBio SMRT and Illumina Pooled deep sequencing. CONCLUSIONS: Overall, we showed that single-virion sequencing yields insight into viral evolution and population dynamics in an efficient and high throughput manner. We believe that single-virion sequencing is widely applicable to the study of viral evolution in the context of drug resistance and host adaptation, allows differentiation between soft or hard selective sweeps, and may be useful in the reconstruction of intra-host viral population demographic history.

A comparative simulation study of AR(1) estimators in short time series.

Various estimators of the autoregressive model exist. We compare their performance in estimating the autocorrelation in short time series. In Study 1, under correct model specification, we compare the frequentist r1 estimator, C-statistic, ordinary least squares estimator (OLS) and maximum likelihood estimator (MLE), and a Bayesian method, considering flat (Bf) and symmetrized reference (Bsr) priors. In a completely crossed experimental design we vary lengths of time series (i.e., T = 10, 25, 40, 50 and 100) and autocorrelation (from -0.90 to 0.90 with steps of 0.10). The results show a lowest bias for the Bsr, and a lowest variability for r1. The power in different conditions is highest for Bsr and OLS. For T = 10, the absolute performance of all measurements is poor, as expected. In Study 2, we study robustness of the methods through misspecification by generating the data according to an ARMA(1,1) model, but still analysing the data with an AR(1) model. We use the two methods with the lowest bias for this study, i.e., Bsr and MLE. The bias gets larger when the non-modelled moving average parameter becomes larger. Both the variability and power show dependency on the non-modelled parameter. The differences between the two estimation methods are negligible for all measurements.

A comparison of confidence/credible interval methods for the area under the ROC curve for continuous diagnostic tests with small sample size.

The receiver operating characteristic (ROC) curve is frequently used as a measure of accuracy of continuous markers in diagnostic tests. The area under the ROC curve (AUC) is arguably the most widely used summary index for the ROC curve. Although the small sample size scenario is common in medical tests, a comprehensive study of small sample size properties of various methods for the construction of the confidence/credible interval (CI) for the AUC has been by and large missing in the literature. In this paper, we describe and compare 29 non-parametric and parametric methods for the construction of the CI for the AUC when the number of available observations is small. The methods considered include not only those that have been widely adopted, but also those that have been less frequently mentioned or, to our knowledge, never applied to the AUC context. To compare different methods, we carried out a simulation study with data generated from binormal models with equal and unequal variances and from exponential models with various parameters and with equal and unequal small sample sizes. We found that the larger the true AUC value and the smaller the sample size, the larger the discrepancy among the results of different approaches. When the model is correctly specified, the parametric approaches tend to outperform the non-parametric ones. Moreover, in the non-parametric domain, we found that a method based on the Mann-Whitney statistic is in general superior to the others. We further elucidate potential issues and provide possible solutions to along with general guidance on the CI construction for the AUC when the sample size is small. Finally, we illustrate the utility of different methods through real life examples.

A method for sensitivity analysis to assess the effects of measurement error in multiple exposure variables using external validation data.

BACKGROUND: Measurement error in self-reported dietary intakes is known to bias the association between dietary intake and a health outcome of interest such as risk of a disease. The association can be distorted further by mismeasured confounders, leading to invalid results and conclusions. It is, however, difficult to adjust for the bias in the association when there is no internal validation data. METHODS: We proposed a method to adjust for the bias in the diet-disease association (hereafter, association), due to measurement error in dietary intake and a mismeasured confounder, when there is no internal validation data. The method combines prior information on the validity of the self-report instrument with the observed data to adjust for the bias in the association. We compared the proposed method with the method that ignores the confounder effect, and with the method that ignores measurement errors completely. We assessed the sensitivity of the estimates to various magnitudes of measurement error, error correlations and uncertainty in the literature-reported validation data. We applied the methods to fruits and vegetables (FV) intakes, cigarette smoking (confounder) and all-cause mortality data from the European Prospective Investigation into Cancer and Nutrition study. RESULTS: Using the proposed method resulted in about four times increase in the strength of association between FV intake and mortality. For weakly correlated errors, measurement error in the confounder minimally affected the hazard ratio estimate for FV intake. The effect was more pronounced for strong error correlations. CONCLUSIONS: The proposed method permits sensitivity analysis on measurement error structures and accounts for uncertainties in the reported validity coefficients. The method is useful in assessing the direction and quantifying the magnitude of bias in the association due to measurement errors in the confounders.

Comparison of Estimation Procedures for Multilevel AR(1) Models.

To estimate a time series model for multiple individuals, a multilevel model may be used. In this paper we compare two estimation methods for the autocorrelation in Multilevel AR(1) models, namely Maximum Likelihood Estimation (MLE) and Bayesian Markov Chain Monte Carlo. Furthermore, we examine the difference between modeling fixed and random individual parameters. To this end, we perform a simulation study with a fully crossed design, in which we vary the length of the time series (10 or 25), the number of individuals per sample (10 or 25), the mean of the autocorrelation (-0.6 to 0.6 inclusive, in steps of 0.3) and the standard deviation of the autocorrelation (0.25 or 0.40). We found that the random estimators of the population autocorrelation show less bias and higher power, compared to the fixed estimators. As expected, the random estimators profit strongly from a higher number of individuals, while this effect is small for the fixed estimators. The fixed estimators profit slightly more from a higher number of time points than the random estimators. When possible, random estimation is preferred to fixed estimation. The difference between MLE and Bayesian estimation is nearly negligible. The Bayesian estimation shows a smaller bias, but MLE shows a smaller variability (i.e., standard deviation of the parameter estimates). Finally, better results are found for a higher number of individuals and time points, and for a lower individual variability of the autocorrelation. The effect of the size of the autocorrelation differs between outcome measures.

Phylogenetic Analysis of Poliovirus Sequences.

Comparative genomic sequencing is a major surveillance tool in the Polio Laboratory Network. Due to the rapid evolution of polioviruses (~1 % per year), pathways of virus transmission can be reconstructed from the pathways of genomic evolution. Here, we describe three main phylogenetic methods; estimation of genetic distances, reconstruction of a maximum-likelihood (ML) tree, and estimation of substitution rates using Bayesian Markov chain Monte Carlo (MCMC). The data set used consists of complete capsid sequences from a survey of poliovirus sequences available in GenBank.

On analysis of longitudinal clinical trials with missing data using reference-based imputation.

Reference-based imputation (RBI) methods have been proposed as sensitivity analyses for longitudinal clinical trials with missing data. The RBI methods multiply impute the missing data in treatment group based on an imputation model built using data from the reference (control) group. The RBI will yield a conservative treatment effect estimate as compared to the estimate obtained from multiple imputation (MI) under missing at random (MAR). However, the RBI analysis based on the regular MI approach can be overly conservative because it not only applies discount to treatment effect estimate but also posts penalty on the variance estimate. In this article, we investigate the statistical properties of RBI methods, and propose approaches to derive accurate variance estimates using both frequentist and Bayesian methods for the RBI analysis. Results from simulation studies and applications to longitudinal clinical trial datasets are presented.

Co-infection of influenza A viruses of swine contributes to effective shuffling of gene segments in a naturally reared pig.

Following the 2009 H1N1 pandemic, surveillance activities have been accelerated globally to monitor the emergence of novel reassortant viruses. However, the mechanism by which influenza A viruses of swine (IAV-S) acquire novel gene constellations through reassortment events in natural settings remains poorly understood. To explore the mechanism, we collected 785 nasal swabs from pigs in a farm in Thailand from 2011 to 2014. H3N2, H3N1, H1N1 and H1N2 IAVs-S were isolated from a single co-infected sample by plaque purification and showed a high degree of diversity of the genome. In particular, the H1N1 isolates, possessing a novel gene constellation previously unreported in Thailand, exhibited greater variation in internal genes than H3N2 IAVs-S. A pair of isolates, designated H3N2-B and H1N1-D, was determined to have been initially introduced to the farm. These results demonstrate that numerous IAVs-S with various gene constellations can be created in a single co-infected pig via reassortment.