Full Bayesian Approach Research Articles

Full and 1‐year runoff risk in the credibility‐based additive loss reserving method

In this paper, we consider the additive loss reserving (ALR) method in a Bayesian and credibility setup. The classical ALR method is a simple claims reserving method that combines prior information (e.g., premiums, number of contracts, market statistics) with claims observations. The Bayesian setup, which we present, in addition, allows for combining the information from a single runoff portfolio (e.g., company‐specific data) with the information from a collective (e.g., industry‐wide data) to analyze the claims reserves and the claims development result. However, in insurance practice, the associated distributions are usually unknown. Therefore, we do not follow the full Bayesian approach but apply credibility theory, which is distribution free and where we only need to know the first and second moments. That is, we derive the credibility predictors that minimize the expected squared loss within the class of affine‐linear functions of the observations (i.e., we derive linear Bayesian predictors). Using non‐informative priors, we link our credibility‐based ALR method to the classical ALR method and show that the credibility predictors coincide with the predictors in the classical ALR method. Moreover, we quantify the 1‐year risk and the full reserve risk by means of the conditional mean square error of prediction. Copyright © 2011 John Wiley & Sons, Ltd.

Genetic Structure of Severe Combined Immunodeficiency Carrier Horses in Morocco Inferred by Microsatellite Data

A total of 17 microsatellite deoxyribonucleic acid loci used routinely for horse parentage control were used to evaluate genetic diversity among normal Arabian horses and severe combined immunodeficiency (SCID) carrier Arabian horses (ArS) and normal Arab–Barb horses and SCID carrier Arab–Barb horses (ArbeS). On the basis of the genotype of 186 horses, mean allelic diversity was estimated as 6.82, 5.53, and 6.7059 in normal Arabian horses, ArS, and for both groups of Arab–Barb horses, respectively. Five specific alleles were observed in ArS and ArbeS, with one common with ArS at HMS6, whereas five alleles common between ArS and ArbeS had a high frequency. Expected and observed heterozygosity showed great heterogeneity in the population studied and were similar or higher when compared with other studies on Arabian horses. Coefficient of gene differentiation Gst of Nei associated with Nei’s genetic distance and multivariate correspondence analysis indicated a possible differentiation between the studied populations when analyzed separately according to breed. Probability of assignment of a horse to a specific group was assessed using a full and partial Bayesian approach. In all, 80.6% of Arab horses and 78.2% of Arab–Barb horses were assigned properly with a partial Bayesian test, which provided better results than the full one. These findings will be useful for identification of SCID carrier horses by using the microsatellite deoxyribonucleic acid loci used routinely for horse parentage control in our laboratory.

Classification in segmented regression problems

Heterogeneity in many datasets stems from the different behaviors of several underlying groups or subpopulations. The aim of this paper is to classify observations in such a dataset into these latent groups when each group’s behavior is piecewise linearly related to a set of covariates. We assume that each group can be represented by a segmented regression model, but the group membership for each observation is unobserved or lost. A full Bayesian approach is proposed to simultaneously classify observations and estimate segmented regression parameters. The estimated marginal likelihood and the Deviance Information Criterion are used to select the number of mixture groups. We demonstrate the accuracy and performance of the proposed MCMC estimators in a simulation study and illustrate the methodology in an empirical study.

Beta Autoregressive Transition Markov-Switching Models for Business Cycle Analysis

We propose a new class of Markov-switching models useful for business cycle analysis, with transition probabilities following independent beta autoregressive processes. We study the effects of the autoregressive dynamics on the regime duration. We propose a full Bayesian inference approach and particular attention is paid to the parameters of the latent beta autoregressive processes. We discuss the choice of the prior distributions and propose a Markov-chain Monte Carlo algorithm for estimating both the parameters and the latent variables. Finally, we provide an application to the Euro area business cycle.

Missing exposure data in stereotype regression model: application to matched case-control study with disease subclassification.

With advances in modern medicine and clinical diagnosis, case-control data with characterization of finer subtypes of cases are often available. In matched case-control studies, missingness in exposure values often leads to deletion of entire stratum, and thus entails a significant loss in information. When subtypes of cases are treated as categorical outcomes, the data are further stratified and deletion of observations becomes even more expensive in terms of precision of the category-specific odds-ratio parameters, especially using the multinomial logit model. The stereotype regression model for categorical responses lies intermediate between the proportional odds and the multinomial or baseline category logit model. The use of this class of models has been limited as the structure of the model implies certain inferential challenges with nonidentifiability and nonlinearity in the parameters. We illustrate how to handle missing data in matched case-control studies with finer disease subclassification within the cases under a stereotype regression model. We present both Monte Carlo based full Bayesian approach and expectation/conditional maximization algorithm for the estimation of model parameters in the presence of a completely general missingness mechanism. We illustrate our methods by using data from an ongoing matched case-control study of colorectal cancer. Simulation results are presented under various missing data mechanisms and departures from modeling assumptions.

A Two-Stage Approximation for Analysis of Mixture Genetic Models in Large Pedigrees

Information from cosegregation of marker and QTL alleles, in addition to linkage disequilibrium (LD), can improve genomic selection. Variance components linear models have been proposed for this purpose, but accommodating dominance and epistasis is not straightforward with them. A full-Bayesian analysis of a mixture genetic model is favorable in this respect, but is computationally infeasible for whole-genome analyses. Thus, we propose an approximate two-step approach that neglects information from trait phenotypes in inferring ordered genotypes and segregation indicators of markers. Quantitative trait loci (QTL) fine-mapping scenarios, using high-density markers and pedigrees of five generations without genotyped females, were simulated to test this strategy against an exact full-Bayesian approach. The latter performed better in estimating QTL genotypes, but precision of QTL location and accuracy of genomic breeding values (GEBVs) did not differ for the two methods at realistically low LD. If, however, LD was higher, the exact approach resulted in a slightly higher accuracy of GEBVs. In conclusion, the two-step approach makes mixture genetic models computationally feasible for high-density markers and large pedigrees. Furthermore, markers need to be sampled only once and results can be used for the analysis of all traits. Further research is needed to evaluate the two-step approach for complex pedigrees and to analyze alternative strategies for modeling LD between QTL and markers.

Probabilistic petrophysical-properties estimation integrating statistical rock physics with seismic inversion

A joint estimation of petrophysical properties is proposed that combines statistical rock physics and Bayesian seismic inversion. Because elastic attributes are correlated with petrophysical variables (effective porosity, clay content, and water saturation) and this physical link is associated with uncertainties, the petrophysical-properties estimation from seismic data can be seen as a Bayesian inversion problem. The purpose of this work was to develop a strategy for estimating the probability distributions of petrophysical parameters and litho-fluid classes from seismics. Estimation of reservoir properties and the associated uncertainty was performed in three steps: linearized seismic inversion to estimate the probabilities of elastic parameters, probabilistic upscaling to include the scale-changes effect, and petrophysical inversion to estimate the probabilities of petrophysical variables andlitho-fluid classes. Rock-physics equations provide the linkbetween reservoir properties and velocities, and linearized seismic modeling connects velocities and density to seismic amplitude. A full Bayesian approach was adopted to propagate uncertainty from seismics to petrophysics in an integrated framework that takes into account different sources of uncertainty: heterogeneity of the real data, approximation of physical models, measurement errors, and scale changes. The method has been tested, as a feasibility step, on real well data and synthetic seismic data to show reliable propagation of the uncertainty through the three different steps and to compare two statistical approaches: parametric and nonparametric. Application to a real reservoir study (including data from two wells and partially stacked seismic volumes) has provided as a main result the probability densities of petrophysical properties and litho-fluid classes. It demonstrated the applicability of the proposed inversion method.

Bayesian Analysis of Hazard Rate, Change Point, and Cost-Optimal Burn-In Time for Electronic Devices

This study develops a full Bayesian approach to analysing hazard rate, change point, and cost-optimal burn-in time for electronic devices. The Weibull-exponential distribution is used to model the L-shaped hazard rate function that is commonly observed for electronic devices. The optimal burn-in time is selected to minimize the prior or posterior total expected costs, which explicitly consider the uncertainties on all the model parameters. The proposed approach is illustrated using an experimental data set consisting of failure times of a nano-scale high-k gate dielectric film.

Simultaneous Confidence Bands for Penalized Spline Estimators

In this article we construct simultaneous confidence bands for a smooth curve using penalized spline estimators. We consider three types of estimation methods: (a) as a standard (fixed effect) nonparametric model, (b) using the mixed-model framework with the spline coefficients as random effects, and (c) a full Bayesian approach. The volume-of-tube formula is applied for the first two methods and compared with Bayesian simultaneous confidence bands from a frequentist perspective. We show that the mixed-model formulation of penalized splines can help obtain, at least approximately, confidence bands with either Bayesian or frequentist properties. Simulations and data analysis support the proposed methods. The R package ConfBands accompanies the article.

Evaluating Strategies for Marker Ranking in Genome-wide Association Studies of Complex Traits

Genome-wide association studies (GWAS) were highly successful in identifying new susceptibility loci of complex traits. Such studies usually start with genotyping fixed arrays of genetic markers in an initial sample. Out of these markers, some are selected which will be further genotyped in independent samples. Due to the very low a priori probability of a true positive association, the vast majority of all marker signals will turn out to be false positive. Thus, several methods to sort marker data have been proposed which will be evaluated here. We compared statistical properties of ranking by p-values, q-values, the False Positive Report Probability (FPRP) and the Bayesian False-Discovery Probability (BFDP). We performed simulation studies for a genomic region derived from GWAS data sets and calculated descriptive statistics as well as mean square errors with regard to the true marker ranking. Additionally, we applied all measures to a GWAS for early onset extreme obesity superimposing a priori information on candidate genes. Despite the known, more extreme probability results for traditional p-values, we observed that both p-values and the BFDP were more precise in reconstructing the "true" order of the markers in a region. In addition, the BFDP was useful to attenuate unexpected effects at a genome-wide scale. For the purpose of selecting markers from an initial GWAS and within the limits of this study, we recommend either ranking by p-values or the application of a full Bayesian approach for which the BFDP is a first approximation.

Bayesian approach with the power prior for road safety analysis

Drawing inference from current data could be more reliable if similar data based on previous studies are used. We propose a full Bayesian approach with the power prior to utilize these data. The power prior is constructed by raising the likelihood function of the historical data to the power where . The power prior is a useful informative prior in Bayesian inference. We use the power prior to estimate regression coefficients and to calculate the accident reduction factors of some covariates including median strips and guardrails. We also compare our method with the empirical Bayes method. We demonstrate our results with several sets of real data. The data were collected for two rural national roads of Korea in the year 2002. The computations are executed with the Metropolis–Hastings algorithm which is a popular technique in the Markov chain and Monte Carlo methods.

A full Bayesian approach to generalized maximum likelihood estimation of generalized extreme value distribution

This study develops a full Bayesian GEV distribution estimation method (BAYBETA), which contains a semi-Bayesian framework of generalized maximum likelihood estimator (GMLE), to make full use of several advantages of the Bayesian approach especially in uncertainty analysis. For the full Bayesian framework, the optimal hyperparameter of beta prior distribution on the shape parameter of the GEV distribution is found as (6.4990, 8.7927) through simulation-based analysis. In a performance comparison analysis, the performances of BAYBETA, which adopts beta(6.4990, 8.7927) as prior density on the shape parameter of the GEV distribution, are almost the same as or slightly better than GML, outperforming MOM, ML, and LM in terms of root mean square error (RMSE) and bias when the shape parameter is negative. Also, a case study of two hydrologic extreme value data shows that the traditional uncertainty analysis using asymptotic approximation of ML and GML has limitations in describing the uncertainty in high upper quantiles, while the proposed full Bayesian estimation method BAYBETA provides a consistent and complete description of the uncertainty.

Case–Control Studies of Gene–Environment Interaction: Bayesian Design and Analysis

With increasing frequency, epidemiologic studies are addressing hypotheses regarding gene-environment interaction. In many well-studied candidate genes and for standard dietary and behavioral epidemiologic exposures, there is often substantial prior information available that may be used to analyze current data as well as for designing a new study. In this article, first, we propose a proper full Bayesian approach for analyzing studies of gene-environment interaction. The Bayesian approach provides a natural way to incorporate uncertainties around the assumption of gene-environment independence, often used in such an analysis. We then consider Bayesian sample size determination criteria for both estimation and hypothesis testing regarding the multiplicative gene-environment interaction parameter. We illustrate our proposed methods using data from a large ongoing case-control study of colorectal cancer investigating the interaction of N-acetyl transferase type 2 (NAT2) with smoking and red meat consumption. We use the existing data to elicit a design prior and show how to use this information in allocating cases and controls in planning a future study that investigates the same interaction parameters. The Bayesian design and analysis strategies are compared with their corresponding frequentist counterparts.

Modelling long-term investment returns via Bayesian infinite mixture time series models

This paper introduces the class of Bayesian infinite mixture time series models first proposed in Lau & So (2004) for modelling long-term investment returns. It is a flexible class of time series models and provides a flexible way to incorporate full information contained in all autoregressive components with various orders by utilizing the idea of Bayesian averaging or mixing. We adopt a Bayesian sampling scheme based on a weighted Chinese restaurant process for generating partitions of investment returns to estimate the Bayesian infinite mixture time series models. Instead of using the point estimates, as in the classical or non-Bayesian approach, the estimation in this paper is performed by the full Bayesian approach, utilizing the idea of Bayesian averaging to incorporate all information contained in the posterior distributions of the random parameters. This provides a natural way to incorporate model risk or uncertainty. The proposed models can also be used to perform clustering of investment returns and detect outliers of returns. We employ the monthly data from the Toronto Stock Exchange 300 (TSE 300) indices to illustrate the implementation of our models and compare the simulated results from the estimated models with the empirical characteristics of the TSE 300 data. We apply the Bayesian predictive distribution of the logarithmic returns obtained by the Bayesian averaging or mixing to evaluate the quantile-based and conditional tail expectation risk measures for segregated fund contracts via stochastic simulation. We compare the risk measures evaluated from our models with those from some well-known and important models in the literature, and highlight some features that can be obtained from our models.

Fast phylogenetic DNA barcoding

We present a heuristic approach to the DNA assignment problem based on phylogenetic inferences using constrained neighbour joining and non-parametric bootstrapping. We show that this method performs as well as the more computationally intensive full Bayesian approach in an analysis of 500 insect DNA sequences obtained from GenBank. We also analyse a previously published dataset of environmental DNA sequences from soil from New Zealand and Siberia, and use these data to illustrate the fact that statistical approaches to the DNA assignment problem allow for more appropriate criteria for determining the taxonomic level at which a particular DNA sequence can be assigned.

A statistical model for detecting jumps and decaying pulses in the presence of a background noise

A statistical modeling technique using full Bayesian approach is proposed for use in the detection of jumps and decaying pulses in the presence of background noises. Two distributions, namely, the exponential-power and the Student- t distributions, are adopted for the purpose. Results suggest that both these distributions can give accurate recovery of the instants when the abrupt changes take place if the background noise level is lower than that of the changes by 3 dB. They also indicate that the exponential-power distribution is more useful when the signal-to-noise ratio falls below 0 dB.

9. Multiple Imputation of Incomplete Categorical Data Using Latent Class Analysis

We propose using latent class analysis as an alternative to log-linear analysis for the multiple imputation of incomplete categorical data. Similar to log-linear models, latent class models can be used to describe complex association structures between the variables used in the imputation model. However, unlike log-linear models, latent class models can be used to build large imputation models containing more than a few categorical variables. To obtain imputations reflecting uncertainty about the unknown model parameters, we use a nonparametric bootstrap procedure as an alternative to the more common full Bayesian approach. The proposed multiple imputation method, which is implemented in Latent GOLD software for latent class analysis, is illustrated with two examples. In a simulated data example, we compare the new method to well-established methods such as maximum likelihood estimation with incomplete data and multiple imputation using a saturated log-linear model. This example shows that the proposed method yields unbiased parameter estimates and standard errors. The second example concerns an application using a typical social sciences data set. It contains 79 variables that are all included in the imputation model. The proposed method is especially useful for such large data sets because standard methods for dealing with missing data in categorical variables break down when the number of variables is so large.

A Bayes Random Fields Approach for Integrative Large-Scale Regulatory Network Analysis

SummaryWe present a Bayes-Random Fields framework which is capable of integrating unlimited data sources for discovering relevant network architecture of large-scale networks. The random field potential function is designed to impose a cluster constraint, teamed with a full Bayesian approach for incorporating heterogenous data sets. The probabilistic nature of our framework facilitates robust analysis in order to minimize the influence of noise inherent in the data on the inferred structure in a seamless and coherent manner. This is later proved in its applications to both large-scale synthetic data sets and Saccharomyces Cerevisiae data sets. The analytical and experimental results reveal the varied characteristic of different types of data and reflect their discriminative ability in terms of identifying direct gene interactions.

Estimating the grid of time-points for the piecewise exponential model

One of the greatest challenges related to the use of piecewise exponential models (PEMs) is to find an adequate grid of time-points needed in its construction. In general, the number of intervals in such a grid and the position of their endpoints are ad-hoc choices. We extend previous works by introducing a full Bayesian approach for the piecewise exponential model in which the grid of time-points (and, consequently, the endpoints and the number of intervals) is random. We estimate the failure rates using the proposed procedure and compare the results with the non-parametric piecewise exponential estimates. Estimates for the survival function using the most probable partition are compared with the Kaplan-Meier estimators (KMEs). A sensitivity analysis for the proposed model is provided considering different prior specifications for the failure rates and for the grid. We also evaluate the effect of different percentage of censoring observations in the estimates. An application to a real data set is also provided. We notice that the posteriors are strongly influenced by prior specifications, mainly for the failure rates parameters. Thus, the priors must be fairly built, say, really disclosing the expert prior opinion.

Conditional clustering of temporal expression profiles

BackgroundMany microarray experiments produce temporal profiles in different biological conditions but common cluster techniques are not able to analyze the data conditional on the biological conditions.ResultsThis article presents a novel technique to cluster data from time course microarray experiments performed across several experimental conditions. Our algorithm uses polynomial models to describe the gene expression patterns over time, a full Bayesian approach with proper conjugate priors to make the algorithm invariant to linear transformations, and an iterative procedure to identify genes that have a common temporal expression profile across two or more experimental conditions, and genes that have a unique temporal profile in a specific condition.ConclusionWe use simulated data to evaluate the effectiveness of this new algorithm in finding the correct number of clusters and in identifying genes with common and unique profiles. We also use the algorithm to characterize the response of human T cells to stimulations of antigen-receptor signaling gene expression temporal profiles measured in six different biological conditions and we identify common and unique genes. These studies suggest that the methodology proposed here is useful in identifying and distinguishing uniquely stimulated genes from commonly stimulated genes in response to variable stimuli. Software for using this clustering method is available from the project home page.