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A new Bayesian–inspired statistic for hypothesis testing is proposed which compares two posterior distributions; the observed posterior and the expected posterior under the null model. The Kullback–Leibler divergence between the two posterior distributions yields a test statistic which can be interpreted as a penalized log–Bayes factor with the penalty term converging to a constant as the sample size increases. Hence, asymptotically, the statistic behaves as a Bayes factor. Viewed as a penalized Bayes factor, this approach solves the long standing issue of using improper priors with the Bayes factor, since only posterior summaries are needed for the new statistic. Further motivation for the new statistic is a minimal move from the Bayes factor which requires no tuning nor splitting of data into training and inference, and can use improper priors. Critical regions for the test can be assessed using frequentist notions of Type I error.

Given a Wiener process with unknown and unobservable drift, we try to estimate this drift as effectively but also as quickly as possible, in the presence of a quadratic penalty for the estimation error and of a fixed, positive cost per unit of observation time. In a Bayesian framework, where the unobservable drift is assumed to have a known “prior” distribution, this question reduces to choosing judiciously a stopping time for an appropriate diffusion process in natural scale. We establish structural properties of the solution for the corresponding problem of optimal stopping. In particular, we show that, regardless of the prior distribution, the continuation region is monotonically shrinking in time. Moreover, we provide conditions on the prior distribution that guarantee a one-sided stopping region. Lastly, some concrete prior distributions are studied to illustrate the theoretical results.

This paper presents a novel Bayesian variable selection approach that accounts for the sign of the regression coefficients based on multivariate one-sided tests. We propose a truncated g prior to specify a prior distribution of coefficients with anticipated signs in a given model. Informative priors for the direction of the effects can be incorporated into prior model probabilities. The best subset of variables is selected by comparing the posterior probabilities of the possible models. The new Bayesian one-sided variable selection procedure has higher chance to include relevant variables and therefore select the best model, if the anticipated direction is accurate. For a large number of candidate variables, we present an adaptation of a Bayesian model search method for the one-sided variable selection problem to ensure fast computation. In addition, a fully Bayesian approach is used to adjust the prior inclusion probability of each one-sided model to correct for multiplicity. The performance of the proposed method is investigated using several simulation studies and two real data examples.

The elicitation of power priors, based on the availability of historical data, is realized by raising the likelihood function of the historical data to a fractional power δ , which quantifies the degree of discounting of the historical information in making inference with the current data. When δ is not pre-specified and is treated as random, it can be estimated from the data using Bayesian updating paradigm. However, in the original form of the joint power prior Bayesian approach, certain positive constants before the likelihood of the historical data could be multiplied when different settings of sufficient statistics are employed. This would change the power priors with different constants, and hence the likelihood principle is violated. In this article, we investigate a normalized power prior approach which obeys the likelihood principle and is a modified form of the joint power prior. The optimality properties of the normalized power prior in the sense of minimizing the weighted Kullback–Leibler divergence are investigated. By examining the posteriors of several commonly used distributions, we show that the discrepancy between the historical and the current data can be well quantified by the power parameter under the normalized power prior setting. Efficient algorithms to compute the scale factor is also proposed. In addition, we illustrate the use of the normalized power prior Bayesian analysis with three data examples, and provide an implementation with an R package NPP.

A Bayesian treatment of the proportional hazard (PH) model is revisited using Dirichlet process and gamma process priors for the baseline survival and cumulative hazard functions respectively. Such priors, due to their discrete support, conflict with the absolutely continuous nature of survival responses expressed through the hazard function structure that defines the PH model. We resolve this conflict through the use of a proposed e -grid likelihood approach which we apply to the PH model to consider marginal inference for the regression parameter β using expansions as e ↓ 0 . Using Dirichlet process priors, the e -grid likelihood approach leads to a new explicit marginal posterior density expansion for β which accommodates the most general setting with arbitrary ties and right censoring. In the previously considered case of gamma process priors, the approach extends the results of Kalbfleisch (1978) to deal with arbitrary arrangements of ties and also provides a rigorous justification for his posterior expressions. As in Kalbfleisch (1978), we show that the leading terms of both expansions approximate Cox’s partial likelihood when there are no ties and the process priors are diffuse. The e -grid likelihood approach is similar in concept to the grouped data likelihood approach of Sinha et al. (2003) but differs in the likelihood approximation. Whereas our expansions are Poincare expansions (with relative error O ( e ) as e ↓ 0 ), those of Sinha et al. (2003) are stochastic expansions and not proper Poincare expansion (as we show), so that they lack relative error O ( e ) . Using a flat improper prior for β , the two marginal posterior expressions for β are shown to be integrable for general arrangements of ties and censoring under weak conditions on the design and failures.

Parallel tempering (PT) methods are a popular class of Markov chain Monte Carlo schemes used to sample complex high-dimensional probability distributions. They rely on a collection of $N$ interacting auxiliary chains targeting tempered versions of the target distribution to improve the exploration of the state-space. We provide here a new perspective on these highly parallel algorithms and their tuning by identifying and formalizing a sharp divide in the behaviour and performance of reversible versus non-reversible PT schemes. We show theoretically and empirically that a class of non-reversible PT methods dominates its reversible counterparts and identify distinct scaling limits for the non-reversible and reversible schemes, the former being a piecewise-deterministic Markov process and the latter a diffusion. These results are exploited to identify the optimal annealing schedule for non-reversible PT and to develop an iterative scheme approximating this schedule. We provide a wide range of numerical examples supporting our theoretical and methodological contributions. The proposed methodology is applicable to sample from a distribution $\pi$ with a density $L$ with respect to a reference distribution $\pi_0$ and compute the normalizing constant. A typical use case is when $\pi_0$ is a prior distribution, $L$ a likelihood function and $\pi$ the corresponding posterior., Comment: 74 pages, 30 figures. The method is implemented in an open source probabilistic programming available at https://github.com/UBC-Stat-ML/blangSDK

In practice, the objects of interest have some shape priors, which would be destroyed by occlusions, distortions and noises. Therefore, the characterization of the shape priors attracts increasing attention. This paper is devoted to characterization of convexity prior and its applications in objects segmentation in two-dimensional (2D) spaces using level set function. The shape convexity can be characterized by the Laplacian nonnegativity of the associated signed distance function on the whole image domain, zero-sublevel set and zero-superlevel set. This result is extended to characterization for multiple convex objects and ring shape object with outer, inner and both convex boundaries. One of the advantages of this method is that only one signed distance function is needed to characterize a single object, multiple objects and ring shape with boundary(ies) convexity prior. The characterization methods are incorporated into image segmentation model. In addition, some labels on the foreground and background and landmarks on the boundary of the object(s) can be taken into account as constraints to improve the accuracy of segmentation. A general and efficient numerical framework is developed to solve the proposed models using alternative direction method. Experiments on various images validated the effectiveness and efficiency of the proposed models and algorithms.

Mixture transition distribution time series models build high-order dependence through a weighted combination of first-order transition densities for each one of a specified number of lags. We present a framework to construct stationary transition mixture distribution models that extend beyond linear, Gaussian dynamics. We study conditions for first-order strict stationarity which allow for different constructions with either continuous or discrete families for the first-order transition densities given a pre-specified family for the marginal density, and with general forms for the resulting conditional expectations. Inference and prediction are developed under the Bayesian framework with particular emphasis on flexible, structured priors for the mixture weights. Model properties are investigated both analytically and through synthetic data examples. Finally, Poisson and Lomax examples are illustrated through real data applications.

It is a pleasure to congratulate Ni et al. (Stat Methods Appl 490:1–32, 2021) on the recent advances in Bayesian graphical models reviewed in Ni et al. (Stat Methods Appl 490:1–32, 2021). The authors have given considerable thought to the construction and estimation of Bayesian graphical models that capture salient features of biological networks. My discussion focuses on computational challenges and opportunities along with priors, pointing out limitations of the Markov random field priors reviewed in Ni et al. (Stat Methods Appl 490:1–32, 2021) and exploring possible generalizations that capture additional features of conditional independence graphs, such as hub structure and clustering. I conclude with a short discussion of the intersection of graphical models and random graph models.

Causal mediation analysis aims to characterize an exposure's effect on an outcome and quantify the indirect effect that acts through a given mediator or a group of mediators of interest. With the increasing availability of measurements on a large number of potential mediators, like the epigenome or the microbiome, new statistical methods are needed to simultaneously accommodate high-dimensional mediators while directly target penalization of the natural indirect effect (NIE) for active mediator identification. Here, we develop two novel prior models for identification of active mediators in high-dimensional mediation analysis through penalizing NIEs in a Bayesian paradigm. Both methods specify a joint prior distribution on the exposure-mediator effect and mediator-outcome effect with either (a) a four-component Gaussian mixture prior or (b) a product threshold Gaussian prior. By jointly modelling the two parameters that contribute to the NIE, the proposed methods enable penalization on their product in a targeted way. Resultant inference can take into account the four-component composite structure underlying the NIE. We show through simulations that the proposed methods improve both selection and estimation accuracy compared to other competing methods. We applied our methods for an in-depth analysis of two ongoing epidemiologic studies: the Multi-Ethnic Study of Atherosclerosis (MESA) and the LIFECODES birth cohort. The identified active mediators in both studies reveal important biological pathways for understanding disease mechanisms.

Responsive survey design (RSD) aims to increase the efficiency of survey data collection via live monitoring of paradata and the introduction of protocol changes when survey errors and increased costs seem imminent. Daily predictions of response propensity for all active sampled cases are among the most important quantities for live monitoring of data collection outcomes, making sound predictions of these propensities essential for the success of RSD. Because it relies on real-time updates of prior beliefs about key design quantities, such as predicted response propensities, RSD stands to benefit from Bayesian approaches. However, empirical evidence of the merits of these approaches is lacking in the literature, and the derivation of informative prior distributions is required for these approaches to be effective. In this paper, we evaluate the ability of two approaches to deriving prior distributions for the coefficients defining daily response propensity models to improve predictions of daily response propensity in a real data collection employing RSD. The first approach involves analyses of historical data from the same survey, and the second approach involves literature review. We find that Bayesian methods based on these two approaches result in higher-quality predictions of response propensity than more standard approaches ignoring prior information. This is especially true during the early-to-middle periods of data collection, when survey managers using RSD often consider interventions.

In recent years, the finite mixture lifetime models have frequently been used in chemical, physical, social science, biological and other fields due to their methodological development and practical applications. The Bayesian analysis of the mixture models has also developed a significant interest among the statisticians especially in the last decade. However, the most of these contributions are limited to the Bayes estimation for the parameters of lifetime models under singly type I censoring. This paper discusses the Bayesian estimation for the two-component mixture of the lifetime models under doubly censored samples with a particular case for the Burr type VII model. A class of improved priors has been proposed for the posterior estimation. The likelihood function, for doubly censored samples using two-component mixture of life time distributions, has been introduced. The hazard rate function for the mixture model has been compared for different parametric values. The performance of various estimators has been compared under a simulation study along with a real life example.

This paper considers D-optimal designs for linear mixed models involving random effects with unknown distributions. From Bayesian point of view, the Dirichlet process as a prior distribution on the...

International audience; his paper proposes randomized controlled clinical trial design to eval-uate external cooling as a means to control fever and thereby reduce mortality in patients with septic shock. The trial will include concurrent external cooling and control arms while adaptively incorporating historical control arm data. Bayesian group sequential monitoring will be done using a posterior comparative test based on the 60-day survival distribution in each concurrent arm. Posterior inference will follow from a Bayesian discrete time survival model that facilitates adap-tive incorporation of the historical control data through an innovative regression framework with a multivariate spike-and-slab prior distribution on the histori-cal bias parameters. For each interim test, the amount of information borrowed from the historical control data will be determined adaptively in a manner that re-flects the degree of agreement between historical and concurrent control arm data. Guidance is provided for selecting Bayesian posterior probability group-sequential monitoring boundaries. Simulation results elucidating how the proposed method borrows strength from the historical control data are reported. In the absence of historical control arm bias, the proposed design controls the type I error rate and provides substantially larger power than reasonable comparators, whereas in the presence bias of varying magnitude, type I error rate inflation is curbed.

In many orphan diseases and pediatric indications, the randomized controlled trials may be infeasible because of their size, duration, and cost. Leveraging information on the control through a prior can potentially reduce sample size. However, unless an objective prior is used to impose complete ignorance for the parameter being estimated, it results in biased estimates and inflated type-I error. Hence, it is essential to assess both the confirmatory and supplementary knowledge available during the construction of the prior to avoid "cherry-picking" advantageous information. For this purpose, propensity score methods are employed to minimize selection bias by weighting supplemental control subjects according to their similarity in terms of pretreatment characteristics to the subjects in the current trial. The latter can be operationalized through a proposed measure of overlap in propensity-score distributions. In this paper, we consider single experimental arm in the current trial and the control arm is completely borrowed from the supplemental data. The simulation experiments show that the proposed method reduces prior and data conflict and improves the precision of the of the average treatment effect.

This paper considers a general Bayesian test for the multi-sample problem. Specifically, for M independent samples, the interest is to determine whether the M samples are generated from the same multivariate population. First, M Dirichlet processes are considered as priors for the true distributions generated the data. Then, the concentration of the distribution of the total distance between the M posterior processes is compared to the concentration of the distribution of the total distance between the M prior processes through the relative belief ratio. The total distance between processes is established based on the energy distance. Various interesting theoretical results of the approach are derived. Several examples covering the high dimensional case are considered to illustrate the approach.

This tutorial shows how to build, fit, and criticize disease transmission models in Stan, and should be useful to researchers interested in modeling the severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) pandemic and other infectious diseases in a Bayesian framework. Bayesian modeling provides a principled way to quantify uncertainty and incorporate both data and prior knowledge into the model estimates. Stan is an expressive probabilistic programming language that abstracts the inference and allows users to focus on the modeling. As a result, Stan code is readable and easily extensible, which makes the modeler's work more transparent. Furthermore, Stan's main inference engine, Hamiltonian Monte Carlo sampling, is amiable to diagnostics, which means the user can verify whether the obtained inference is reliable. In this tutorial, we demonstrate how to formulate, fit, and diagnose a compartmental transmission model in Stan, first with a simple susceptible-infected-recovered model, then with a more elaborate transmission model used during the SARS-CoV-2 pandemic. We also cover advanced topics which can further help practitioners fit sophisticated models; notably, how to use simulations to probe the model and priors, and computational techniques to scale-up models based on ordinary differential equations.

The article presents a collective risk model for the insurance claims. The objective is to estimate a premium, which is defined as a functional specified up to unknown parameters. For this purpose, the Bayesian methodology, which combines the prior knowledge about certain unknown parameters with the knowledge in the form of a random sample, has been adopted. The generalised Bregman loss function is considered. In effect, the results can be applied to numerous loss functions, including the square-error, LINEX, weighted square-error, Brown, entropy loss. Some uncertainty about a prior is assumed by a distorted band class of priors. The range of collective and Bayes premiums is calculated and posterior regret Γ-minimax premium as a robust procedure has been implemented. Two examples are provided to illustrate the issues considered - the first one with an unknown parameter of the Poisson distribution, and the second one with unknown parameters of distributions of the number and severity of claims.

This article works with an expression of the mean of log Bayes Factor to elucidate its dependence on specified priors. Such explication answers some basic questions about interpreting Bayes Factor ...

International audience; Robust statistical data modelling under potential model mis-specification often requires leaving the parametric world for the nonparametric. In the latter, parameters are infinite dimensional objects such as functions, probability distributions or infinite vectors. In the Bayesian nonparametric approach, prior distributions are designed for these parameters, which provide a handle to manage the complexity of nonparametric models in practice. However, most modern Bayesian nonparametric models seem often out of reach to practitioners, as inference algorithms need careful design to deal with the infinite number of parameters. The aim of this work is to facilitate the journey by providing computational tools for Bayesian nonparametric inference. The article describes a set of functions available in the R package BNPdensity in order to carry out density estimation with an infinite mixture model, including all types of censored data. The package provides access to a large class of such models based on normalized random measures, which represent a generalization of the popular Dirichlet process mixture. One striking advantage of this generalization is that it offers much more robust priors on the number of clusters than the Dirichlet. Another crucial advantage is the complete flexibility in specifying the prior for the scale and location parameters of the clusters, because conjugacy is not required. Inference is performed using a theoretically grounded approximate sampling methodology known as the Ferguson & Klass algorithm. The package also offers several goodness of fit diagnostics such as QQ-plots, including a cross-validation criterion, the conditional predictive ordinate. The proposed methodology is illustrated on a classical ecological risk assessment method called the Species Sensitivity Distribution (SSD) problem, showcasing the benefits of the Bayesian nonparametric framework.

Inter-rater agreement measures are used to estimate the degree of agreement between two or more assessors. When the agreement table is ordinal, different weight functions that incorporate row and column scores are used along with the agreement measures. The selection of row and column scores is effectual on the estimated degree of agreement. The weighted measures are prone to the anomalies frequently seen in agreement tables such as unbalanced table structures or grey zones due to the assessment behaviour of the raters. In this study, Bayesian approaches for the estimation of inter-rater agreement measures are proposed. The Bayesian approaches make it possible to include prior information on the assessment behaviour of the raters in the analysis and impose order restrictions on the row and column scores. In this way, we improve the accuracy of the agreement measures and mitigate the impact of the anomalies in the estimation of the strength of agreement between the raters. The elicitation of prior distributions is described theoretically and practically for the Bayesian estimation of five agreement measures with three different weights using an agreement table having two grey zones. A Monte Carlo simulation study is conducted to assess the classification accuracy of the Bayesian and classical approaches for the considered agreement measures for a given level of agreement. Recommendations for the selection of the highest performing agreement measure and weight combination are made in the breakdown of the table structure and sample size.

In model-based clustering, the Galaxy data set is often used as a benchmark data set to study the performance of different modeling approaches. Aitkin (Stat Model 1:287–304) compares maximum likelihood and Bayesian analyses of the Galaxy data set and expresses reservations about the Bayesian approach due to the fact that the prior assumptions imposed remain rather obscure while playing a major role in the results obtained and conclusions drawn. The aim of the paper is to address Aitkin’s concerns about the Bayesian approach by shedding light on how the specified priors influence the number of estimated clusters. We perform a sensitivity analysis of different prior specifications for the mixtures of finite mixture model, i.e., the mixture model where a prior on the number of components is included. We use an extensive set of different prior specifications in a full factorial design and assess their impact on the estimated number of clusters for the Galaxy data set. Results highlight the interaction effects of the prior specifications and provide insights into which prior specifications are recommended to obtain a sparse clustering solution. A simulation study with artificial data provides further empirical evidence to support the recommendations. A clear understanding of the impact of the prior specifications removes restraints preventing the use of Bayesian methods due to the complexity of selecting suitable priors. Also, the regularizing properties of the priors may be intentionally exploited to obtain a suitable clustering solution meeting prior expectations and needs of the application.

This article is motivated by the challenge of analysing an agricultural field experiment with observations that are positive on a continuous scale or zero. Such data can be analysed using two-part models, where the distribution is a mixture of a positive distribution and a Bernoulli distribution. However, traditional two-part models do not include any dependencies between the two parts of the model. Since the probability of zero is anticipated to be high when the expected value of the positive part is low, and the other way around, this article introduces dependency-extended two-part models. In addition, these extensions allow for modelling the median instead of the mean, which has advantages when distributions are skewed. The motivating example is an incomplete block trial comparing ten treatments against weed. Gamma and lognormal distributions were used for the positive response, although any density on the support of real numbers can be accommodated. In a cross-validation study, the proposed new models were compared with each other and with a baseline model without dependencies. Model performance and sensitivity to choice of priors were investigated through simulation. A dependency-extended two-part model for the median of the lognormal distribution performed best with regard to mean square error in prediction. Supplementary materials accompanying this paper appear online.

Although Bayesian variable selection methods have been intensively studied, their routine use in practice has not caught up with their non-Bayesian counterparts such as Lasso, likely due to difficu...

Various objective priors have been defined for the common correlation coefficient concerning several bivariate normal populations. In this paper, the proposed approach relies on the asymptotic matching of coverage probabilities corresponding to Bayesian credible intervals considering the corresponding frequentist ones. In the present paper, we focus on several matching criteria including quantile matching, distribution function matching, highest posterior density matching, and matching via inversion of test statistics. In addition, we consider reference priors for different groups of ordering. The proposed methods are investigated and compared between each other in terms of a frequentist coverage probability and then, they are illustrated through a simulation study and two real data examples.

In order to conduct a comparative lifetime experiment in life testing and reliability theory, the joint censoring scheme has received immense popularity in the last decade. Recently, a new improved joint progressive censoring scheme has been introduced in statistical literature, known as balanced joint progressive censoring scheme. The present study deals with the statistical inferences for the balanced jointly progressive type-II censored two Lindley populations. Maximum likelihood estimators of the model parameters are derived and construction of the asymptotic confidence intervals based on the observed Fisher information matrix is discussed. From the Bayesian point of view, the posterior estimates of the unknown model parameters are calculated assuming the informative priors. A numerical study is carried out to evaluate the efficiency and performance of the proposed estimates. A real data set is analyzed to exemplify all the estimation techniques. Lastly, the criteria for an optimum censoring scheme are given.

This article accentuates the estimation of a two-parameter generalized Topp-Leone distribution using dual generalized order statistics (dgos). In the part of estimation, we obtain maximum likelihood (ML) estimates and approximate confidence intervals of the model parameters using dgos, in particular, based on order statistics and lower record values. The Bayes estimate is derived with respect to a squared error loss function using gamma priors. The highest posterior density credible interval is computed based on the MH algorithm. Furthermore, the explicit expressions for single and product moments of dgos from this distribution are also derived. Based on order statistics and lower records, a simulation study is carried out to check the efficiency of these estimators. Two real life data sets, one is for order statistics and another is for lower record values have been analyzed to demonstrate how the proposed methods may work in practice. © 2021 - IOS Press. All rights reserved.

In this paper, we adopt a nonparametric Bayesian approach and investigate the asymptotic behavior of the posterior distribution in continuous-time and general state space semi-Markov processes. In particular, we obtain posterior concentration rates for semi-Markov kernels. For the purposes of this study, we construct robust statistical tests between Hellinger balls around semi-Markov kernels and present some specifications to particular cases, including discrete-time semi-Markov processes and countable state space Markov processes. The objective of this paper is to provide sufficient conditions on priors and semi-Markov kernels that enable us to establish posterior concentration rates.

MotivationPrecise time calibrations needed to estimate ages of species divergence are not always available due to fossil records’ incompleteness. Consequently, clock calibrations available for Bayesian dating analyses can be few and diffused, i.e., phylogenies are calibration-poor, impeding reliable inference of the timetree of life. We examined the role of speciation birth-death tree prior on Bayesian node age estimates in calibration-poor phylogenies and tested the usefulness of an informative, data-driven tree prior to enhancing the accuracy and precision of estimated times.ResultsWe present a simple method to estimate parameters of the birth-death tree prior from the molecular phylogeny for use in Bayesian dating analyses. The use of a data-driven birth-death (ddBD) tree prior leads to improvement in Bayesian node age estimates for calibration-poor phylogenies. We show that the ddBD tree prior, along with only a few well-constrained calibrations, can produce excellent node ages and credibility intervals, whereas the use of an uninformative, uniform (flat) tree prior may require more calibrations. Relaxed clock dating with ddBD tree prior also produced better results than a flat tree prior when using diffused node calibrations. We also suggest using ddBD tree priors to improve the detection of outliers and influential calibrations in cross-validation analyses.ConclusionEmpirical Bayesian dating analyses with ddBD tree priors enable more accurate and precise node age estimates for calibration-poor phylogenies. Our results have practical applications because the ddBD tree prior reduces the number of well-constrained calibrations necessary to obtain reliable node age estimates. This would help address key impediments in building the grand timetree of life, revealing the process of speciation, and elucidating the dynamics of biological diversification.AvailabilityAn R module for computing the ddBD tree prior, simulated datasets, and empirical datasets are available at https://github.com/cathyqqtao/ddBD-tree-prior.

This paper presents reference priors for non-regular model whose support depends on an unknown parameter. A multi-parameter family which includes both regular and non-regular structures is considered. The resulting priors are obtained by asymptotically maximizing the expected α -divergence between the prior and the corresponding posterior distribution. Some examples of reference priors for typical multi-parameter non-regular distributions such as the location-scale family of distributions and the truncated Weibull distribution are also given.

We propose a novel class of convex risk measures, based on the concept of the Fr\'echet mean, designed in order to handle uncertainty which arises from multiple information sources regarding the risk factors of interest. The proposed risk measures robustly characterize the exposure of the firm, by filtering out appropriately the partial information available in individual sources into an aggregate model for the risk factors of interest. Importantly, the proposed risks can be expressed in closed analytic forms allowing for interesting qualitative interpretations as well as comparative statics and thus facilitate their use in the everyday risk management process of the insurance firms. The potential use of the proposed risk measures in insurance is illustrated by two concrete applications, capital risk allocation and premia calculation under uncertainty., Comment: 32 pages

As a principled dimension reduction technique, factor models have been widely adopted in applications. However, conducting a proper Bayesian factor analysis can be subtle in high-dimensional settings since it requires both a careful prescription of the prior distribution and a suitable computational strategy. We analyze issues of posterior inconsistency and sensitivity under different priors for high-dimensional sparse normal factor models, and show why adopting the n-orthonormal factor assumption can resolve these issues and lead to a more robust and efficient Bayesian analysis. We also provide an efficient Gibbs sampler to conduct the required computation, and show that it can be orders of magnitude more efficient than compared existing algorithms.

This study aims to determine the most appropriate warranty period and policy with the lowest warranty cost from the manufacturer/seller point of view. The warranty policy to be put forward and the warranty period to be offered under this policy should ensure customer satisfaction while at the same time causing a minimum cost to the manufacturer/seller. For this reason, the optimum warranty period within the scope of Free-Replacement Warranty (FRW) policy, Pro-Rata Warranty (PRW) policy, and Combined FRW/PRW policy which was the combination of those two warranty policies were tried to be determined. In the study which was done to determine the most appropriate warranty period, economic benefit and the benefit function obtained from warranty cost and dissatisfaction cost functions were used. While obtaining necessary formulas, exponential distribution, which was widely used in life tests as density function and gamma and inverse-gamma functions as prior distribution of the exponential distribution were used. To demonstrate the applicability and flexibility of the model, some typical sales models and numerical values for exponential lifetime distribution were used, and an algorithm was created to find the optimal solution. When all of the results were analyzed it was seen that Combined FRW/PRW policy was the most appropriate warranty cost as a result of testing the models obtained and it was also found that the warranty cost was almost 3% of the sale price. Within the frame of these obtained results, Combined FRW/PRW policy was suggested for the warranty service to be served with the product to the manufacturer/seller. If the warranty period number of revolutions were chosen almost g1=0.054., g2=0.120. the warranty cost will be in the minimum level and it will be almost 3% of the product sale price. The validity and accuracy of the proposed strategy was verified by a case study with a numerical sample providing a scientific basis. WOS:000665658800001 2-s2.0-85108637834

Bayesian methods are often suggested as a solution for issues encountered in small sample research, however, Bayesian methods often require informative priors to outperform classical methods in these settings. Specifying accurate priors with respect to the true value of the parameter of interest is challenging and inaccurate informative priors can have detrimental effects on conclusions from the statistical analysis. This paper proposes an objective procedure for creating informative priors for mediation analysis based on a historical data set; the only requirements for implementing the procedure are that the data from the current study constitute a representative sample from the population of interest, and that the historical and current data sets contain measures of the same covariates and independent variable, mediator, and outcome. The simulation study findings show that the proposed method leads to appropriate amount of borrowing from the historical data set, which leads to increases in precision and power when the historical data and current data are exchangeable, and does not induce bias when the historical and current studies are not exchangeable. The proposed method is illustrated using data from the project PROsetta Stone, and we provide rstan code for implementing the proposed method.

In the paper, we revisit the problem of class prior probability estimation with positive and unlabelled data gathered in a single-sample scenario. The task is important as it is known that in positive unlabelled setting, a classifier can be successfully learned if the class prior is available. We show that without additional assumptions, class prior probability is not identifiable and thus the existing non-parametric estimators are necessarily biased in general if extra assumptions are not imposed. The magnitude of their bias is also investigated. The problem becomes identifiable when the probabilistic structure satisfies mild semi-parametric assumptions. Consequently, we propose a method based on a logistic fit and a concave minorization of its (non-concave) log-likelihood. The experiments conducted on artificial and benchmark datasets as well as on a large clinical database MIMIC indicate that the estimation errors for the proposed method are usually lower than for its competitors and that it is robust against departures from logistic settings.

Diabetes prevalence is on the rise in the United Kingdom, and for public health strategy, estimation of relative disease risk and subsequent mapping is important. We consider an application to London data on diabetes prevalence and mortality. In order to improve the estimation of relative risks, we analyse jointly prevalence and mortality data to ensure borrowing strength over the two outcomes. The available data involve two spatial frameworks, areas (Middle Layer Super Output Areas, MSOAs) and general practices (GPs) recruiting patients from several areas. This raises a spatial misalignment issue that we deal with by employing the multiple membership principle. Specifically, we translate areal spatial effects to explain GP practice prevalence according to proportions of GP populations resident in different areas. A sparse implementation in RStan of both the multivariate conditional autoregressive (MCAR) and generalised MCAR (GMCAR) with multiple membership allows the comparison of these bivariate priors as well as exploring the different implications for the mapping patterns for both outcomes. The necessary causal precedence of diabetes prevalence over mortality allows a specific conditionality assumption in the GMCAR, not always present in the context of disease mapping. Additionally, an area-locality comparison is considered to locate high versus low relative risk clusters.

Traditional psychometric modeling focuses on observed categorical item responses, which can over-simplify the respondent cognitive response process. A further weakness is that analysis of ordinal responses has been primarily limited to a single substantive trait at one time point. We propose a significant expansion of this modeling framework to account for complex response processes across multiple waves of data collection using the beneficial item response tree framework. This study proposes a novel model, the longitudinal IRTree, for response processes in longitudinal studies, and investigates whether the response style changes are proportional to changes in the substantive trait of interest. A simulation study demonstrates adequate item parameter recovery in a Bayesian framework, especially with larger sample sizes of 2000. The longitudinal change parameters were recovered similarly well, with improved recovery using informative priors over default priors in Mplus. The empirical application demonstrates that relatively stable observed scores are due to a decrease in response styles offsetting an increase in the latent trait of interest.

In many applications, variables or features can be naturally partitioned into different groups. In this article, we propose a new Bayesian hierarchical model for group selection problem when the group structure is known. We use spike and slab priors for regression coefficients, and the slab component is assumed to come from the family of nonlocal priors. Contrary to local priors commonly used in Bayesian group selection, nonlocal density priors vanish when a regression coefficient in the model is zero. We use simulation studies to assess the performance of our method and apply it to data collected from individuals undergoing cardiac catheterization at Duke University Medical center between 2001 and 2010.

Adaptive Type-II progressive hybrid censoring scheme has been proposed to increase the efficiency of statistical analysis and save the total test time on a life-testing experiment. This article deals with the problem of estimating the parameters, survival and hazard rate functions of the two-parameter Hjorth distribution under adaptive Type-II progressive hybrid censoring scheme using maximum likelihood and Bayesian approaches. The two-sided approximate confidence intervals of the unknown quantities are constructed. Under the assumption of independent gamma priors, the Bayes estimators are obtained using squared error loss function. Since the Bayes estimators cannot be expressed in closed forms, Lindley’s approximation and Markov chain Monte Carlo methods are considered and the highest posterior density credible intervals are also obtained. To study the behavior of the various estimators, a Monte Carlo simulation study is performed. The performances of the different estimators have been compared on the basis of their average root mean squared error and relative absolute bias. Finally, to show the applicability of the proposed estimators a data set of industrial devices has been analyzed.

Bayesian sequential monitoring is widely used in adaptive phase II studies where the objective is to examine whether an experimental drug is efficacious. Common approaches for Bayesian sequential monitoring are based on posterior or predictive probabilities and Bayesian hypothesis testing procedures using Bayes factors. In the first part of the paper, we briefly show the connections between test-based (TB) and posterior probability-based (PB) sequential monitoring approaches. Next, we extensively investigate the choice of local and nonlocal priors for the TB monitoring procedure. We describe the pros and cons of different priors in terms of operating characteristics. We also develop a user-friendly Shiny application to implement the TB design.

This work discourages using the logistic regression (LR) model for estimative purposes when the sample size is small. We propose a new model called the “Robust Bayesian Logistic (RBL) model” that minimizes bias in the estimated logistic regression coefficients when the sample size is small, and covariate corruption is suspected. For the prior specification in the proposed RBL model, all the logistic regression coefficients are assigned independent Student’s t-distribution with the location parameter 0, scale parameter 1, and degree of freedom 7 for the constant term and degree of freedom of 1 for all other regression coefficients. In our experimental study, the proposed RBL model outperforms the Logistic Regression (LR) model by having a lower mean squared error (MSE) in the regression coefficients estimated for all the sample sizes considered. The proposed RBL model has a lower standard deviation than the LR model for all the estimated regression coefficients on the real-life dataset. We suggest that the proposed RBL model be considered for logistic modeling since it generates stable, consistent, and reliable estimates, especially when the sample size is small. The proposed RBL model is a fully Bayesian method implemented in the R environment using the RJAGS package.

Specific bivariate classes of distributions with given marginals can be used for contribution of the linking distribution between conditional and unconditional effectiveness using copulas. In this paper, a Bayesian model is proposed for meta-analysis of treatment effectiveness data which are generally discrete Binomial and sparse. A bivariate class of priors is imposed to accommodate a wide range of heterogeneity between the multicenter clinical trials involved in the study. Applications to real data are provided.

In this paper, robust Bayesian estimators of error variance in a normal linear model with uncertain hierarchical prior information are investigated. The posterior regret gamma minimax estimator, th...

In 2020, Korea Disease Control and Prevention Agency reported three rounds of surveys on seroprevalence of severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) antibodies in South Korea. SARS-CoV-2 is the virus which inflicts the coronavirus disease 2019 (COVID-19). We analyze the seroprevalence surveys using a Bayesian method with an informative prior distribution on the seroprevalence parameter, and the sensitivity and specificity of the diagnostic test. We construct the informative prior of the sensitivity and specificity of the diagnostic test using the posterior distribution obtained from the clinical evaluation data. The constraint of the seroprevalence parameter induced from the known confirmed coronavirus 2019 cases can be imposed naturally in the proposed Bayesian model. We also prove that the confidence interval of the seroprevalence parameter based on the Rao’s test can be the empty set, while the Bayesian method renders interval estimators with coverage probability close to the nominal level. As of the 30th of October 2020, the \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\,\,\,\,\,\,95\%\,\,\,\,\,\,$$\end{document}95% credible interval of the estimated SARS-CoV-2 positive population does not exceed 318, 685, approximately \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$0.62\%$$\end{document}0.62% of the Korean population. Supplementary Information The online version contains supplementary material available at 10.1007/s42952-021-00131-7.

In this paper, we consider some objective priors for the ratio of variabilities in a bivariate normal distribution. We develop the first and second order matching priors and reference priors. We obtain that the second order matching prior matches the alternative coverage probabilities up to the same order. It is also an HPD matching priors. It turns out that the derived reference priors do not satisfy a second order matching criterion. The simulation result shows that the second order matching prior performs better than reference priors based on matching the target coverage probabilities in a frequentist sense. Finally, we show that the second order matching prior and reference priors produce confidence sets with an expected length shorter than the Cox and Reid adjustment.

This paper outlines a framework for quantifying the prior’s contribution to posterior inference in the presence of prior-likelihood discordance, a broader concept than the usual notion of prior-likelihood conflict. We achieve this dual purpose by extending the classic notion of prior sample size, M, in three directions: (I) estimating M beyond conjugate families; (II) formulating M as a relative notion that is as a function of the likelihood sample size k, M(k), which also leads naturally to a graphical diagnosis; and (III) permitting negative M, as a measure of prior-likelihood conflict, that is, harmful discordance. Our asymptotic regime permits the prior sample size to grow with the likelihood data size, hence making asymptotic arguments meaningful for investigating the impact of the prior relative to that of likelihood. It leads to a simple asymptotic formula for quantifying the impact of a proper prior that only involves computing a centrality and a spread measure of the prior and the posterior. We use simulated and real data to illustrate the potential of the proposed framework, including quantifying how weak is a ‘weakly informative’ prior adopted in a study of lupus nephritis. Whereas we take a pragmatic perspective in assessing the impact of a prior on a given inference problem under a specific evaluative metric, we also touch upon conceptual and theoretical issues such as using improper priors and permitting priors with asymptotically non-vanishing influence.

Few problems in statistics are as perplexing as variable selection in the presence of very many redundant covariates. The variable selection problem is most familiar in parametric environments such as the linear model or additive variants thereof. In this work, we abandon the linear model framework, which can be quite detrimental when the covariates impact the outcome in a non-linear way, and turn to tree-based methods for variable selection. Such variable screening is traditionally done by pruning down large trees or by ranking variables based on some importance measure. Despite heavily used in practice, these ad hoc selection rules are not yet well understood from a theoretical point of view. In this work, we devise a Bayesian tree-based probabilistic method and show that it is consistent for variable selection when the regression surface is a smooth mix of p > n covariates. These results are the first model selection consistency results for Bayesian forest priors. Probabilistic assessment of variable importance is made feasible by a spike-and-slab wrapper around sum-of-trees priors. Sampling from posterior distributions over trees is inherently very difficult. As an alternative to Markov Chain Monte Carlo (MCMC), we propose approximate Bayesian computation (ABC) Bayesian forests, a new ABC sampling method based on data-splitting that achieves higher ABC acceptance rate. We show that the method is robust and successful at finding variables with high marginal inclusion probabilities. Our ABC algorithm provides a new avenue towards approximating the median probability model in non-parametric setups where the marginal likelihood is intractable.

Sparse convex clustering is to group observations and conduct variable selection simultaneously in the framework of convex clustering. Although a weighted $$L_1$$ L 1 norm is usually employed for the regularization term in sparse convex clustering, its use increases the dependence on the data and reduces the estimation accuracy if the sample size is not sufficient. To tackle these problems, this paper proposes a Bayesian sparse convex clustering method based on the ideas of Bayesian lasso and global-local shrinkage priors. We introduce Gibbs sampling algorithms for our method using scale mixtures of normal distributions. The effectiveness of the proposed methods is shown in simulation studies and a real data analysis.

A central theme in the field of survey statistics is estimating population-level quantities through data coming from potentially non-representative samples of the population. Multilevel Regression and Poststratification (MRP), a model-based approach, is gaining traction against the traditional weighted approach for survey estimates. MRP estimates are susceptible to bias if there is an underlying structure that the methodology does not capture. This work aims to provide a new framework for specifying structured prior distributions that lead to bias reduction in MRP estimates. We use simulation studies to explore the benefit of these prior distributions and demonstrate their efficacy on non-representative US survey data. We show that structured prior distributions offer absolute bias reduction and variance reduction for posterior MRP estimates in a large variety of data regimes., Comment: Minor revision. Added plots showing share of simulations where structured priors outperformed baseline priors in MRP