Bayesian model learning based on a parallel MCMC strategy

We introduce a novel Markov chain Monte Carlo algorithm for estimation of posterior probabilities over discrete model spaces. Our learning approach is applicable to families of models for which the marginal likelihood can be analytically calculated, either exactly or approximately, given any fixed structure. It is argued that for certain model neighborhood structures, the ordinary reversible Metropolis-Hastings algorithm does not yield an appropriate solution to the estimation problem. Therefore, we develop an alternative, non-reversible algorithm which can avoid the scaling effect of the neighborhood. To efficiently explore a model space, a finite number of interacting parallel stochastic processes is utilized. Our interaction scheme enables exploration of several local neighborhoods of a model space simultaneously, while it prevents the absorption of any particular process to a relatively inferior state. We illustrate the advantages of our method by an application to a classification model. In particular, we use an extensive bacterial database and compare our results with results obtained by different methods for the same data.     

A Bayesian multiple structural change regression model with autocorrelated errors

This paper develops a new Bayesian approach to change-point modeling that allows the number of change-points in the observed autocorrelated times series to be unknown. The model we develop assumes that the number of change-points have a truncated Poisson distribution. A genetic algorithm is used to estimate a change-point model, which allows for structural changes with autocorrelated errors. We focus considerable attention on the construction of autocorrelated structure for each regime and for the parameters that characterize each regime. Our techniques are found to work well in the simulation with a few change-points. An empirical analysis is provided involving the annual flow of the Nile River and the monthly total energy production in South Korea to lead good estimates for structural change-points.     

A Bayesian multiple comparison procedure for simply ordered treatment medians

This article considers a Bayesian hierarchical model for multiple comparisons in linear models where the population medians satisfy a simple order restriction. Representing the asymmetric Laplace distribution as a scale mixture of normals with an exponential mixing density and a continuous prior restricted to order constraints, a Gibbs sampling algorithm for parameter estimation and simultaneous comparison of treatment medians is proposed. Posterior probabilities of all possible hypotheses on the equality/inequality of treatment medians are estimated using Bayes factors that are computed via the Savage-Dickey density ratios. The performance of the proposed median-based model is investigated in the simulated and real datasets. The results show that the proposed method can outperform the commonly used method that is based on treatment means, when data are from nonnormal distributions.     

Bayesian inference and prediction analysis of the power law process based on a natural conjugate prior

Under a natural conjugate prior with four hyperparameters, the importance sampling (IS) technique is applied to the Bayesian analysis of the power law process (PLP). Samples of the parameters of the PLP are obtained from IS. Based on these samples, not only the posterior analysis of parameters and some parameter functions in the PLP are performed conveniently, but also single-sample and two-sample prediction procedures are constructed easily. Furthermore, the sensitivity of the posterior mean of the parameter functions in the PLP is studied with respect to the hyperparameters of the natural conjugate prior and it can guide the selections of the hyperparameters directly. Coupled this sensitivity with the relations between the prior moments and the hyperparameters in the natural conjugate prior, it is possible to give directions about the selections of the prior moments to a certain degree. After some numerical experiments illustrate the rationality and feasibility of the proposed methods, an engineering example demonstrates its application.     

A new multivariate imputation method based on Bayesian networks

Dealing with incomplete data is a pervasive problem in statistical surveys. Bayesian networks have been recently used in missing data imputation. In this research, we propose a new methodology for the multivariate imputation of missing data using discrete Bayesian networks and conditional Gaussian Bayesian networks. Results from imputing missing values in coronary artery disease data set and milk composition data set as well as a simulation study from cancer-neapolitan network are presented to demonstrate and compare the performance of three Bayesian network-based imputation methods with those of multivariate imputation by chained equations (MICE) and the classical hot-deck imputation method. To assess the effect of the structure learning algorithm on the performance of the Bayesian network-based methods, two methods called Peter-Clark algorithm and greedy search-and-score have been applied. Bayesian network-based methods are: first, the method introduced by Di Zio et al. [Bayesian networks for imputation, J. R. Stat. Soc. Ser. A 167 (2004), 309–322] in which, each missing item of a variable is imputed using the information given in the parents of that variable; second, the method of Di Zio et al. [Multivariate techniques for imputation based on Bayesian networks, Neural Netw. World 15 (2005), 303–310] which uses the information in the Markov blanket set of the variable to be imputed and finally, our new proposed method which applies the whole available knowledge of all variables of interest, consisting the Markov blanket and so the parent set, to impute a missing item. Results indicate the high quality of our new proposed method especially in the presence of high missingness percentages and more connected networks. Also the new method have shown to be more efficient than the MICE method for small sample sizes with high missing rates.     

A multiple group item response theory model with centered skew-normal latent trait distributions under a Bayesian framework

Very often, in psychometric research, as in educational assessment, it is necessary to analyze item response from clustered respondents. The multiple group item response theory (IRT) model proposed by Bock and Zimowski [12] provides a useful framework for analyzing such type of data. In this model, the selected groups of respondents are of specific interest such that group-specific population distributions need to be defined. The usual assumption for parameter estimation in this model, which is that the latent traits are random variables following different symmetric normal distributions, has been questioned in many works found in the IRT literature. Furthermore, when this assumption does not hold, misleading inference can result. In this paper, we consider that the latent traits for each group follow different skew-normal distributions, under the centered parameterization. We named it skew multiple group IRT model. This modeling extends the works of Azevedo et al. [4], Bazán et al. [11] and Bock and Zimowski [12] (concerning the latent trait distribution). Our approach ensures that the model is identifiable. We propose and compare, concerning convergence issues, two Monte Carlo Markov Chain (MCMC) algorithms for parameter estimation. A simulation study was performed in order to evaluate parameter recovery for the proposed model and the selected algorithm concerning convergence issues. Results reveal that the proposed algorithm recovers properly all model parameters. Furthermore, we analyzed a real data set which presents asymmetry concerning the latent traits distribution. The results obtained by using our approach confirmed the presence of negative asymmetry for some latent trait distributions.     

A Bayesian procedure for assessing process performance based on the third-generation capability index

Capability indices that qualify process potential and process performance are practical tools for successful quality improvement activities and quality program implementation. Most existing methods to assess process capability were derived on the basis of the traditional frequentist point of view. This paper considers the problem of estimating and testing process capability based on the third-generation capability index C _pmk from the Bayesian point of view. We first derive the posterior probability p for the process under investigation is capable. The one-sided credible interval, a Bayesian analog of the classical lower confidence interval, can be obtained to assess process performance. To investigate the effectiveness of the derived results, a series of simulation was undertaken. The results indicate that the performance of the proposed Bayesian approach depends strongly on the value of ξ=(μ?T)/σ. It performs very well with the accurate coverage rate when μ is sufficiently far from T. In those cases, they have the same acceptable performance even though the sample size n is as small as 25.     

A semiparametric Bayesian approach for joint modeling of longitudinal trait and event time

Inference on the whole biological system is the recent focus in bioscience. Different biomarkers, although seem to function separately, can actually control some event(s) of interest simultaneously. This fundamental biological principle has motivated the researchers for developing joint models which can explain the biological system efficiently. Because of the advanced biotechnology, huge amount of biological information can be easily obtained in current years. Hence dimension reduction is one of the major issues in current biological research. In this article, we propose a Bayesian semiparametric approach of jointly modeling observed longitudinal trait and event-time data. A sure independence screening procedure based on the distance correlation and a modified version of Bayesian Lasso are used for dimension reduction. Traditional Cox proportional hazards model is used for modeling the event-time. Our proposed model is used for detecting marker genes controlling the biomass and first flowering time of soybean plants. Simulation studies are performed for assessing the practical usefulness of the proposed model. Proposed model can be used for the joint analysis of traits and diseases for humans, animals and plants.     

Two-sample Bayesian prediction for sequential order statistics from exponential distribution based on multiply Type-II censored samples

In this paper, the problem of predicting the future sequential order statistics based on observed multiply Type-II censored samples of sequential order statistics from one- and two-parameter exponential distributions is addressed. Using the Bayesian approach, the predictive and survival functions are derived and then the point and interval predictions are obtained. Finally, two numerical examples are presented for illustration.     

Bayesian modelling of effects of prenatal alcohol exposure on child cognition based on data from multiple cohorts

High levels of prenatal alcohol exposure (PAE) result in significant cognitive deficits in children, but the exact nature of the dose-response relationship is less well understood. To investigate this relationship, data were assembled from six longitudinal birth cohort studies examining the effects of PAE on cognitive outcomes from early school age through adolescence. Structural equation models (SEMs) are a natural approach to consider, because of the way they conceptualise multiple observed outcomes as relating to an underlying latent variable of interest, which can then be modelled as a function of exposure and other predictors of interest. However, conventional SEMs could not be fitted in this context because slightly different outcome measures were used in the six studies. In this paper we propose a multi-group Bayesian SEM that maps the unobserved cognition variable to a broad range of observed outcomes. The relation between these variables and PAE is then examined while controlling for potential confounders via propensity score adjustment. By examining different possible dose-response functions, the proposed framework is used to investigate whether there is a threshold PAE level that results in minimal cognitive deficit.     

A comparison of Bayesian model selection based on MCMC with an application to GARCH-type models

This paper presents a comprehensive review and comparison of five computational methods for Bayesian model selection, based on MCMC simulations from posterior model parameter distributions. We apply these methods to a well-known and important class of models in financial time series analysis, namely GARCH and GARCH-t models for conditional return distributions (assuming normal and t-distributions). We compare their performance with the more common maximum likelihood-based model selection for simulated and real market data. All five MCMC methods proved reliable in the simulation study, although differing in their computational demands. Results on simulated data also show that for large degrees of freedom (where the t-distribution becomes more similar to a normal one), Bayesian model selection results in better decisions in favor of the true model than maximum likelihood. Results on market data show the instability of the harmonic mean estimator and reliability of the advanced model selection methods.     

A Bayesian dose‐finding design for drug combination clinical trials based on the logistic model

In early phase dose‐finding cancer studies, the objective is to determine the maximum tolerated dose, defined as the highest dose with an acceptable dose‐limiting toxicity rate. Finding this dose for drug‐combination trials is complicated because of drug–drug interactions, and many trial designs have been proposed to address this issue. These designs rely on complicated statistical models that typically are not familiar to clinicians, and are rarely used in practice. The aim of this paper is to propose a Bayesian dose‐finding design for drug combination trials based on standard logistic regression. Under the proposed design, we continuously update the posterior estimates of the model parameters to make the decisions of dose assignment and early stopping. Simulation studies show that the proposed design is competitive and outperforms some existing designs. We also extend our design to handle delayed toxicities. Copyright © 2014 John Wiley & Sons, Ltd.     

A Bayesian model for multiple change point to extremes,with application to environmental and financial data

Abrupt changes often occur for environmental and financial time series. Most often, these changes are due to human intervention. Change point analysis is a statistical tool used to analyze sudden changes in observations along the time series. In this paper, we propose a Bayesian model for extreme values for environmental and economic datasets that present a typical change point behavior. The model proposed in this paper addresses the situation in which more than one change point can occur in a time series. By analyzing maxima, the distribution of each regime is a generalized extreme value distribution. In this model, the change points are unknown and considered parameters to be estimated. Simulations of extremes with two change points showed that the proposed algorithm can recover the true values of the parameters, in addition to detecting the true change points in different configurations. Also, the number of change points was a problem to be considered, and the Bayesian estimation can correctly identify the correct number of change points for each application. Environmental and financial data were analyzed and results showed the importance of considering the change point in the data and revealed that this change of regime brought about an increase in the return levels, increasing the number of floods in cities around the rivers. Stock market levels showed the necessity of a model with three different regimes.     

A coefficient of multiple association based on ranks

A generalization of Kendall's tau is formulated for describing the association between a dependent variable and a collection of independent variables. The coefficient may be defined in terms of the proportional reduction in prediction errors obtained by predicting the ordering of pairs of observations on the dependent variable based on orderings of the pairs on the independent variables. The coefficient is formulated both for continuous and discrete variables. Approximate large-sample distributions are considered for both cases. Some of the properties of this coefficient are discussed and compared with those of other multiple measures of association based on ranks.     

Curtailed Bayesian sampling plans for exponential distributions based on Type-II censored samples

This paper studies the problem of designing a curtailed Bayesian sampling plan (CBSP) with Type-II censored data. We first derive the Bayesian sampling plan (BSP) for exponential distributions based on Type-II censored samples in a general loss function. For the conjugate prior with quadratic loss function, an explicit expression for the Bayes decision function is derived. Using the property of monotonicity of the Bayes decision function, a new Bayesian sampling plan modified by the curtailment procedure, called a CBSP, is proposed. It is shown that the risk of CBSP is less than or equal to that of BSP. Comparisons among some existing BSPs and the proposed CBSP are given. Monte Carlo simulations are conducted, and numerical results indicate that the CBSP outperforms those early existing sampling plans if the time loss is considered in the loss function.     

A Framework for Monte Carlo based Multiple Testing

We are concerned with a situation in which we would like to test multiple hypotheses with tests whose p‐values cannot be computed explicitly but can be approximated using Monte Carlo simulation. This scenario occurs widely in practice. We are interested in obtaining the same rejections and non‐rejections as the ones obtained if the p‐values for all hypotheses had been available. The present article introduces a framework for this scenario by providing a generic algorithm for a general multiple testing procedure. We establish conditions that guarantee that the rejections and non‐rejections obtained through Monte Carlo simulations are identical to the ones obtained with the p‐values. Our framework is applicable to a general class of step‐up and step‐down procedures, which includes many established multiple testing corrections such as the ones of Bonferroni, Holm, Sidak, Hochberg or Benjamini–Hochberg. Moreover, we show how to use our framework to improve algorithms available in the literature in such a way as to yield theoretical guarantees on their results. These modifications can easily be implemented in practice and lead to a particular way of reporting multiple testing results as three sets together with an error bound on their correctness, demonstrated exemplarily using a real biological dataset.     

Bayesian two-stage design for drug screening trials with switching hypothesis tests based on continuous endpoints

Abstract

In this paper, we propose a Bayesian two-stage design with changing hypothesis test by bridging a single-arm study and a double-arm randomized trial in one phase II clinical trial based on continuous endpoints rather than binary endpoints. We have also calibrated with respect to frequentist and Bayesian error rates. The proposed design minimizes the Bayesian expected sample size if the new candidate has low or high efficacy activity subject to the constraint upon error rates in both frequentist and Bayesian perspectives. Tables of designs for various combinations of design parameters are also provided.     

Bayesian estimation and prediction for some life distributions based on record values

Some statistical data are most easily accessed in terms of record values. Examples include meteorology, hydrology and athletic events. Also, there are a number of industrial situations where experimental outcomes are a sequence of record-breaking observations. In this paper, Bayesian estimation for the two parameters of some life distributions, including Exponential, Weibull, Pareto and Burr type XII, are obtained based on upper record values. Prediction, either point or interval, for future upper record values is also presented from a Bayesian view point. Some of the non-Bayesian results can be achieved as limiting cases from our results. Numerical computations are given to illustrate the results.     

A Bayesian optimal interval design for dose optimization with a randomization scheme based on pharmacokinetics outcomes in oncology

The primary objective of an oncology dose-finding trial for novel therapies, such as molecularly targeted agents and immune-oncology therapies, is to identify the optimal dose (OD) that is tolerable and therapeutically beneficial for subjects in subsequent clinical trials. Pharmacokinetic (PK) information is considered an appropriate indicator for evaluating the level of drug intervention in humans from a pharmacological perspective. Several novel anticancer agents have been shown to have significant exposure-efficacy relationships, and some PK information has been considered an important predictor of efficacy. This paper proposes a Bayesian optimal interval design for dose optimization with a randomization scheme based on PK outcomes in oncology. A simulation study shows that the proposed design has advantages compared to the other designs in the percentage of correct OD selection and the average number of patients allocated to OD in various realistic settings.