Weibull multi-state models with misclassification

It is often important to allow multi-state models (MSMs) to accommodate misclassification of states. We introduce Bayesian parametric MSMs with unknown misclassification of states and Weibull distributed waiting times between states. This allows transitions between states to depend on the time spent in the current state, a feature lacking in commonly used exponential waiting times model. To fit the proposed model, a MCMC algorithm was employed. An example on the progression of bipolar disorder is presented along with simulation results. There was evidence that Weibull waiting times are an improvement over exponential in the study of bipolar disorder.     

Bayesian and robust Bayesian analysis in a general setting

In this paper we introduce a broad family of loss functions based on the concept of Bregman divergence. We deal with both Bayesian estimation and prediction problems and show that all Bayes solutions associated with loss functions belonging to the introduced family of losses satisfy the same equation. We further concentrate on the concept of robust Bayesian analysis and provide one equation that explicitly leads to robust Bayes solutions. The results are model-free and include many existing results in Bayesian and robust Bayesian contexts in the literature.     

Four comments for the paper from Liu et al. (2019)

We give comments for the paper from Liu et al. (2019) about the Item Response Theory (IRT) model under consideration, the justification to compute Marginal likelihood, about what we learn with the data analysis performed and finally, about the computational issues in this paper.     

Deprivation analysis based on Bayesian latent class models

This article seeks to measure deprivation among Portuguese households, taking into account four well-being dimensions – housing, durable goods, economic strain and social relationships – with survey data from the European Community Household Panel. We propose a multi-stage approach to a cross-sectional analysis, side-stepping the sparse nature of the contingency tables caused by the large number of variables considered and bringing together partial and overall analyses of deprivation that are based on Bayesian latent class models via Markov Chain Monte Carlo methods. The outcomes demonstrate that there was a substantial improvement on household overall well-being between 1995 and 2001. The dimensions that most contributed to the risk of household deprivation were found to be economic strain and social relationships.     

Life prediction under random censorship

Based on censored samples, this paper proposes a statistic to predict the average value of some future samples which denotes the average life of the second round sampling. Differing from the usual Bayesian prediction, we do not specify the prior distribution of the parameter, and only some moment conditions are assumed. Simulation studies are conducted to investigate the prediction results.     

A new approach to default priors and robust bayes methodology

Following the developments in DasGupta et al. (2000), the authors propose and explore a new method for constructing proper default priors and a method for selecting a Bayes estimate from a family. Their results are based on asymptotic expansions of certain marginal correlations. For ease of exposition, most results are presented for location families and squared error loss only. The default prior methodology amounts, ultimately, to the minimization of Fisher information, and hence, Bickel's prior works out as the default prior if the location parameter is bounded. As for the selected Bayes estimate, it corresponds to ‘Gaussian tilting’ of an initial reference prior.     

GSH Dependence Modeling with an Application to Risk Management

The generalized secant hyperbolic distribution (GSH) can be used to represent financial data with heavy tails as an alternative to the Student-t, because it guarantees the existence of all moments, also with a high kurtosis value. In order to obtain a multivariate extension of the GSH distribution, in this article we present two approaches to model the dependence, the copula approach and independent component analysis. Since the methodologies considered allow to simulate the GSH dependence, we show also the empirical results obtained in the estimation of risk of a financial portfolio by the Monte Carlo method.     

Hierarchical Bayes estimation in small area estimation using cross-sectional and time-series data

Bayesian methods have been extensively used in small area estimation. A linear model incorporating autocorrelated random effects and sampling errors was previously proposed in small area estimation using both cross-sectional and time-series data in the Bayesian paradigm. There are, however, many situations that we have time-related counts or proportions in small area estimation; for example, monthly dataset on the number of incidence in small areas. This article considers hierarchical Bayes generalized linear models for a unified analysis of both discrete and continuous data with incorporating cross-sectional and time-series data. The performance of the proposed approach is evaluated through several simulation studies and also by a real dataset.     

Bayesian statistical inference of the loglogistic model with interval-censored lifetime data

Interval-censored data arise when a failure time say, T cannot be observed directly but can only be determined to lie in an interval obtained from a series of inspection times. The frequentist approach for analysing interval-censored data has been developed for some time now. It is very common due to unavailability of software in the field of biological, medical and reliability studies to simplify the interval censoring structure of the data into that of a more standard right censoring situation by imputing the midpoints of the censoring intervals. In this research paper, we apply the Bayesian approach by employing Lindley's 1980, and Tierney and Kadane 1986 numerical approximation procedures when the survival data under consideration are interval-censored. The Bayesian approach to interval-censored data has barely been discussed in literature. The essence of this study is to explore and promote the Bayesian methods when the survival data been analysed are is interval-censored. We have considered only a parametric approach by assuming that the survival data follow a loglogistic distribution model. We illustrate the proposed methods with two real data sets. A simulation study is also carried out to compare the performances of the methods.     

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.