Analysis of the amended Davidson model with order effect for paired comparison in the Bayesian paradigm

We commonly observe many types of paired nature of competitions in which the objects are compared by the respondents pairwise in a subjective manner. The Bayesian statistics, contrary to the classical statistics, presents a generic tool to incorporate new experimental evidence and update the existing information. These and other properties have ushered the statisticians to focus their attention on the Bayesian analysis of different paired comparison models. The present article focuses on the amended Davidson model for paired comparison in which an amendment has been introduced that accommodates the option of not distinguishing the effects of two treatments when they are compared pairwise. However, Bayesian analysis of the amended Davidson model is performed using the noninformative priors after making another small modification of incorporating the parameter of order effect factor. The joint and marginal posterior distributions of the parameters, their posterior estimates, predictive and posterior probabilities to compare the treatment parameters are obtained.     

The behrens‐fisher problem revisited: A bayes‐frequentist synthesis

The Behrens‐Fisher problem concerns the inference for the difference between the means of two normal populations whose ratio of variances is unknown. In this situation, Fisher's fiducial interval differs markedly from the Neyman‐Pearson confidence interval. A prior proposed by Jeffreys leads to a credible interval that is equivalent to Fisher's solution but it carries a different interpretation. The authors propose an alternative prior leading to a credible interval whose asymptotic coverage probability matches the frequentist coverage probability more accurately than the interval of Jeffreys. Their simulation results indicate excellent matching even in small samples.     

A likelihood based approach for joint modeling of longitudinal trajectories and informative censoring process

We propose a joint modeling likelihood-based approach for studies with repeated measures and informative right censoring. Joint modeling of longitudinal and survival data are common approaches but could result in biased estimates if proportionality of hazards is violated. To overcome this issue, and given that the exact time of dropout is typically unknown, we modeled the censoring time as the number of follow-up visits and extended it to be dependent on selected covariates. Longitudinal trajectories for each subject were modeled to provide insight into disease progression and incorporated with the number follow-up visits in one likelihood function.     

言语行为动词告知关系及其语义认知解释

由言语行为动词所构成的句子涉及复杂的告知关系,从不同的认知角度看这些复杂的告知关系会有种种不同的认知分类框架及不同的认知解释。通过对这些认知分类框架的详细讨论和分析,立足于旁听人的言语行为动词认知分类及其语义认知解释是具有说服力的。     

Bayesian analysis for a stress-strength system under noninformative priors

Noninformative priors are used for estimating the reliability of a stress-strength system. Several reference priors (cf. Berger and Bernardo 1989, 1992) are derived. A class of priors is found by matching the coverage probabilities of one-sided Bayesian credible intervals with the corresponding frequentist coverage probabilities. It turns out that none of the reference priors is a matching prior. Sufficient conditions for propriety of posteriors under reference priors and matching priors are provided. A simple matching prior is compared with three reference priors when sample sizes are small. The study shows that the matching prior performs better than Jeffreys's prior and reference priors in meeting the target coverage probabilities.     

Empirical Bayes estimation for archaeological stratigraphy

Models and algorithms are presented for the stratigraphic analysis of earth core samples collected at archaeological sites. The aim is to separate the occupation of the site into distinct periods, by dividing the earth core into well-defined blocks of uniform magnetic susceptibility. The models describe the response of detector equipment by using both a spread function and an error process, and they incorporate prior beliefs regarding the nature of the true susceptibility values. The prior parameters are estimated by using pseudolikelihood and the susceptibilities by maximum a posteriori methods via the one-step-late algorithm. These procedures are illustrated with data from synthetic and real core specimens. The new procedures prove to be far superior to other approaches, producing reconstructions which clearly show distinct periods of uniform magnetic susceptibility separated by sharp discontinuities.     

Markov chain Monte Carlo estimation of a mixture item response theory model

Markov chain Monte Carlo (MCMC) algorithms have been shown to be useful for estimation of complex item response theory (IRT) models. Although an MCMC algorithm can be very useful, it also requires care in use and interpretation of results. In particular, MCMC algorithms generally make extensive use of priors on model parameters. In this paper, MCMC estimation is illustrated using a simple mixture IRT model, a mixture Rasch model (MRM), to demonstrate how the algorithm operates and how results may be affected by some commonly used priors. Priors on the probabilities of mixtures, label switching, model selection, metric anchoring, and implementation of the MCMC algorithm using WinBUGS are described, and their effects illustrated on parameter recovery in practical testing situations. In addition, an example is presented in which an MRM is fitted to a set of educational test data using the MCMC algorithm and a comparison is illustrated with results from three existing maximum likelihood estimation methods.     

Higher order asymptotic computation of Bayesian significance tests for precise null hypotheses in the presence of nuisance parameters

The full Bayesian significance test (FBST) was introduced by Pereira and Stern for measuring the evidence of a precise null hypothesis. The FBST requires both numerical optimization and multidimensional integration, whose computational cost may be heavy when testing a precise null hypothesis on a scalar parameter of interest in the presence of a large number of nuisance parameters. In this paper we propose a higher order approximation of the measure of evidence for the FBST, based on tail area expansions of the marginal posterior of the parameter of interest. When in particular focus is on matching priors, further results are highlighted. Numerical illustrations are discussed.     

The Prediction of Time Series With Trends and Seasonalities

A maximization of the expected entropy of the predictive distribution interpretation of Akaike's minimum AIC procedure is exploited for the modeling and prediction of time series with trend and seasonal mean value functions and stationary covariances. The AIC criterion best one-step-ahead and best twelve-step-ahead prediction models can be different. The different models exhibit the relative optimality properties for which they were designed. The results are related to open questions on optimal trend estimation and optimal seasonal adjustment of time series.     

Full Bayesian wavelet inference with a nonparametric prior

In this paper, we introduce a new Bayesian nonparametric model for estimating an unknown function in the presence of Gaussian noise. The proposed model involves a mixture of a point mass and an arbitrary (nonparametric) symmetric and unimodal distribution for modeling wavelet coefficients. Posterior simulation uses slice sampling ideas and the consistency under the proposed model is discussed. In particular, the method is shown to be computationally competitive with some of best Empirical wavelet estimation methods.