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In many applications, modeling based on a normal kernel is preferred because not only does the normal kernel belong to the family of stable distributions, but also it is easy to satisfy the stationary condition in the stochastic process. However, the characteristic of the data, such as count or proportion, is a major obstacle to complete modeling based on a normal distribution. To solve a limited boundary or non-normal distribution problem, we provided a novel transformation method and proposed a nonparametric Bayesian approach based on a normal kernel of the transformed variable. In particular, the provided transformation transforms any probability space into a real space and is free from the constraints of the previous transformation, such as skewness, presence of power, and bounded domains. Another advantage was that it was possible to use the Dirichlet process mixture model with full conditional posterior distributions for all parameters, leading to a fast convergence rate in the Markov chain Monte Carlo. The proposed methodology was illustrated with simulated datasets and two real datasets with non-normal distribution problems. In addition, to demonstrate the superiority of the proposed methodology, the comparison with the transformed Bernstein polynomial model was made in the real data analysis. [ABSTRACT FROM AUTHOR]

In radiation epidemiology, the excess relative risk (ERR) model is used to determine the dose–response relationship. In general, the dose-response relationship for the ERR model is assumed to be linear, linear-quadratic, linear-threshold, quadratic, and so on. However, since none of these functions dominate other functions for expressing the dose-response relationship, a Bayesian semiparametric method using splines has recently been proposed. Thus, we improve the Bayesian semiparametric method for the selection of the tuning parameters for splines as the number and location of knots using a Bayesian knot selection method. Equally spaced knots cannot capture the characteristic of radiation exposed dose distribution which is highly skewed in general. Therefore, we propose a nonparametric Bayesian knot selection method based on a Dirichlet process mixture model. Inference of the spline coefficients after obtaining the number and location of knots is performed in the Bayesian framework. We apply this approach to the life span study cohort data from the radiation effects research foundation in Japan, and the results illustrate that the proposed method provides competitive curve estimates for the dose-response curve and relatively stable credible intervals for the curve. [ABSTRACT FROM AUTHOR]

The Bayesian approach is a suitable alternative in constructing appropriate models for observed record values because the number of these values is small. This paper provides an objective Bayesian analysis method for upper record values arising from the Rayleigh distribution. For the objective Bayesian analysis, the Fisher information matrix for unknown parameters is derived in terms of the second derivative of the log-likelihood function by using Leibniz's rule; subsequently, objective priors are provided, resulting in proper posterior distributions. We examine if these priors are the PMPs. In a simulation study, inference results under the provided priors are compared through Monte Carlo simulations. Through real data analysis, we reveal a limitation of the appropriate confidence interval based on the maximum likelihood estimator for the scale parameter and evaluate the models under the provided priors. [ABSTRACT FROM AUTHOR]

In this paper, we provide an entropy inference method that is based on an objective Bayesian approach for upper record values having a two-parameter logistic distribution. We derive the entropy that is based on the i-th upper record value and the joint entropy that is based on the upper record values. Moreover, we examine their properties. For objective Bayesian analysis, we obtain objective priors, namely, the Jeffreys and reference priors, for the unknown parameters of the logistic distribution. The priors are based on upper record values. Then, we develop an entropy inference method that is based on these objective priors. In real data analysis, we assess the quality of the proposed models under the objective priors and compare them with the model under the informative prior. [ABSTRACT FROM AUTHOR]

This paper considers the multiple comparisons problem for normal variances. We propose a solution based on a Bayesian model selection procedure to this problem in which no subjective input is considered. We construct the intrinsic and fractional priors for which the Bayes factors and model selection probabilities are well defined. The posterior probability of each model is used as a model selection tool. The behaviour of these Bayes factors is compared with the Bayesian information criterion of Schwarz and some frequentist tests. [ABSTRACT FROM AUTHOR]

This manuscript summarized advances in bootstrap methods for long-range dependent time series data. The stationary linear long-memory process is briefly described, which is a target process for bootstrap methodologies on time-domain and frequency-domain in this review. We illustrate time-domain bootstrap under long-range dependence, moving or non-overlapping block bootstraps, and the autoregressive-sieve bootstrap. In particular, block bootstrap methodologies need an adjustment factor for the distribution estimation of the sample mean in contrast to applications to weak dependent time processes. However, the autoregressive-sieve bootstrap does not need any other modification for application to long-memory. The frequency domain bootstrap for Whittle estimation is provided using parametric spectral density estimates because there is no current nonparametric spectral density estimation method using a kernel function for the linear long-range dependent time process. [ABSTRACT FROM AUTHOR]

Large quantities of air pollutants are released into the atmosphere and hence, must be monitored and routinely assessed for their health implications. This paper proposes a stochastic technique to predict unobserved hazardous air pollutants (HAPs), especially Benzo[a]pyrene (BaP), which can have negative effects on human health. The proposed approach constructs a nearest-neighbor structure by incorporating the linkage between BaP and meteorology and meteorological effects. This approach is adopted in order to predict unobserved BaP concentrations based on observed (or forecasted) meteorological conditions, including temperature, precipitation, wind speed, and air quality. The effects of BaP on human health are examined by characterizing the cancer risk. The efficient prediction provides useful information relating to the optimal monitoring period and projections of future BaP concentrations for both industrial and residential areas within Korea. [ABSTRACT FROM AUTHOR]

In many case-control genetic association studies, a secondary phenotype that may have common genetic factors with disease status can be identified. When information on the secondary phenotype is available only for the case group due to cost and different data sources, a fitting linear regression model ignoring supplementary phenotype data may provide limited knowledge regarding genetic association. We set up a joint model and use a Bayesian framework to estimate and test the effect of genetic covariates on disease status considering the secondary phenotype as an instrumental variable. The application of our proposed procedure is demonstrated through the rheumatoid arthritis data provided by the 16th Genetic Analysis Workshop. [ABSTRACT FROM AUTHOR]

In models with nuisance parameters, Bayesian procedures based on Markov Chain Monte Carlo (MCMC) methods have been developed to approximate the posterior distribution of the parameter of interest. Because these procedures require burdensome computations related to the use of MCMC, approximation and convergence in these procedures are important issues. In this paper, we explore Gibbs sensitivity by using an alternative to the full conditional distribution of the nuisance parameter. The approximate sensitivity of the posterior distribution of interest is studied in terms of an information measure, including Kullback-Leibler divergence. As an illustration, we then apply these results to simple spatial model settings. [ABSTRACT FROM AUTHOR]

The authors develop statistical data models to combine ensembles from multiple climate models in a fashion that accounts for uncertainty. This formulation enables treatment of model specific means, biases, and covariance matrices of the ensembles. In addition, the authors model the uncertainty in using computer model results to estimate true states of nature. Based on these models and principles of decision making in the presence of uncertainty, this paper poses the problem of superensemble experimental design in a quantitative fashion. Simple examples of the resulting optimal designs are presented. The authors also provide a Bayesian climate modeling and forecasting analysis. The climate variables of interest are Northern and Southern Hemispheric monthly averaged surface temperatures. A Bayesian hierarchical model for these quantities is constructed, including time-varying parameters that are modeled as random variables with distributions depending in part on atmospheric CO2 levels. This allows the authors to do Bayesian forecasting of temperatures under different Special Report on Emissions Scenarios (SRES). These forecasts are based on Bayesian posterior distributions of the unknowns conditional on observational data for 1882–2001 and climate system model output for 2002–97. The latter dataset is a small superensemble from the Parallel Climate Model (PCM) and the Community Climate System Model (CCSM). After summarizing the results, the paper concludes with discussion of potential generalizations of the authors’ strategies. [ABSTRACT FROM AUTHOR]