Higher-order Bayesian Approximations for Pseudo-posterior Distributions

The theory of higher-order asymptotics provides accurate approximations to posterior distributions for a scalar parameter of interest, and to the corresponding tail area, for practical use in Bayesian analysis. The aim of this article is to extend these approximations to pseudo-posterior distributions, e.g., posterior distributions based on a pseudo-likelihood function and a suitable prior, which are proved to be particularly useful when the full likelihood is analytically or computationally infeasible. In particular, from a theoretical point of view, we derive the Laplace approximation for a pseudo-posterior distribution, and for the corresponding tail area, for a scalar parameter of interest, also in the presence of nuisance parameters. From a computational point of view, starting from these higher-order approximations, we discuss the higher-order tail area (HOTA) algorithm useful to approximate marginal posterior distributions, and related quantities. Compared to standard Markov chain Monte Carlo methods, the main advantage of the HOTA algorithm is that it gives independent samples at a negligible computational cost. The relevant computations are illustrated by two examples.     

Analysis of Regional Scale Risk of Whirling Disease in Populations of Colorado and Rio Grande Cutthroat Trout Using a Bayesian Belief Network Model

Introduction and spread of the parasite Myxobolus cerebralis, the causative agent of whirling disease, has contributed to the collapse of wild trout populations throughout the intermountain west. Of concern is the risk the disease may have on conservation and recovery of native cutthroat trout. We employed a Bayesian belief network to assess probability of whirling disease in Colorado River and Rio Grande cutthroat trout (Oncorhynchus clarkii pleuriticus and Oncorhynchus clarkii virginalis, respectively) within their current ranges in the southwest United States. Available habitat (as defined by gradient and elevation) for intermediate oligochaete worm host, Tubifex tubifex, exerted the greatest influence on the likelihood of infection, yet prevalence of stream barriers also affected the risk outcome. Management areas that had the highest likelihood of infected Colorado River cutthroat trout were in the eastern portion of their range, although the probability of infection was highest for populations in the southern, San Juan subbasin. Rio Grande cutthroat trout had a relatively low likelihood of infection, with populations in the southernmost Pecos management area predicted to be at greatest risk. The Bayesian risk assessment model predicted the likelihood of whirling disease infection from its principal transmission vector, fish movement, and suggested that barriers may be effective in reducing risk of exposure to native trout populations. Data gaps, especially with regard to location of spawning, highlighted the importance in developing monitoring plans that support future risk assessments and adaptive management for subspecies of cutthroat trout.     

Preferences of the Central Bank of Brazil under the inflation targeting regime: Estimation using a DSGE model for a small open economy

The main objective of this paper is to estimate the preferences of the Central Bank of Brazil after the inflation targeting regime (January 2000 to December 2013), using a DSGE model with microeconomic foundations for a small open economy, based especially on the work of Kam et al. (2009). The model used in this study considers that the Central Bank minimizes a loss function, taking into account the deviation of inflation from its target, output stabilization, the interest rate smoothing and, unlike the previous works, the exchange rate. The results show that the major concern of the monetary authority in the period was the stabilization of inflation, followed by interest rate smoothing, exchange stabilization and, finally, output stabilization. The large value for the exchange rate smoothing parameter suggests the presence of fear of floating in the Brazilian case. An improved inflation targeting strategy should allow for less Central Bank intervention in the exchange rate market.     

Confidence intervals for the mean of a normal distribution with restricted parameter space

For a normal distribution with known variance, the standard confidence interval of the location parameter is derived from the classical Neyman procedure. When the parameter space is known to be restricted, the standard confidence interval is arguably unsatisfactory. Recent articles have addressed this problem and proposed confidence intervals for the mean of a normal distribution where the parameter space is not less than zero. In this article, we propose a new confidence interval, rp interval, and derive the Bayesian credible interval and likelihood ratio interval for general restricted parameter space. We compare these intervals with the standard interval and the minimax interval. Simulation studies are undertaken to assess the performances of these confidence intervals.     

Multivariate log-skewed distributions with normal kernel and their applications

We introduce two classes of multivariate log-skewed distributions with normal kernel: the log canonical fundamental skew-normal (log-CFUSN) and the log unified skew-normal. We also discuss some properties of the log-CFUSN family of distributions. These new classes of log-skewed distributions include the log-normal and multivariate log-skew normal families as particular cases. We discuss some issues related to Bayesian inference in the log-CFUSN family of distributions, mainly we focus on how to model the prior uncertainty about the skewing parameter. Based on the stochastic representation of the log-CFUSN family, we propose a data augmentation strategy for sampling from the posterior distributions. This proposed family is used to analyse the US national monthly precipitation data. We conclude that a high-dimensional skewing function lead to a better model fit.     

Data envelopment analysis in the presence of measurement error: case study from the National Database of Nursing Quality Indicators® (NDNQI®)

Data envelopment analysis (DEA) is the most commonly used approach for evaluating healthcare efficiency [B. Hollingsworth, The measurement of efficiency and productivity of health care delivery. Health Economics 17(10) (2008), pp. 1107–1128], but a long-standing concern is that DEA assumes that data are measured without error. This is quite unlikely, and DEA and other efficiency analysis techniques may yield biased efficiency estimates if it is not realized [B.J. Gajewski, R. Lee, M. Bott, U. Piamjariyakul, and R.L. Taunton, On estimating the distribution of data envelopment analysis efficiency scores: an application to nursing homes’ care planning process. Journal of Applied Statistics 36(9) (2009), pp. 933–944; J. Ruggiero, Data envelopment analysis with stochastic data. Journal of the Operational Research Society 55 (2004), pp. 1008–1012]. We propose to address measurement error systematically using a Bayesian method (Bayesian DEA). We will apply Bayesian DEA to data from the National Database of Nursing Quality Indicators^® to estimate nursing units’ efficiency. Several external reliability studies inform the posterior distribution of the measurement error on the DEA variables. We will discuss the case of generalizing the approach to situations where an external reliability study is not feasible.     

A Method to Handle Zero Counts in the Multinomial Model

In the context of an objective Bayesian approach to the multinomial model, Dirichlet(a, …, a) priors with a < 1 have previously been shown to be inadequate in the presence of zero counts, suggesting that the uniform prior (a = 1) is the preferred candidate. In the presence of many zero counts, however, this prior may not be satisfactory either. A model selection approach is proposed, allowing for the possibility of zero parameters corresponding to zero count categories. This approach results in a posterior mixture of Dirichlet distributions and marginal mixtures of beta distributions, which seem to avoid the problems that potentially result from the various proposed Dirichlet priors, in particular in the context of extreme data with zero counts.     

A Hellinger distance approach to MCMC diagnostics

Bayesian analysis often requires the researcher to employ Markov Chain Monte Carlo (MCMC) techniques to draw samples from a posterior distribution which in turn is used to make inferences. Currently, several approaches to determine convergence of the chain as well as sensitivities of the resulting inferences have been developed. This work develops a Hellinger distance approach to MCMC diagnostics. An approximation to the Hellinger distance between two distributions f and g based on sampling is introduced. This approximation is studied via simulation to determine the accuracy. A criterion for using this Hellinger distance for determining chain convergence is proposed as well as a criterion for sensitivity studies. These criteria are illustrated using a dataset concerning the Anguilla australis, an eel native to New Zealand.     

统计显著性:一个被误读的P值——基于美国统计学会的声明

美国统计学会"关于统计显著性与P值"的官方声明发布之后,再次引发国内外研究学者对P值的广泛关注。在介绍国内统计教材中假设检验的基本内容和步骤的基础上,以"硬币投掷"与"背影识人"为例直观性解释P值、统计显著性与统计功效等相关概念,并引用心理学统计经典调查案例分析P值被误读的原因。同时,基于美国统计学会的声明,给出正确使用P值的建议。     

Model Uncertainty and Bayesian Model Averaged Benchmark Dose Estimation for Continuous Data

The benchmark dose (BMD) approach has gained acceptance as a valuable risk assessment tool, but risk assessors still face significant challenges associated with selecting an appropriate BMD/BMDL estimate from the results of a set of acceptable dose‐response models. Current approaches do not explicitly address model uncertainty, and there is an existing need to more fully inform health risk assessors in this regard. In this study, a Bayesian model averaging (BMA) BMD estimation method taking model uncertainty into account is proposed as an alternative to current BMD estimation approaches for continuous data. Using the “hybrid” method proposed by Crump, two strategies of BMA, including both “maximum likelihood estimation based” and “Markov Chain Monte Carlo based” methods, are first applied as a demonstration to calculate model averaged BMD estimates from real continuous dose‐response data. The outcomes from the example data sets examined suggest that the BMA BMD estimates have higher reliability than the estimates from the individual models with highest posterior weight in terms of higher BMDL and smaller 90th percentile intervals. In addition, a simulation study is performed to evaluate the accuracy of the BMA BMD estimator. The results from the simulation study recommend that the BMA BMD estimates have smaller bias than the BMDs selected using other criteria. To further validate the BMA method, some technical issues, including the selection of models and the use of bootstrap methods for BMDL derivation, need further investigation over a more extensive, representative set of dose‐response data.