Nonparametric empirical Bayes for the Dirichlet process mixture model

The Dirichlet process prior allows flexible nonparametric mixture modeling. The number of mixture components is not specified in advance and can grow as new data arrive. However, analyses based on the Dirichlet process prior are sensitive to the choice of the parameters, including an infinite-dimensional distributional parameter G ₀. Most previous applications have either fixed G ₀ as a member of a parametric family or treated G ₀ in a Bayesian fashion, using parametric prior specifications. In contrast, we have developed an adaptive nonparametric method for constructing smooth estimates of G ₀. We combine this method with a technique for estimating α, the other Dirichlet process parameter, that is inspired by an existing characterization of its maximum-likelihood estimator. Together, these estimation procedures yield a flexible empirical Bayes treatment of Dirichlet process mixtures. Such a treatment is useful in situations where smooth point estimates of G ₀ are of intrinsic interest, or where the structure of G ₀ cannot be conveniently modeled with the usual parametric prior families. Analysis of simulated and real-world datasets illustrates the robustness of this approach.     

Hepatitis C psychoeducation curriculum topics generated by group members

ABSTRACT

Educational programs for hepatitis C (HCV) have been created by professionals. There has not been a focus on whether what clients want to know about HCV differs from what providers want patients to know. This study addresses this gap by examining topics selected by participants in an education/support group model. Data were collected as part of a randomized psychoeducation trial for patients with HCV. Topics were systematically generated by the members uniquely for each group. Topics and rank order for each group were generated and a combined variable was created. Twenty-eight different topics were identified across 12 groups. The total number of topics was 102, averaging 8.5 per group. Topics are divided into three separate conceptual groups, members’ personal relationship to HCV, medical aspects of HCV, and unique concerns. A patient-centered approach that addresses the needs of HCV patients first provides an optimal starting point to discuss HCV disease management.     

How Plant Managers' Experiences and Attitudes Toward Sustainability Relate to Operational Performance

Managers are increasingly faced with pressure to think not just about profits, but also about their organization's environmental and social performance. This research provides a first examination of operational managers' experiences with and attitudes about employee well‐being and environmental issues, how these factors impact employee well‐being and environmental performance, and how the three performance measures interrelate. We use violations of Occupational Safety and Health Administration regulations and Toxic Release Inventory reports of emissions as proxies for employee well‐being and environmental performance. Our findings suggest that operational managers do not (yet) think in sustainability terms. However, employee well‐being and environmental performance do interact in a significant way with operational performance. Hence, operational managers would benefit from a more complete understanding of the relationships among the elements of the triple bottom line.     

Is Psychological Well-Being Linked to the Consumption of Fruit and Vegetables?

Little is known about the influence of people’s diet on their psychological well-being. This study provides evidence of a link between the consumption of fruit and vegetables and high well-being. In cross-sectional data, happiness and mental health rise in an approximately dose–response way with the number of daily portions of fruit and vegetables. Well-being peaks at approximately 7 portions per day. We document this relationship in three data sets, covering approximately 80,000 randomly selected British individuals, and for seven measures of well-being (life satisfaction, WEMWBS mental well-being, GHQ mental disorders, self-reported health, happiness, nervousness, and feeling low). The pattern is robust to adjustment for a large number of other demographic, social and economic variables. Reverse causality and problems of confounding remain possible. We discuss the strengths and weaknesses of our analysis, how government policy-makers might wish to react to it, and what kinds of further research—especially randomized trials—would be valuable.     

中国新疆维吾尔族乐器制作工艺

本调查通过对中国新疆喀什的一位乐器制作工匠的采访发现,维吾尔族的技能手工业是以维吾尔家庭为单位的,维吾尔族家庭的文化支持着维吾尔人的产业,并允许它在大规模生产和大量广告投放的今天继续生存下去,具体来说,维吾尔族家庭文化是制作工艺的强大后盾,所有权世代继承,同时客户也具有连续性。     

Coherent Frequentism: A Decision Theory Based on Confidence Sets

By representing fair betting odds according to one or more pairs of confidence set estimators, dual parameter distributions called confidence posteriors secure the coherence of actions without any prior distribution. This theory reduces to the maximization of expected utility when the pair of posteriors is induced by an exact or approximate confidence set estimator or when a reduction rule is applied to the pair. Unlike the p-value, the confidence posterior probability of an interval hypothesis is suitable as an estimator of the indicator of hypothesis truth since it converges to 1 if the hypothesis is true or to 0 otherwise.     

On the Bias of the Maximum Likelihood Estimator for the Two-Parameter Lomax Distribution

The Lomax (Pareto II) distribution has found wide application in a variety of fields. We analyze the second-order bias of the maximum likelihood estimators of its parameters for finite sample sizes, and show that this bias is positive. We derive an analytic bias correction which reduces the percentage bias of these estimators by one or two orders of magnitude, while simultaneously reducing relative mean squared error. Our simulations show that this performance is very similar to that of a parametric bootstrap correction based on a linear bias function. Three examples with actual data illustrate the application of our bias correction.     

An Improved Test for Continuous Local Martingales

We present a new test for the “continuous martingale hypothesis”. That is, a test for the hypothesis that observed data are from a process which is a continuous local martingale. The basis of the test is an embedded random walk at first passage times, obtained from the well-known representation of a continuous local martingale as a continuous time-change of Brownian motion. With a variety of simulated diffusion processes our new test shows higher power than existing tests using either the crossing tree or the quadratic variation, including the situation where non-negligible drift is present. The power of the test in the presence of jumps is also explored with a variety of simulated jump diffusion processes. The test is also applied to two sequences of high-frequency foreign exchange trade-by-trade data. In both cases the continuous martingale hypothesis is rejected at times less than hourly and we identify significant dependence in price movements at these small scales.     

Gamma shared frailty model based on reversed hazard rate

Abstract

Frailty models are used in survival analysis to account for unobserved heterogeneity in individual risks to disease and death. To analyze bivariate data on related survival times (e.g., matched pairs experiments, twin, or family data), shared frailty models were suggested. Shared frailty models are frequently used to model heterogeneity in survival analysis. The most common shared frailty model is a model in which hazard function is a product of random factor(frailty) and baseline hazard function which is common to all individuals. There are certain assumptions about the baseline distribution and distribution of frailty. In this paper, we introduce shared gamma frailty models with reversed hazard rate. We introduce Bayesian estimation procedure using Markov Chain Monte Carlo (MCMC) technique to estimate the parameters involved in the model. We present a simulation study to compare the true values of the parameters with the estimated values. Also, we apply the proposed model to the Australian twin data set.     

Modeling bivariate survival data using shared inverse Gaussian frailty model

ABSTRACT

The shared frailty models are often used to model heterogeneity in survival analysis. The most common shared frailty model is a model in which hazard function is a product of a random factor (frailty) and the baseline hazard function which is common to all individuals. There are certain assumptions about the baseline distribution and the distribution of frailty. In this paper, we consider inverse Gaussian distribution as frailty distribution and three different baseline distributions, namely the generalized Rayleigh, the weighted exponential, and the extended Weibull distributions. With these three baseline distributions, we propose three different inverse Gaussian shared frailty models. We also compare these models with the models where the above-mentioned distributions are considered without frailty. We develop the Bayesian estimation procedure using Markov Chain Monte Carlo (MCMC) technique to estimate the parameters involved in these models. We present a simulation study to compare the true values of the parameters with the estimated values. A search of the literature suggests that currently no work has been done for these three baseline distributions with a shared inverse Gaussian frailty so far. We also apply these three models by using a real-life bivariate survival data set of McGilchrist and Aisbett (1991 McGilchrist, C.A., Aisbett, C.W. (1991). Regression with frailty in survival analysis. Biometrics 47:461–466.[Crossref], [PubMed], [Web of Science ®] , [Google Scholar]) related to the kidney infection data and a better model is suggested for the data using the Bayesian model selection criteria.