Discussion of paper “nonparametric Bayesian inference in applications” by Peter Müller,Fernando A. Quintana and Garritt L. Page

This is an invited discussion of review paper “Nonparametric Bayesian Inference in Applications” by Peter Müller, Fernando A. Quintana and Garritt L. Page.     

Bayesian Procrustes analysis with applications to hydrology

In this paper, we introduce Procrustes analysis in a Bayesian framework, by treating the classic Procrustes regression equation from a Bayesian perspective, while modeling shapes in two dimensions. The Bayesian approach allows us to compute point estimates and credible sets for the full Procrustes fit parameters. The methods are illustrated through an application to radar data from short-term weather forecasts (nowcasts), a very important problem in hydrology and meteorology.     

A Unified Approach to Prior and Loss Robustness

ABSTRACT

We introduce a new statistical framework in order to study Bayesian loss robustness under classes of priors distributions, thus unifying both concepts of robustness. We propose measures that capture variation with respect to both prior selection and selection of loss function and explore general properties of these measures. We illustrate the approach for the continuous exponential family. Robustness in this context is studied first with respect to prior selection where we consider several classes of priors for the parameter of interest, including unimodal and symmetric and unimodal with positive support. After prior variation has been measured we investigate robustness to loss function, using Hellinger and Linex (Linear Exponential) classes of loss functions. The methods are applied to standard examples.     

Testing the Fit of Gamma Distributions Using the Empirical Moment Generating Function

ABSTRACT

This article presents goodness-of-fit tests for two and three-parameter gamma distributions that are based on minimum quadratic forms of standardized logarithmic differences of values of the moment generating function and its empirical counterpart. The test statistics can be computed without reliance to special functions and have asymptotic chi-squared distributions. Monte Carlo simulations are used to compare the proposed test for the two-parameter gamma distribution with goodness-of-fit tests employing empirical distribution function or spacing statistics. Two data sets are used to illustrate the various tests.     

Cumulant Plots for Assessing the Gamma Distribution

This article introduces graphical procedures for assessing the fit of the gamma distribution. The procedures are based on a standardized version of the cumulant generating function. Plots with bands of 95% simultaneous confidence level are developed by utilizing asymptotic and finite-sample results. The plots have linear scales and do not rely on the use of tables or values of special functions. Further, it is found through simulation, that the goodness-of-fit test implied by these plots compares favorably with respect to power to other known tests for the gamma distribution in samples drawn from lognormal and inverse Gaussian distributions.     

Household‐Level Coastal Adaptation and Its Drivers: A Systematic Case Study Review

Evidence‐based information on household‐level adaptation is an important element of integrated management of vulnerable coastal regions. A growing number of empirical studies deal with household‐level adaptation at the coast in different regions. This article provides a systematic review of these studies. We analyze studies according to how households in different parts of the world are currently adapting, or how they are intending to adapt, and identify explanatory factors for adaptation behavior and intention. We find that households implement a broad range of adaptation measures and that adaptation behavior is explained by individual factors such as socioeconomic and cognitive variables, experience, and perceived responsibilities. Nonpersonal characteristics have also been used to explain adaptation behavior and intention but have not been extensively investigated. Few studies employ qualitative research methods and use inductive approaches as well as models stemming from behavioral economics. Our findings suggest that coastal risk management policies should communicate the efficacy of household‐level adaptation, in addition to information about flood risk, in order to encourage coastal households in their adaptation activities. In this context, we discuss the role of resources and responsibility of households for their adaptation behavior. We describe the lessons learnt and formulate a research agenda on household‐level adaptation to coastal flood risk. In practice, coastal risk management policies should further promote individually driven adaptation by integrating it in adaptation strategies and processes.     

The relationship between foreign direct investment and economic growth: evidence from transition countries

This paper examines the importance of foreign direct investment on economic growth. Using a panel data set for 27 transition economies over the period 1991–2004 as well as the methodology of panel cointegration and causality tests, the empirical findings show that foreign direct investment does exhibit a significant relationship with economic growth, at least for those transition countries that are characterized by high levels of income and have implemented successful privatization programs.     

Bayesian semiparametric modeling for stochastic precedence,with applications in epidemiology and survival analysis

We propose a prior probability model for two distributions that are ordered according to a stochastic precedence constraint, a weaker restriction than the more commonly utilized stochastic order constraint. The modeling approach is based on structured Dirichlet process mixtures of normal distributions. Full inference for functionals of the stochastic precedence constrained mixture distributions is obtained through a Markov chain Monte Carlo posterior simulation method. A motivating application involves study of the discriminatory ability of continuous diagnostic tests in epidemiologic research. Here, stochastic precedence provides a natural restriction for the distributions of test scores corresponding to the non-infected and infected groups. Inference under the model is illustrated with data from a diagnostic test for Johne’s disease in dairy cattle. We also apply the methodology to the comparison of survival distributions associated with two distinct conditions, and illustrate with analysis of data on survival time after bone marrow transplantation for treatment of leukemia.     

Runs rules schemes for monitoring process variability

To increase the sensitivity of Shewhart control charts in detecting small process shifts sensitizing rules based on runs and scans are often used in practice. Shewhart control charts supplemented with runs rules for detecting shifts in process variance have not received as much attention as their counterparts for detecting shifts in process mean. In this article, we examine the performance of simple runs rules schemes for monitoring increases and/or decreases in process variance based on the sample standard deviation. We introduce one-sided S charts that overcome the weakness of high false-alarm rates when runs rules are added to a Shewhart control chart. The average run length performance and design aspects of the charts are studied thoroughly. The performance of associated two-sided control schemes is investigated as well.