Subjective elicitation of hyperparameters of a conjugate Dirichlet prior and the corresponding Bayes analysis

Abstract

The paper elicits subjectively the Dirichlet prior hyperparameters based on the realistic opinion collected from the experts. The procedure used for subjective elicitation considers several stages such as the choice of experts, formation of some relevant questions to be asked to the experts for getting their opinion, pooling of opinion, quantification of information and then the formation of exact prior distribution through quantile assessment based on an iterative procedure. The resulting prior distribution is used to provide the Bayes analysis assuming multinomial sampling plan. The results are illustrated by means of a data set involving two life style factors of gallbladder carcinoma patients. The results convey the message that matches closely with the opinion given by the medical experts.     

Prbposterior expected loss as a scoring rule for prior distributions

A scoring rule for evaluating the usefulness of an assessed prior distribution should reflect the purpose for which the distribution is to be used. In this paper we suppose that sample data is to become available and that the posterior distribution will be used to estimate some quantity under a quadratic loss function. The utility of a prior distribution is consequently determined by its preposterior expected quadratic loss. It is shown that this loss function has properties desirable in a scoring rule and formulae are derived for calculating the scores it gives in some common problems. Many scoring rules give a very poor score to any improper prior distribution but, in contrast, the scoring rule proposed here provides a meaningful measure for comparing the usefulness of assessed prior distributions and non-informative (improper) prior distributions. Results for making this comparison in various situations are also given.     

Adversarial risk analysis for counterterrorism modeling

Recent large-scale terrorist attacks have raised interest in models for resource allocation against terrorist threats. The unifying theme in this area is the need to develop methods for the analysis of allocation decisions when risks stem from the intentional actions of intelligent adversaries. Most approaches to these problems have a game-theoretic flavor although there are also several interesting decision-analytic-based proposals. One of them is the recently introduced framework for adversarial risk analysis, which deals with decision-making problems that involve intelligent opponents and uncertain outcomes. We explore how adversarial risk analysis addresses some standard counterterrorism models: simultaneous defend-attack models, sequential defend-attack-defend models, and sequential defend-attack models with private information. For each model, we first assess critically what would be a typical game-theoretic approach and then provide the corresponding solution proposed by the adversarial risk analysis framework, emphasizing how to coherently assess a predictive probability model of the adversary's actions, in a context in which we aim at supporting decisions of a defender versus an attacker. This illustrates the application of adversarial risk analysis to basic counterterrorism models that may be used as basic building blocks for more complex risk analysis of counterterrorism problems.     

Structured expert elicitation about Listeria monocytogenes cross-contamination in the environment of retail deli operations in the United States

Listeria monocytogenes is among the foodborne pathogens with the highest death toll in the United States. Ready‐to‐eat foods contaminated at retail are an important source of infection. Environmental sites in retail deli operations can be contaminated. However, commonly contaminated sites are unlikely to come into direct contact with food and the public health relevance of environmental contamination has remained unclear. To identify environmental sites that may pose a considerable cross‐contamination risk, to elucidate potential transmission pathways, and to identify knowledge gaps, we performed a structured expert elicitation of 41 experts from state regulatory agencies and the food retail industry with practical experience in retail deli operations. Following the “Delphi” method, the elicitation was performed in three consecutive steps: questionnaire, review and discussion of results, second questionnaire. Hands and gloves were identified as important potential contamination sources. However, bacterial transfers to and from hands or gloves represented a major data gap. Experts agreed about transfer probabilities from cutting boards, scales, deli cases, and deli preparation sinks to product, and about transfer probabilities from floor drains, walk‐in cooler floors, and knife racks to food contact surfaces. Comparison of experts' opinions to observational data revealed a tendency among experts with certain demographic characteristics and professional opinions to overestimate prevalence. Experts’ votes clearly clustered into separate groups not defined by place of employment, even though industry experts may have been somewhat overrepresented in one cluster. Overall, our study demonstrates the value and caveats of expert elicitation to identify data gaps and prioritize research efforts.     

Advances on a Decision Analytic Approach to Exposure-Based Chemical Prioritization

The volume and variety of manufactured chemicals is increasing, although little is known about the risks associated with the frequency and extent of human exposure to most chemicals. The EPA and the recent signing of the Lautenberg Act have both signaled the need for high-throughput methods to characterize and screen chemicals based on exposure potential, such that more comprehensive toxicity research can be informed. Prior work of Mitchell et al. using multicriteria decision analysis tools to prioritize chemicals for further research is enhanced here, resulting in a high-level chemical prioritization tool for risk-based screening. Reliable exposure information is a key gap in currently available engineering analytics to support predictive environmental and health risk assessments. An elicitation with 32 experts informed relative prioritization of risks from chemical properties and human use factors, and the values for each chemical associated with each metric were approximated with data from EPA's CP_CAT database. Three different versions of the model were evaluated using distinct weight profiles, resulting in three different ranked chemical prioritizations with only a small degree of variation across weight profiles. Future work will aim to include greater input from human factors experts and better define qualitative metrics.     

The Value of Performance Weights and Discussion in Aggregated Expert Judgments

In risky situations characterized by imminent decisions, scarce resources, and insufficient data, policymakers rely on experts to estimate model parameters and their associated uncertainties. Different elicitation and aggregation methods can vary substantially in their efficacy and robustness. While it is generally agreed that biases in expert judgments can be mitigated using structured elicitations involving groups rather than individuals, there is still some disagreement about how to best elicit and aggregate judgments. This mostly concerns the merits of using performance‐based weighting schemes to combine judgments of different individuals (rather than assigning equal weights to individual experts), and the way that interaction between experts should be handled. This article aims to contribute to, and complement, the ongoing discussion on these topics.     

Nonparametric goodness-of-fit

This paper develops an approach to testing the adequacy of both classical and Bayesian models given sample data. An important feature of the approach is that we are able to test the practical scientific hypothesis of whether the true underlying model is close to some hypothesized model. The notion of closeness is based on measurement precision and requires the introduction of a metric for which we consider the Kolmogorov distance. The approach is nonparametric in the sense that the model under the alternative hypothesis is a Dirichlet process.     

A Method for Eliciting Utilities and its Application to Collective Choice

Designing a mechanism that provides a direct incentive for an individual to report her utility function over several alternatives is a difficult task. A framework for such mechanism design is the following: an individual (a decision maker) is faced with an optimization problem (e.g., maximization of expected utility), and a mechanism designer observes the decision maker’s action. The mechanism does reveal the individual’s utility truthfully if the mechanism designer, having observed the decision maker’s action, infers the decision maker’s utilities over several alternatives. This paper studies an example of such a mechanism and discusses its application to the problem of optimal social choice. Under certain simplifying assumptions about individuals’ utility functions and about how voters choose their voting strategies, this mechanism selects the alternative that maximizes Harsanyi’s social utility function and is Pareto-efficient.     

Bayesian analysis of multivariate mortality data with large families

This paper presents a Bayesian method for the analysis of toxicological multivariate mortality data when the discrete mortality rate for each family of subjects at a given time depends on familial random effects and the toxicity level experienced by the family. Our aim is to model and analyse one set of such multivariate mortality data with large family sizes: the potassium thiocyanate (KSCN) tainted fish tank data of O'Hara Hines. The model used is based on a discretized hazard with additional time-varying familial random effects. A similar previous study (using sodium thiocyanate (NaSCN)) is used to construct a prior for the parameters in the current study. A simulation-based approach is used to compute posterior estimates of the model parameters and mortality rates and several other quantities of interest. Recent tools in Bayesian model diagnostics and variable subset selection have been incorporated to verify important modelling assumptions regarding the effects of time and heterogeneity among the families on the mortality rate. Further, Bayesian methods using predictive distributions are used for comparing several plausible models.