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.     

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.     

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.     

Using Probability Boxes to Model Elicited Information: A Case Study

Governments are responsible for making policy decisions, often in the face of severe uncertainty about the factors involved. Expert elicitation can be used to fill information gaps where data are not available, cannot be obtained, or where there is no time for a full‐scale study and analysis. Various features of distributions for variables may be elicited, for example, the mean, standard deviation, and quantiles, but uncertainty about these values is not always recorded. Distributional and dependence assumptions often have to be made in models and although these are sometimes elicited from experts, modelers may also make assumptions for mathematical convenience (e.g., assuming independence between variables). Probability boxes (p‐boxes) provide a flexible methodology to analyze elicited quantities without having to make assumptions about the distribution shape. If information about distribution shape(s) is available, p‐boxes can provide bounds around the results given these possible input distributions. P‐boxes can also be used to combine variables without making dependence assumptions. This article aims to illustrate how p‐boxes may help to improve the representation of uncertainty for analyses based on elicited information. We focus on modeling elicited quantiles with nonparametric p‐boxes, modeling elicited quantiles with parametric p‐boxes where the elicited quantiles do not match the elicited distribution shape, and modeling elicited interval information.     

启发式教学在化工原理多媒体教学中的应用

结合化工原理多媒体教学的实践,介绍了启发式教学方法在电子教案制作中的体现,并就如何充分发挥多媒体教学优势提出了看法。     

A new class of mixture models for differential gene expression in DNA microarray data

One of the fundamental issues in analyzing microarray data is to determine which genes are expressed and which ones are not for a given group of subjects. In datasets where many genes are expressed and many are not expressed (i.e., underexpressed), a bimodal distribution for the gene expression levels often results, where one mode of the distribution represents the expressed genes and the other mode represents the underexpressed genes. To model this bimodality, we propose a new class of mixture models that utilize a random threshold value for accommodating bimodality in the gene expression distribution. Theoretical properties of the proposed model are carefully examined. We use this new model to examine the problem of differential gene expression between two groups of subjects, develop prior distributions, and derive a new criterion for determining which genes are differentially expressed between the two groups. Prior elicitation is carried out using empirical Bayes methodology in order to estimate the threshold value as well as elicit the hyperparameters for the two component mixture model. The new gene selection criterion is demonstrated via several simulations to have excellent false positive rate and false negative rate properties. A gastric cancer dataset is used to motivate and illustrate the proposed methodology.     

Measuring the Utility of Losses by Means of the Tradeoff Method

This paper investigates the shape of the utility function for losses. From a rational point of view it can be argued that utility should be concave. Empirically, measurements of the utility for losses show mixed results but most evidence supports convex rather than concave utilities. However, these measurements use methods that are either biased by the certainty effect or require complex parametrical estimations. This paper re-examines utility for losses, avoiding the mentioned pitfalls by using the tradeoff method. We find that utility for losses is convex. This is contrary to common assumption in the economics literature. Also, we investigate properties of the tradeoff method showing a new violation of procedure invariance. Our findings demonstrate that diminishing sensitivity is an important phenomenon for utility elicitation.