The evaluation of DNA evidence in pedigrees requiring population inference

Summary. The evaluation of nuclear DNA evidence for identification purposes is performed here taking account of the uncertainty about population parameters. Graphical models are used to detail the hypotheses being debated in a trial with the aim of obtaining a directed acyclic graph. Graphs also clarify the set of evidence that contributes to population inferences and they also describe the conditional independence structure of DNA evidence. Numerical illustrations are provided by re-examining three case-studies taken from the literature. Our calculations of the weight of evidence differ from those given by the authors of case-studies in that they reveal more conservative values.     

Three-level main-effects designs exploiting prior information about model uncertainty

To explore the projection efficiency of a design, Tsai, et al [2000. Projective three-level main effects designs robust to model uncertainty. Biometrika 87, 467–475] introduced the Q criterion to compare three-level main-effects designs for quantitative factors that allow the consideration of interactions in addition to main effects. In this paper, we extend their method and focus on the case in which experimenters have some prior knowledge, in advance of running the experiment, about the probabilities of effects being non-negligible. A criterion which incorporates experimenters’ prior beliefs about the importance of each effect is introduced to compare orthogonal, or nearly orthogonal, main effects designs with robustness to interactions as a secondary consideration. We show that this criterion, exploiting prior information about model uncertainty, can lead to more appropriate designs reflecting experimenters’ prior beliefs.     

Predictive Bayesian Microbial Dose-Response Assessment Based on Suggested Self-Organization in Primary Illness Response: Cryptosporidium parvum

The probability of illness caused by very low doses of pathogens cannot generally be tested due to the numbers of subjects that would be needed, though such assessments of illness dose response are needed to evaluate drinking water standards. A predictive Bayesian dose-response assessment method was proposed previously to assess the unconditional probability of illness from available information and avoid the inconsistencies of confidence-based approaches. However, the method uses knowledge of the conditional dose-response form, and this form is not well established for the illness endpoint. A conditional parametric dose-response function for gastroenteric illness is proposed here based on simple numerical models of self-organized host-pathogen systems and probabilistic arguments. In the models, illnesses terminate when the host evolves by processes of natural selection to a self-organized critical value of wellness. A generalized beta-Poisson illness dose-response form emerges for the population as a whole. Use of this form is demonstrated in a predictive Bayesian dose-response assessment for cryptosporidiosis. Results suggest that a maximum allowable dose of 5.0 x 10(-7) oocysts/exposure (e.g., 2.5 x 10(-7) oocysts/L water) would correspond with the original goals of the U.S. Environmental Protection Agency Surface Water Treatment Rule, considering only primary illnesses resulting from Poisson-distributed pathogen counts. This estimate should be revised to account for non-Poisson distributions of Cryptosporidium parvum in drinking water and total response, considering secondary illness propagation in the population.     

Causal Reasoning from Longitudinal Data*

Abstract. This paper reviews some of the key statistical ideas that are encountered when trying to find empirical support to causal interpretations and conclusions, by applying statistical methods on experimental or observational longitudinal data. In such data, typically a collection of individuals are followed over time, then each one has registered a sequence of covariate measurements along with values of control variables that in the analysis are to be interpreted as causes, and finally the individual outcomes or responses are reported. Particular attention is given to the potentially important problem of confounding. We provide conditions under which, at least in principle, unconfounded estimation of the causal effects can be accomplished. Our approach for dealing with causal problems is entirely probabilistic, and we apply Bayesian ideas and techniques to deal with the corresponding statistical inference. In particular, we use the general framework of marked point processes for setting up the probability models, and consider posterior predictive distributions as providing the natural summary measures for assessing the causal effects. We also draw connections to relevant recent work in this area, notably to Judea Pearl's formulations based on graphical models and his calculus of so‐called do‐probabilities. Two examples illustrating different aspects of causal reasoning are discussed in detail.     

Bayesian locally optimal design of knockout tournaments

The elimination or knockout format is one of the most common designs for pairing competitors in tournaments and leagues. In each round of a knockout tournament, the losers are eliminated while the winners advance to the next round. Typically, the goal of such a design is to identify the overall best player. Using a common probability model for expressing relative player strengths, we develop an adaptive approach to pairing players each round in which the probability that the best player advances to the next round is maximized. We evaluate our method using simulated game outcomes under several data-generating mechanisms, and compare it to random pairings, to the standard knockout format, and to two variants of the standard format.     

On an adaptive version of the Metropolis–Hastings algorithm with independent proposal distribution

In this paper, we present a general formulation of an algorithm, the adaptive independent chain (AIC), that was introduced in a special context in Gåsemyr et al . [ Methodol. Comput. Appl. Probab. 3 (2001)]. The algorithm aims at producing samples from a specific target distribution Π, and is an adaptive, non-Markovian version of the Metropolis–Hastings independent chain. A certain parametric class of possible proposal distributions is fixed, and the parameters of the proposal distribution are updated periodically on the basis of the recent history of the chain, thereby obtaining proposals that get ever closer to Π. We show that under certain conditions, the algorithm produces an exact sample from Π in a finite number of iterations, and hence that it converges to Π. We also present another adaptive algorithm, the componentwise adaptive independent chain (CAIC), which may be an alternative in particular in high dimensions. The CAIC may be regarded as an adaptive approximation to the Gibbs sampler updating parametric approximations to the conditionals of Π.     

A bayesian estimator for the dependence function of a bivariate extreme‐value distribution

Any continuous bivariate distribution can be expressed in terms of its margins and a unique copula. In the case of extreme‐value distributions, the copula is characterized by a dependence function while each margin depends on three parameters. The authors propose a Bayesian approach for the simultaneous estimation of the dependence function and the parameters defining the margins. They describe a nonparametric model for the dependence function and a reversible jump Markov chain Monte Carlo algorithm for the computation of the Bayesian estimator. They show through simulations that their estimator has a smaller mean integrated squared error than classical nonparametric estimators, especially in small samples. They illustrate their approach on a hydrological data set.     

Modeling External Risks in Project Management

To ascertain the viability of a project, undertake resource allocation, take part in bidding processes, and other related decisions, modern project management requires forecasting techniques for cost, duration, and performance of a project, not only under normal circumstances, but also under external events that might abruptly change the status quo. We provide a Bayesian framework that provides a global forecast of a project's performance. We aim at predicting the probabilities and impacts of a set of potential scenarios caused by combinations of disruptive events, and using this information to deal with project management issues. To introduce the methodology, we focus on a project's cost, but the ideas equally apply to project duration or performance forecasting. We illustrate our approach with an example based on a real case study involving estimation of the uncertainty in project cost while bidding for a contract.     

Bayesian analysis of outlier problems using divergence measures

A Bayesian approach is presented for detecting influential observations using general divergence measures on the posterior distributions. A sampling-based approach using a Gibbs or Metropolis-within-Gibbs method is used to compute the posterior divergence measures. Four specific measures are proposed, which convey the effects of a single observation or covariate on the posterior. The technique is applied to a generalized linear model with binary response data, an overdispersed model and a nonlinear model. An asymptotic approximation using Laplace method to obtain the posterior divergence is also briefly discussed.     

Modelling map positional error to infer true feature location

The authors consider the issue of map positional error, or the difference between location as represented in a spatial database (i.e., a map) and the corresponding unobservable true location. They propose a fully model‐based approach that incorporates aspects of the map registration process commonly performed by users of geographic informations systems, including rubber‐sheeting. They explain how estimates of positional error can be obtained, hence estimates of true location. They show that with multiple maps of varying accuracy along with ground truthing data, suitable model averaging offers a strategy for using all of the maps to learn about true location.