Methods for incorporating imprecision in engineering design decision-making are briefly reviewed and compared. A tutorial is presented on the Method of Imprecision (MoI), a formal method, based on the mathematics of fuzzy sets, for representing and manipulating imprecision in engineering design. The results of a design cost estimation example, utilizing a new informal cost specification, are presented. The MoI can provide formal information upon which to base decisions during preliminary engineering design and can facilitate set-based concurrent design.

Elicitation is a key task for subjectivist Bayesians. While skeptics hold that it cannot (or perhaps should not) be done, in practice it brings statisticians closer to their clients and subjectmatter-expert colleagues. This paper reviews the state-of-the-art, reflecting the experience of statisticians informed by the fruits of a long line of psychological research into how people represent uncertain information cognitively, and how they respond to questions about that information. In a discussion of the elicitation process, the first issue to address is what it means for an elicitation to be successful, i.e. what criteria should be employed? Our answer is that a successful elicitation faithfully represents the opinion of the person being elicited. It is not necessarily “true ” in some objectivistic sense, and cannot be judged that way. We see elicitation as simply part of the process of statistical modeling. Indeed in a hierarchical model it is ambiguous at which point the likelihood ends and the prior begins. Thus the same kinds of judgment that inform statistical modeling in general also inform elicitation of prior distributions.

The decision to examine a message at a particular point in time should be made rationally and economically if the message recipient is to operate efficiently.

With the increasing role of computational modeling in engineering design, performance estimation, and safety assessment, improved methods are needed for comparing computational results and experimental measurements. Traditional methods of graphically comparing computational and experimental results, though valuable, are essentially qualitative. Computable measures are needed that can quantitatively compare computational and experimental results over a range of input, or control, variables to sharpen assessment of computational accuracy. This type of measure has been recently referred to as a validation metric. We discuss various features that we believe should be incorporated in a validation metric, as well as features that we believe should be excluded. We develop a new validation metric that is based on the statistical concept of confidence intervals. Using this fundamental concept, we construct two specific metrics: one that requires interpolation of experimental data and one that requires regression (curve fitting) of experimental data. We apply the metrics to three example problems: thermal decomposition of a polyurethane foam, a turbulent buoyant plume of helium, and compressibility effects on the growth rate of a turbulent free-shear layer. We discuss how the present metrics are easily interpretable for assessing computational model accuracy, as well as the impact of experimental measurement uncertainty on the accuracy assessment.

A basic issue in social influence is how best to change one’s judgment in response to learning the opinions of others. This article examines the strategies that people use to revise their quantitative estimates on the basis of the estimates of another person. The authors note that people tend to use 2 basic strategies when revising estimates: choosing between the 2 estimates and averaging them. The authors developed the probability, accuracy, redundancy (PAR) model to examine the relative effectiveness of these two strategies across judgment environments. A surprising result was that averaging was the more effective strategy across a wide range of commonly encountered environments. The authors observed that despite this finding, people tend to favor the choosing strategy. Most participants in these studies would have achieved greater accuracy had they always averaged. The identification of intuitive strategies, along with a formal analysis of when they are accurate, provides a basis for examining how effectively people use the judgments of others. Although a portfolio of strategies that includes averaging and choosing can be highly effective, the authors argue that people are not generally well adapted to the environment in terms of strategy selection.

As we are moving into the post genome-sequencing era, various high-throughput experimental techniques have been developed to characterize biological systems at the genome scale. Discovering new biological knowledge from high-throughput biological data is a major challenge for bioinformatics today. To address this challenge, we developed a Bayesian statistical method together with Boltzmann machine and simulated annealing for protein function prediction in the yeast Saccharomyces cerevisiae through integrating various high-throughput biological data, including protein binary interactions, protein complexes and microarray gene expression profiles. In our approach, we quantified the relationship between functional similarity and high-throughput data. Based on our method, 1802 out of 2280 unannotated proteins in the yeast were assigned functions systematically. The related computer package is available upon request. 1.

Bayesian statistics is based on the subjective definition of probability as "degree of belief " and on Bayes' theorem, the basic tool for assigning probabilities to hypotheses combining a priori judgements and experimental information. This was the original point of view of Bayes, Bernoulli, Gauss, Laplace, etc. and contrasts with later "conventional" (pseudo-)definitions of probabilities, which implicitly presuppose the concept of probability. These notes show that the Bayesian approach is the natural one for data analysis in the most general sense, and for assigning uncertainties to the results of physical measurements - while at the same time resolving philosophical aspects of the problems. The approach, although little known and usually misunderstood among the High Energy Physics community, has become the standard way of reasoning in several fields of research and has recently been adopted by the international metrology organizations in their recommendations for asses...

Abstract. In this paper we present a novel approach to modelling a manufacturing process that allows one to learn about causal mechanisms of manufacturing defects through a Process Modelling and Executable Bayesian Network (PMEBN). The method combines probabilistic reasoning with time dependent parameters which are of crucial interest to quality control in manufacturing environments. We demonstrate the concept through a case study of a caravan manufacturing line using inspection data. 1

Our goal is to assess how confident we can be in rules induced from training data, rather than propose how they should be induced in the first place. The standard confirmation-theoretic approach is rejected in favour of estimating the domain accuracies of rules. This is done in both the Classical and Bayesian paradigms. We account for the effect of noisy data. Some recent empirical results on the significance of compressive clauses are explained. Keywords: confirmation, machine learning, Classical estimation, Bayesian estimation, compression, significance, noise. 1 Confirmation Theory and Machine Learning Confirmation theory concerns the relation between three objects; a hypothesis, a set of evidence and background knowledge. The task is to measure the confirmation of the hypothesis by the evidence relative to the given background knowledge. Typically the hypothesis is some universal formula (rule) : H = 8x : A(x) ! C(x) (1) the evidence is a finite set of ground atoms (facts), rele...

this report was to study the value of climate data from the