this paper we try our hands at it. One version of the classical theory of factorial experiments, going back to Fisher and further developed by Kempthorne (1955), completely avoids distributional assumptions, assuming only additivity, and uses randomisation to derive the standard tests of hypotheses about treatment effects. Here, we are interested in the more familiar classical approach via linear modelling and normal distribution theory. The corresponding Bayesian analysis has been developed mainly in the pioneering works of Box & Tiao (1973) and Lindley & Smith (1972). Box & Tiao (1973, Chapter 6) discuss Bayesian analysis of cross classified designs, including fixed, random and mixed effects models. They point out that in a Bayesian approach the appropriate inference procedure for fixed and random effects "depends upon the nature of the prior distribution used to represent the behavior of the factors". They also show (Chapter 7) that shrinkage estimates of specific effects may result when a random effects model is assumed. Lindley & Smith (1972) use a hierarchically structured linear model built on multivariate normal components (special cases of the model are considered by Lindley, 1972 and Smith, 1973), with the focus on estimation of treatment effects. These are authoritative and attractive approaches, albeit with modest compromises to the Bayesian paradigm -- in respect of the estimation of the variance components -- necessitated by the computational limitations of the time. Nevertheless, the inference is almost entirely estimative: questions about the indistinguishability of factor levels, or more general hypotheses about contrasts, are answered indirectly trough their joint posterior distribution, e.g. by checking whether the hypothesis falls in a highest poster...

Text classification involves deciding whether or not a document is about a given topic. It is an important problem in machine learning, because automated text classifiers have enormous potential for application in information retrieval systems. It is also an interesting problem for cognitive science, because it involves real world human decision making with complicated stimuli. This paper develops two models of human text document classification based on random walk and accumulator sequential sampling processes. The models are evaluated using data from an experiment where participants classify text documents presented one word at a time under task instructions that emphasize either speed or accuracy, and rate their confidence in their decisions. Fitting the random walk and accumulator models to these data shows that the accumulator provides a better account of the decisions made, and a “balance of evidence ” measure provides the best account of confidence. Both models are also evaluated in the applied information retrieval context, by comparing their performance to established machine learning techniques on the standard Reuters-21578 corpus. It is found that they are almost as accurate as the benchmarks, and make decisions much more quickly because they only need to examine a small proportion of the words in the document. In addition, the ability of the accumulator model to produce useful confidence measures is shown to have application in prioritizing the results of classification decisions.

By rejecting the use of a prior distribution over parameters, orthodox statistics is forced to focus on estimators, functions which guess parameter values, and to invent heuristics for choosing among estimators. Two popular heuristics are unbiasedness and maximum likelihood. Since these heuristics are not consistent with Bayes' rule, they are also not consistent with the axioms of common sense from which Bayes' rule is derived. Hence we expect there to be situations in which they violate common sense and indeed it is not hard to find such situations. This paper reviews a few simple, realistic scenarios where pathologies occur with either the unbiasedness heuristic or the maximum likelihood heuristic. 1 Introduction Many inference problems work like this: we observe some data and want to infer something about the process that generated it. If we have a probability distribution over possible processes, parameterized by `, then there is general agreement that Bayes' rule solves ...

This paper appeared in the proceedings of the ECML 2006,

Feedback control schemes have been widely used in many engineering applications for a long time. Despite this, there has been very little work done on efficient design of experiments for modeling feedback control processes in order to select the appropriate feedback variables. This paper considers a general statistical formulation of this problem and studies the properties of optimal designs in the first-order case. Locally optimal designs under A- and D-optimality criteria as well as Bayesian optimal designs are developed. These results are used to characterize the properties of these designs and to contrast them with traditional optimal designs without feedback variables. In particular, the relative efficiency of the traditional designs is studied for various situations of practical interest.

Medical devices often contain many tunable parameters. The optimal setting of these parameters depends on the patient’s utility function, which is often unknown. This raises two questions. First, how should we optimize the parameters given partial information about the patient’s utility? And secondly, what questions do we ask to efficiently elicit this utility information? In this paper, we present a coherent probabilistic decision-theoretic framework to answer these questions. We illustrate the potential of this framework on a toy problem and discuss directions for future research. 1

DISTRIBUTION STATEMENT A. Approved for public release; distribution is unlimited. This document has been reproduced from the best available copy. Available to DOE and DOE contractors from ES&H Technical Information

this paper, wec9W;W2 twoapproac hes to understanding how humans solve visually presented SPs. he first assumes a global-to-loc al proc essing strategy, in whic h a rough globalreferenc frame is first established, into whic h loc al information is then integrated. We foc9 on a well-developed spec;C instantiation of this approac h, known as the cT vex hull hypothesis (Mac Gregor & Ormerod 1996), whic h assumes that solutions are guided by the boundary points in the stimulus array. We review the theoretic; and empiricT evidenc e for and against this hypothesis, before suggesting an alternative loc al-to-global approac h. Under this alternativeapproac h, solutions are assumed to be primarily guided by lo procT9;01 cT9;019T ts, suc h as the avoidanc of intersecTGII incC20R1TGIIC a tour. oc ompare these twoapproac hes empiric ally, we present an experiment that measures the di#erent e#ec; the number of points on thec onvex hull and the number of potential intersec9T ns have on human performanc; GwGwwwG cal Processing Gregor and Ormerod (1996) found that the group performanc e of observers in two experiments surpassed that of a suite ofc omputational heuristic and was soc lose to the best known solutions that there were no individual di#erencG and there was zero c rrelation between performa ac6 ss di#erent problems. On this basis, theyc ncyTCW that thec onsistent ability to arrive at near-optimal solutions argued for the operation of ac ommon underlying pro coT or set of procoT6I and suggested thatsuc h procoTC0 might c orrespond to natural organizing tendenc ies of the visual system. This lastc onc lusion isc onsistent with an experiment by Pomerantz (1981), who found that observers, asked tocTI6;I up the dots in arrays, to illustrate how they percR9 ed the arrays, frequentl...

Testing the hypothesis H that k>1 binomial parameters are equal and jointly estimating these parameters are related problems. A Bayesian argument can simultaneously answer these inference questions: to test the hypothesis H the posterior probability λ = λ(H | x) ofH given the experimental data x can be used; to estimate each binomial parameter, their Bayesian estimates under H and its complement ¯ H are combined, with weights λ and 1 − λ, respectively.

This dissertation generalizes Duncan/s k-ratio methodology to include a covariate. The analysis assumes proportionality between the covariance matrix of the prior distribution for the true treatment means and the covariance matrix of the conditional distribution of the observations given the values of the true treatment means. When the covariance matrices are known, analysis demonstrates that the power for the covariate k-ratio procedure is increasingly greater than the power of Duncan/s k-ratio test as the correlation between the variable under investigation and the covariate increases. The dissertation also investigates the effect of three nuisance parameters on the power function: