Alleviating inflation of conditional predictions

Previous studies indicated that conditional predictions—the assessed probability that a certain outcome will occur given a certain condition—tend to be markedly inflated. Five experiments tested the effects of manipulations that were expected to alleviate this inflation by inducing participants to engage in analytic processing. Rewarding participants for accurate predictions proved ineffective. A training procedure in which participants assessed the likelihood of each of several outcomes before assessing the probability of a target outcome was partly effective in reducing overestimation. Most effective was the requirement to work in dyads and to come to an agreement about the assessed likelihood. Working in dyads helped alleviate prediction inflation even after participants made their individual predictions alone, and its debiasing effect also transferred to the estimates that were made individually on a new set of stimuli. The results were discussed in terms of the factors that make prediction inflation resistant to change.     

A short proof of a theorem of Falmagne

Falmagne (J. Math. Psychol. 18 (1978) 52) proved the sufficiency of the Block-Marschak inequalities (in: I. Olkin, S. Ghurye, W. Hoefding, W. Madow, H. Mann (Eds.), Contributions to Probability and Statistics, Stanford University Press, Stanford, CA, 1960, pp. 97-132) and normalization equalities for a complete system of choice probabilities to be induced by rankings. Here, we give a considerably shorter proof of this result. Our approach combines Möbius inversion and network flows.     

An overview of algorithmic approaches to compute optimum entropy distributions in the expert system shell MECore (extended version)

The expert system shell MECore provides a series of knowledge management operations to define probabilistic knowledge bases and to reason under uncertainty. To provide a reference work for MECore algorithmics, we bring together results from different sources that have been applied in MECore and explain their intuitive ideas. Additionally, we report on our ongoing work regarding further development of MECore's algorithms to compute optimum entropy distributions and provide some empirical results. Altogether this paper explains the intuition of important theoretical results and their practical implications, compares old and new algorithmic approaches and points out their benefits as well as possible limitations and pitfalls.     

Single-case probabilities and the case of Monty Hall: Levy’s view

In Baumann (American Philosophical Quarterly 42: 71–79, 2005) I argued that reflections on a variation of the Monty Hall problem throws a very general skeptical light on the idea of single-case probabilities. Levy (Synthese, forthcoming, 2007) puts forward some interesting objections which I answer here.     

Nonmonotonic conditionals that behave like conditional probabilities above a threshold

I'll describe a range of systems for nonmonotonic conditionals that behave like conditional probabilities above a threshold. The rules that govern each system are probabilistically sound in that each rule holds when the conditionals are interpreted as conditional probabilities above a threshold level specific to that system. The well-known preferential and rational consequence relations turn out to be special cases in which the threshold level is 1. I'll describe systems that employ weaker rules appropriate to thresholds lower than 1, and compare them to these two standard systems.     

Ordinal data,ordered scale points,and order statistics

This paper concerns ordinal responses. An ordered Dirichlet distribution describes prior and posterior beliefs about the cumulative probabilities of response categories. Associating the response categories with intervals of a latent random variable then induces a distribution on the order statistics of that variable. The psychometrician can use the asymptotic theory of order statistics to learn how distributional assumptions about the latent variable effect inference. An example relates the skewness of a latent variable to the proportional odds and proportional hazards models of McCullagh [1980].     

On Holland's Dutch identity conjecture

The manifest probabilities of observed examinee response patterns resulting from marginalization with respect to the latent ability distribution produce the marginal likelihood function in item response theory. Under the conditions that the posterior distribution of examinee ability given some test response pattern is normal and the item logit functions are linear, Holland (1990a) gives a quadratic form for the log-manifest probabilities by using the Dutch Identity. Further, Holland conjectures that this special quadratic form is a limiting one for all smooth unidimensional item response models as test length tends to infinity. The purpose of this paper is to give three counterexamples to demonstrate that Holland's Dutch Identity conjecture does not hold in general. The counterexamples suggest that only under strong assumptions can it be true that the limits of log-manifest probabilities are quadratic. Three propositions giving sets of such strong conditions are given.