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Bayesian inference for the information gain model.

ABSTRACT: One of the most popular paradigms to use for studying human reasoning involves the Wason card selection task. In this task, the participant is presented with four cards and a conditional rule (e.g., "If there is an A on one side of the card, there is always a 2 on the other side"). Participants are asked which cards should be turned to verify whether or not the rule holds. In this simple task, participants consistently provide answers that are incorrect according to formal logic. To account for these errors, several models have been proposed, one of the most prominent being the information gain model (Oaksford & Chater, Psychological Review, 101, 608-631, 1994). This model is based on the assumption that people independently select cards based on the expected information gain of turning a particular card. In this article, we present two estimation methods to fit the information gain model: a maximum likelihood procedure (programmed in R) and a bayesian procedure (programmed in WinBUGS). We compare the two procedures and illustrate the flexibility of the bayesian hierarchical procedure by applying it to data from a meta-analysis of the Wason task (Oaksford & Chater, Psychological Review, 101, 608-631, 1994). We also show that the goodness of fit of the information gain model can be assessed by inspecting the posterior predictives of the model. These bayesian procedures make it easy to apply the information gain model to empirical data. Supplemental materials may be downloaded along with this article from www.springerlink.com.

SUBMITTER: Stringer S

PROVIDER: S-EPMC3098374 | biostudies-literature |

REPOSITORIES: biostudies-literature

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Project description:BackgroundThe problems of correlation and classification are long-standing in the fields of statistics and machine learning, and techniques have been developed to address these problems. We are now in the era of high-dimensional data, which is data that can concern billions of variables. These data present new challenges. In particular, it is difficult to discover predictive variables, when each variable has little marginal effect. An example concerns Genome-wide Association Studies (GWAS) datasets, which involve millions of single nucleotide polymorphism (SNPs), where some of the SNPs interact epistatically to affect disease status. Towards determining these interacting SNPs, researchers developed techniques that addressed this specific problem. However, the problem is more general, and so these techniques are applicable to other problems concerning interactions. A difficulty with many of these techniques is that they do not distinguish whether a learned interaction is actually an interaction or whether it involves several variables with strong marginal effects.Methodology/findingsWe address this problem using information gain and Bayesian network scoring. First, we identify candidate interactions by determining whether together variables provide more information than they do separately. Then we use Bayesian network scoring to see if a candidate interaction really is a likely model. Our strategy is called MBS-IGain. Using 100 simulated datasets and a real GWAS Alzheimer's dataset, we investigated the performance of MBS-IGain.Conclusions/significanceWhen analyzing the simulated datasets, MBS-IGain substantially out-performed nine previous methods at locating interacting predictors, and at identifying interactions exactly. When analyzing the real Alzheimer's dataset, we obtained new results and results that substantiated previous findings. We conclude that MBS-IGain is highly effective at finding interactions in high-dimensional datasets. This result is significant because we have increasingly abundant high-dimensional data in many domains, and to learn causes and perform prediction/classification using these data, we often must first identify interactions.

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Bayesian inference for the information gain model.

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