Processing Data from Social Dilemma Experiments: A Bayesian Comparison of Parametric Estimators

Observed choices in Social Dilemma Games usually take the form of bounded integers. We propose a doubly-truncated count data framework to process such data. We compare this framework to past approaches based on ordered outcomes and truncated continuous densities using Bayesian estimation and model selection techniques. We find that all three frameworks (i) support the presence of unobserved heterogeneity in individual decision-making, and (ii) agree on the ranking of regulatory treatment effects. The count data framework exhibits superior efficiency and produces more informative predictive distributions for outcomes of interest. The continuous framework fails to allocate adequate probability mass to boundary outcomes, which are often of pivotal importance in these games.Social dilemma games; Hierarchical modeling; Bayesian simulation; Common property resource

Bayesian variable selection with shrinking and diffusing priors

We consider a Bayesian approach to variable selection in the presence of high dimensional covariates based on a hierarchical model that places prior distributions on the regression coefficients as well as on the model space. We adopt the well-known spike and slab Gaussian priors with a distinct feature, that is, the prior variances depend on the sample size through which appropriate shrinkage can be achieved. We show the strong selection consistency of the proposed method in the sense that the posterior probability of the true model converges to one even when the number of covariates grows nearly exponentially with the sample size. This is arguably the strongest selection consistency result that has been available in the Bayesian variable selection literature; yet the proposed method can be carried out through posterior sampling with a simple Gibbs sampler. Furthermore, we argue that the proposed method is asymptotically similar to model selection with the $L_0$ penalty. We also demonstrate through empirical work the fine performance of the proposed approach relative to some state of the art alternatives.Comment: Published in at http://dx.doi.org/10.1214/14-AOS1207 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

The latent process decomposition of cDNA microarray data sets

We present a new computational technique (a software implementation, data sets, and supplementary information are available at http://www.enm.bris.ac.uk/lpd/) which enables the probabilistic analysis of cDNA microarray data and we demonstrate its effectiveness in identifying features of biomedical importance. A hierarchical Bayesian model, called latent process decomposition (LPD), is introduced in which each sample in the data set is represented as a combinatorial mixture over a finite set of latent processes, which are expected to correspond to biological processes. Parameters in the model are estimated using efficient variational methods. This type of probabilistic model is most appropriate for the interpretation of measurement data generated by cDNA microarray technology. For determining informative substructure in such data sets, the proposed model has several important advantages over the standard use of dendrograms. First, the ability to objectively assess the optimal number of sample clusters. Second, the ability to represent samples and gene expression levels using a common set of latent variables (dendrograms cluster samples and gene expression values separately which amounts to two distinct reduced space representations). Third, in contrast to standard cluster models, observations are not assigned to a single cluster and, thus, for example, gene expression levels are modeled via combinations of the latent processes identified by the algorithm. We show this new method compares favorably with alternative cluster analysis methods. To illustrate its potential, we apply the proposed technique to several microarray data sets for cancer. For these data sets it successfully decomposes the data into known subtypes and indicates possible further taxonomic subdivision in addition to highlighting, in a wholly unsupervised manner, the importance of certain genes which are known to be medically significant. To illustrate its wider applicability, we also illustrate its performance on a microarray data set for yeast

ISIPTA'07: Proceedings of the Fifth International Symposium on Imprecise Probability: Theories and Applications

B