Bayesian Model of Behaviour in Economic Games

Classical game theoretic approaches that make strong rationality assumptions have difficulty modeling human behaviour in economic games. We investigate the role of finite levels of iterated reasoning and non-selfish utility functions in a Partially Observable Markov Decision Process model that incorporates game theoretic notions of interactivity. Our generative model captures a broad class of characteristic behaviours in a multi-round Investor-Trustee game. We invert the generative process for a recognition model that is used to classify 200 subjects playing this game against randomly matched opponents

Bayesian Model comparison of Higgs couplings

We investigate the possibility of contributions from physics beyond the Standard Model (SM) to the Higgs couplings, in the light of the LHC data. The work is performed within an interim framework where the magnitude of the Higgs production and decay rates are rescaled though Higgs coupling scale factors. We perform Bayesian parameter inference on these scale factors, concluding that there is good compatibility with the SM. Furthermore, we carry out Bayesian model comparison on all models where any combination of scale factors can differ from their SM values and find that typically models with fewer free couplings are strongly favoured. We consider the evidence that each coupling individually equals the SM value, making the minimal assumptions on the other couplings. Finally, we make a comparison of the SM against a single "not-SM" model, and find that there is moderate to strong evidence for the SM.Comment: 24 pages, 4 figure

Bayesian model selection and isocurvature perturbations

Present cosmological data are well explained assuming purely adiabatic perturbations, but an admixture of isocurvature perturbations is also permitted. We use a Bayesian framework to compare the performance of cosmological models including isocurvature modes with the purely adiabatic case; this framework automatically and consistently penalizes models which use more parameters to fit the data. We compute the Bayesian evidence for fits to a data set comprised of WMAP and other microwave anisotropy data, the galaxy power spectrum from 2dFGRS and SDSS, and Type Ia supernovae luminosity distances. We find that Bayesian model selection favors the purely adiabatic models, but so far only at low significance

Introducing doubt in Bayesian model comparison

There are things we know, things we know we dont know, and then there are things we dont know we dont know. In this paper we address the latter two issues in a Bayesian framework, introducing the notion of doubt to quantify the degree of (dis)belief in a model given observational data in the absence of explicit alternative models. We demonstrate how a properly calibrated doubt can lead to model discovery when the true model is unknown

Entropic Priors and Bayesian Model Selection

We demonstrate that the principle of maximum relative entropy (ME), used judiciously, can ease the specification of priors in model selection problems. The resulting effect is that models that make sharp predictions are disfavoured, weakening the usual Bayesian "Occam's Razor". This is illustrated with a simple example involving what Jaynes called a "sure thing" hypothesis. Jaynes' resolution of the situation involved introducing a large number of alternative "sure thing" hypotheses that were possible before we observed the data. However, in more complex situations, it may not be possible to explicitly enumerate large numbers of alternatives. The entropic priors formalism produces the desired result without modifying the hypothesis space or requiring explicit enumeration of alternatives; all that is required is a good model for the prior predictive distribution for the data. This idea is illustrated with a simple rigged-lottery example, and we outline how this idea may help to resolve a recent debate amongst cosmologists: is dark energy a cosmological constant, or has it evolved with time in some way? And how shall we decide, when the data are in?Comment: Presented at MaxEnt 2009, the 29th International Workshop on Bayesian Inference and Maximum Entropy Methods in Science and Engineering (July 5-10, 2009, Oxford, Mississippi, USA

Computational methods for Bayesian model choice

In this note, we shortly survey some recent approaches on the approximation of the Bayes factor used in Bayesian hypothesis testing and in Bayesian model choice. In particular, we reassess importance sampling, harmonic mean sampling, and nested sampling from a unified perspective.Comment: 12 pages, 4 figures, submitted to the proceedings of MaxEnt 2009, July 05-10, 2009, to be published by the American Institute of Physic

Bayesian Model Averaging in R

Bayesian model averaging has increasingly witnessed applications across an array of empirical contexts. However, the dearth of available statistical software which allows one to engage in a model averaging exercise is limited. It is common for consumers of these methods to develop their own code, which has obvious appeal. However, canned statistical software can ameliorate one's own analysis if they are not intimately familiar with the nuances of computer coding. Moreover, many researchers would prefer user ready software to mitigate the inevitable time costs that arise when hard coding an econometric estimator. To that end, this paper describes the relative merits and attractiveness of several competing packages in the statistical environment R to implement a Bayesian model averaging exercise.Model Averaging, Zellner's g Prior, BMS