A Hierarchical Bayesian meta-analysis model developed by Dumouchel is derived by implementing the General Bayesian Linear model (GBLM) theorem. The aim is to obtain the joint posterior distribution of all parameters in the model. Simulation study is conducted to confirm the estimation of all parameters of interest. Results show parameter estimates as close to the true values indicating paramete...

We study algorithmic randomness and monotone complexity on product of the set of infinite binary sequences. We explore the following problems: monotone complexity on product space, Lambalgen’s theorem for correlated probability, classification of random sets by likelihood ratio tests, decomposition of complexity and independence, Bayesian statistics for individual random sequences. Formerly Lam...

This paper provides new foundations for Bayesian Decision Theory based on a representation theorem for preferences de…ned on a set of prospects containing both factual and conditional possibilities. This use of a rich set of prospects not only provides a framework within which the main theoretical claims of Savage, Ramsey, Je¤rey and others can be stated and compared, but also allows for the po...

Hierarchical latent class (HLC) models are tree-structured Bayesian networks where leaf nodes are observed while internal nodes are latent. There are no theoretically well justified model selection criteria for HLC models in particular and Bayesian networks with latent nodes in general. Nonetheless, empirical studies suggest that the BIC score is a reasonable criterion to use in practice for le...

Extends McAllester’s PAC-Bayesian theorem [4], allowing for other tail bounds than Hoeffding’s, and simplifies the proof somewhat. 1 McAllester’s PAC-Bayesian theorem McAllester’s PAC-Bayesian theorem is an astonishing result. Although its proof requires only elementary techniques, it can be used to obtain very tight generalization error bounds for the Gibbs versions of (approximate) Bayesian c...

In this work, a method which can generate high quality inverse halftone images from halftone images is proposed. This method uses least-mean-square (LMS) trained filters to establish the relationship between the current processing position and its corresponding neighbor positions in each kind of halftone image. This includes direction binary search (DBS), error diffusion, dot diffusion, and ord...

We introduce a novel notion of probability within quantum history theories and give a Gleasonesque proof for these assignments. This involves introducing a tentative novel axiom of probability. We also discuss the use of these probabilities and we introduce a tentative generalised notion of Shannon entropy.

Kuhn’s Theorem shows that extensive games with perfect recall can equivalently be analyzed using mixed or behavioral strategies, as long as players are expected utility maximizers. This note constructs an example that illustrates the limits of Kuhn’s Theorem in an environment with ambiguity averse players who use a maxmin decision rule and full Bayesian updating.

Bayesian Networks (BNs) are popular graphical models for the representation of statistical problems embodying dependence relationships between a number of variables. Much of this popularity is due to the d-separation theorem of Pearl and Lauritzen, which allows an analyst to identify the conditional independence statements that a model of the problem embodies using only the topology of the grap...

The term ”global games” was introduced by Carlson and Van Damme in their classic 1993 Econometrica paper to describe a type of Bayesian game. In this type of game, the players’ payoffs for a given strategy profile also depends on the realization of a fundamental ”state of the economy”, which is unobserved.The fundamental has a prior distribution which is common knowledge. At the start of the pl...