We propose an original particle-based implementation of the Loopy Belief Propagation (LPB) algorithm for pairwise Markov Random Fields (MRF) on a continuous state space. The algorithm constructs adaptively efficient proposal distributions approximating the local beliefs at each note of the MRF. This is achieved by considering proposal distributions in the exponential family whose parameters are...

This is a set of very hurriedly compiled notes. It has not been proof-checked and is likely to have some errors. These, though, should be minor errors and maybe cleared up by referring to the relevant texts. The texts that have been used in the preparation of the notes are Feller; Grimmett and Stirzaker; Goswami and Rao; David Williams; and Mitzenmacher and Upfal. The purpose behind the notes i...

4 groups of Ss were exposed to a probability learning situation in which they guessed which of 2 stimuli would next appear. One set of stimuli contained angry and smiling faces, while the other or neutral set contained big and little kangaroos. When the input ratio was 70% angry faces to 30% smiling faces, Ss markedly underestimated the dominant input. When the ratio was reversed (70% smiling, ...

This paper introduces a mathematical framework within which a wide variety of known and new inequalities can be viewed from a common perspective. Probability and expectation inequalities of the following types are considered: (a) P(ZEA) ~ P(Z'EA) for some class of sets A, (b) Ek(Z) ~ Ek(Z') for some class of functions k, and (c) Et(Z) ~ Ek(Z') for some class of pairs of functions t and k. It is...

In this short note we will re-derive the Gaussian expectation propagation (Gaussian EP) algorithm as presented in Minka (2001) and demonstrate an application of Gaussian EP to approximate multi-dimensional truncated Gaussians. 1 On Gaussian Distributions Here we will summarise some important equalities about the Gaussian density. A Gaussian density in Rn is defined by N (x;μ,6) := (2π)− 2 |6|− ...

Although Chinese government has got remarkable achievement in e-Government development, the difficult issue that citizen use behaviour cannot last toward many e-Government services has long been troubling to government in different levels. Based on expectation-confirmation theory (ECT), this paper proposed an extended model by divide the expectation and perceived performance into two categories...

we prove that the limit of a sequence of pettis integrable bounded scalarly measurable weak random elements, of finite weak norm, with values in the dual of a non-separable banach space is pettis integrable. then we provide basic properties for the pettis conditional expectation, and prove that it is continuous. calculus of pettis conditional expectations in general is very different from the c...