Entropic Priors for Discrete Probabilistic Networks and for Mixtures of Gaussians Models

The ongoing unprecedented exponential explosion of available computing power, has radically transformed the methods of statistical inference. What used to be a small minority of statisticians advocating for the use of priors and a strict adherence to bayes theorem, it is now becoming the norm across disciplines. The evolutionary direction is now clear. The trend is towards more realistic, flexible and complex likelihoods characterized by an ever increasing number of parameters. This makes the old question of: What should the prior be? to acquire a new central importance in the modern bayesian theory of inference. Entropic priors provide one answer to the problem of prior selection. The general definition of an entropic prior has existed since 1988, but it was not until 1998 that it was found that they provide a new notion of complete ignorance. This paper re-introduces the family of entropic priors as minimizers of mutual information between the data and the parameters, as in [rodriguez98b], but with a small change and a correction. The general formalism is then applied to two large classes of models: Discrete probabilistic networks and univariate finite mixtures of gaussians. It is also shown how to perform inference by efficiently sampling the corresponding posterior distributions.Comment: 24 pages, 3 figures, Presented at MaxEnt2001, APL Johns Hopkins University, August 4-9 2001. See also http://omega.albany.edu:8008

History of Supersymmetric Extensions of the Standard Model

We recall the many obstacles which seemed, long ago, to prevent supersymmetry from possibly being a fundamental symmetry of Nature. We also present their solutions, leading to the construction of the supersymmetric extensions of the Standard Model. Finally we discuss briefly the early experimental searches for Supersymmetry.Comment: 40 pages, 10 figures, 3 Table

Wrong Priors

All priors are not created equal. There are right and there are wrong priors. That is the main conclusion of this contribution. I use, a cooked-up example designed to create drama, and a typical textbook example to show the pervasiveness of wrong priors in standard statistical practice.Comment: 9 pages, 8 figures. MaxEnt2007.org pape

Factors affecting the continued use of the mobile flash dryers by farmer co-operatives, Nueva Ecija, Philippines : a thesis submitted in partial fulfilment of the requirements for the degree Master of Applied Science (Agricultural Systems Management), Massey University, Palmerston North, New Zealand

Harvest of the Philippines second and larger rice crop occurs during the end of the wet season. For members of the rice industry this wet season harvest poses a problem: grain cannot be dried reliably using traditional sundrying methods. Poor drying results in quality reductions and hence farmers receive lower returns. To address this situation the Philippines Government introduced locally manufactured mechanical dryers. This study was undertaken to examine variables which enhance or limit the continued use of the mobile flash dryers in farmers' co-operatives in Nueva Ecija, the Philippines. Two case studies, each consisting of three farmers' co-operatives were investigated using semi-structured interviews. One case comprised co-operatives that continue to use the dryer while the other comprised those that have stopped using it. Results showed that a combination of factors influenced the adoption decisions of the co-operatives. Economic factors, especially the volume of rice handled by the co-operative appeared to be most important. Furthermore, the way that the dryer fitted with the other postharvest systems in the co-operatives was a determinant of adoption decisions. In particular, the co-operatives with rice milling operations or with inadequate alternative drying options utilised the mechanical dryers. The leadership and management of the co- operative appeared also to be a factor. These results indicate that both organisational factors and the characteristics of a technology need to be considered in the development and extension of innovation. Overall the results of this work support the individual and organisational adoption literature. Further work could explore this issue on a wider basis across more co-operatives within the region and across more regions in the country. Key words: Technology adoption, co-operatives, mechanical grain dryer

A supersymmetric 3-4-1 model

We build the complete supersymmetric version of a 3-4-1 gauge model using the superfield formalism. We point out that a discrete symmetry, similar to the R-symmetry in the minimal supersymmetric standard model, is possible to be defined in this model. Hence we have both R-conserving and R-violating possibilities. We also discuss some phenomenological results coming from this model.Comment: 23 pages, 2 figures and 1tabl

Optimal Recovery of Local Truth

Probability mass curves the data space with horizons. Let f be a multivariate probability density function with continuous second order partial derivatives. Consider the problem of estimating the true value of f(z) > 0 at a single point z, from n independent observations. It is shown that, the fastest possible estimators (like the k-nearest neighbor and kernel) have minimum asymptotic mean square errors when the space of observations is thought as conformally curved. The optimal metric is shown to be generated by the Hessian of f in the regions where the Hessian is definite. Thus, the peaks and valleys of f are surrounded by singular horizons when the Hessian changes signature from Riemannian to pseudo-Riemannian. Adaptive estimators based on the optimal variable metric show considerable theoretical and practical improvements over traditional methods. The formulas simplify dramatically when the dimension of the data space is 4. The similarities with General Relativity are striking but possibly illusory at this point. However, these results suggest that nonparametric density estimation may have something new to say about current physical theory.Comment: To appear in Proceedings of Maximum Entropy and Bayesian Methods 1999. Check also: http://omega.albany.edu:8008