In this paper, we propose an approach to modeling functional magnetic resonance imaging (fMRI) data that combines hierarchical polynomial models, Bayes estimation, and clustering. A cubic polynomial is used to fit the voxel time courses of event-related design experiments. The coefficients of the polynomials are estimated by Bayes estimation, in a two-level hierarchical model, which allows us t...

Recent work in supervised learning has shown that a surprisingly simple Bayesian classifier called naı̈ve Bayes is competitive with state of the art classifiers. This simple approach stands from assumptions of conditional independence among features given the class. Improvements in accuracy of naı̈ve Bayes has been demonstrated by a number of approaches, collectively named semi naı̈ve Bayes classi...

This paper provides the estimation of the scale parameter of the exponential distribution under multiply type-II censoring. Using generalized non-informative prior and natural conjugate prior, Bayes estimator and approximate Bayes estimators of the scale parameter have been obtained under square error loss function. The proposed Bayes estimators and approximate Bayes estimators are compared wit...

We introduce herein a new class of autoregressive models in which the regression parameters and error variances may undergo changes at unknown time points while staying constant between adjacent change-points. Assuming conjugate priors, we derive closed-form recursive Bayes estimates of the regression parameters and error variances. Approximations to the Bayes estimates are developed that have ...

Recent work in supervised learning has shown that a surprisingly simple Bayesian classifier called naı̈ve Bayes is competitive with state of the art classifiers. This simple approach stands from assumptions of conditional independence among features given the class. Improvements in accuracy of naı̈ve Bayes has been demonstrated by a number of approaches, collectively named semi naı̈ve Bayes classi...

Naïve Bayes classifier has proved to be very effective on many real data applications. Its performances usually benefit from an accurate estimation of univariate conditional probabilities and from variable selection. However, although variable selection is a desirable feature, it is prone to overfitting. In this paper, we introduce a new regularization technique to select the most probable subs...

Bayesian predictions are stochastic just like predictions of any other inference scheme that generalize from a finite sample. While a simple variational argument shows that Bayes averaging is generalization optimal given that the prior matches the teacher parameter distribution the situation is less clear if the teacher distribution is unknown. I define a class of averaging procedures, the temp...

• In this paper, we propose Bayes estimators of the parameter of the exponentiated gamma distribution and associated reliability function under General Entropy loss function for a censored sample. The proposed estimators have been compared with the corresponding Bayes estimators obtained under squared error loss function and maximum likelihood estimators through their simulated risks (average l...

The aim of this paper is to study the estimation of Pareto distribution on the basis of progressive type-II censored sample. First, the maximum likelihood estimator (MLE) is derived. Then the Bayes estimator of the unknown parameter of Pareto distribution is derived on the basis of Gamma prior distribution under entropy loss function. Further the empirical Bayes estimator also obtained by using...

The goal of this thesis is to examine methods of statistical inference based on upper record values. This includes estimation of parameters based on samples of record values and prediction of future record values. We first define and discuss record times and record values and their distributions. Then we propose an efficient algorithm to generate random samples of record values. The algorithm, ...