Bayes' theorem

About: Bayes' theorem is a research topic. Over the lifetime, 13158 publications have been published within this topic receiving 563695 citations. The topic is also known as: Bayes theorem & Bayes' rule.

Asymptotic non-deficiency of the Bayes sequential estimation in a family of transformed Chi-square distributions

Abstract: Bayes sequential estimation in a family of transformed Chi-square distributions using a linex loss function and a cost c > 0 for each observation is considered in this paper. It is shown that an asymptotic pointwise optimal rule (A.P.O.) is asymptotically non-deficient, i.e., the difference between the Bayes risk of the A.P.O. rule and the Bayes risk of the optimal procedure is of smaller order of magnitude than c, the cost of single observation, as c → 0.

Interval probability and its application to decision problems

Abstract: Probability measures are well-defined ones that satisfy additivity However, it is slightly tight because of its condition of additivity Fuzzy measures that do not satisfy additivity have been proposed as the substitute measures The only belief function involves a density function among them In this paper, we propose two density functions by extending values of the probability functions to interval values, which do not satisfy additivity According to the definition of interval probability functions, lower and upper probabilities are defined, respectively Given interval probabilities by human intuition, the identification method for obtaining interval probabilities satisfying the normality condition is proposed A combination rule and a conditional probability can be defined well The properties of the proposed measure are clarified Finally, a numerical example with respect to the Bayes theorem is shown

Bagging Bayes Text Classification Based on Map Reduce

Abstract: In order to solve the problem that the classification is difficult on massive text data under the framework of a centralized system,this paper proposes a Bagging Bayes text classification algorithm based on Map Reduce.It introduces the Naive Bayes text classification algorithm.Combined with the Bagging algorithm,it uses Map Reduce parallel programming model to realize the algorithm on Hadoop platform.Experimental results show that this algorithm can be used in the classification of large scale text data sets,have good accuracy and short running time.

Autoregressive Image Generative Models with Normal and t-distributed Noise and the Bayes Codes for Them

Abstract: In this paper, we propose an autoregressive stochastic generative model for images. This model should be one of the most basic models for the new type of lossless image compression which explicitly assume the stochastic generative model. We can easily expand it and theoretically interpret the implicitly assumed stochastic generative models in the various previous predictive coding methods as the expanded versions of our model. Moreover, we can utilize the achievements in the related fields where the linear regression analysis and its expansion are studied to construct the Bayes codes for these generative models. As an example, we expand our generative model from the one with normal noise to the one with the t-distributed noise. Then, we construct the sub-optimal Bayes codes for this generative model by utilizing the variational Bayesian method.