Approximate Bayesian Computation is a family of likelihood-free inference techniques that are tailored to models defined in terms of a stochastic generating mechanism. In a nutshell, Approximate Bayesian Computation proceeds by computing summary statistics from the data and giving more weight to the values of the parameters for which the simulated summary statistics resemble the observed ones. ...

We investigate the posterior rate of convergence for wavelet shrinkage using a Bayesian approach in general Besov spaces. Instead of studying the Bayesian estimator related to a particular loss function, we focus on the posterior distribution itself from a nonparametric Bayesian asymptotics point of view and study its rate of convergence. We obtain the same rate as in Abramovich et al. (2004) w...

The estimation of the parameters of Burr type III distribution based on dual generalized order statistics is considered by using the maximum likelihood (ML) approach as well as the Bayesian approach. The exact expression of the expected Fisher information matrix of the parameters in the distribution is obtained. Also, an approximation based on Lindley is used to obtain the Bayes estimator. To c...

An efficient estimate for the change point in the hazard function is obtained. This is based on a Bayesian estimator which uses equations concerning the parameters of a recently proposed hazard function. It is found through a simulation study that the proposed estimator is more efficient than the traditional estimators in many cases. Furthermore, experimental results that use data of breast can...

Bayesian phylogenetic methods are generating noticeable enthusiasm in the field of molecular systematics. Many phylogenetic models are often at stake and different approaches are used to compare them within a Bayesian framework. The Bayes factor, defined as the ratio of the marginal likelihoods of two competing models, plays a key role in Bayesian model selection. We focus on an alternative est...

In this paper, we first propose a new family of Bayesian estimators for speech enhancement where the cost function includes both a power law and a weighting factor. Secondly, we set the parameters of the estimator based on perceptual considerations by taking into account the masking properties of the ear and the perceived loudness of sound. Our results show that the new estimator achieves bette...

Abstract-This paper presents the reliability computation and Bayesian estimation of system reliability when the applied stress and strength follows the power function distribution. The Power Function Distribution is considered as a simple model to assess component reliability and may exhibit a better fit for failure data and also provide more appropriate information about hazard rate. The resul...

Often times there is a need to infer the true underlying probability based on the observations, such as in, including but not limited to, data-mining, optimizing the process control parameters etc., Histograms, very rudimentary empirical density estimators, divide the whole data range into either equal or unequal sub intervals (bins) and then obtain the frequency of occurrence of each bin. They...