Bayesian statistics and Markov Chain Monte Carlo (MCMC) algorithms have found their place in the field of Cosmology. They become important mathematical numerical tools, especially parameter estimation model comparison. In this paper, we review some fundamental concepts to understand then introduce MCMC samplers that allow us perform inference procedure. We also a general description standard co...

Probability theory and statistics are two main tools in signal and image processing. Bayesian inference has a privileged place in developing methods for inverse problems arising in signal and image processing which can be applied in real world applications. In this tutorial presentation, first I will breifly present the Bayesian estimation approach in signal and image processing. Then, I will s...

Neural spike train analysis is an important task in computational neuroscience which aims to understand neural mechanisms and gain insights into neural circuits. With the advancement of multielectrode recording and imaging technologies, it has become increasingly demanding to develop statistical tools for analyzing large neuronal ensemble spike activity. Here we present a tutorial overview of B...

Bensmail, Celeux, Raftery and Robert (1997) introduced a new approach to cluster analysis based on geometric modeling based on the within-group covariance in a mixture of multivariate normal distributions using a fully Bayesian framework. This is a model-based methodology, where the covariance matrix structure is involved. Previously, similar structures were used (using a maximum likelihood app...

This paper reviews Bayesian Nonparametric methods and discusses how parametric predictive densities can be constructed using nonparametric ideas.

Obtaining an explanation for SQL query result can enrich the analysis experience, reveal data errors, and provide deeper insight into data. Inference seeks to explain unexpected aggregate results on inference data; such queries are challenging because may need be derived from source, training, or in ML pipeline. In this paper, we model objective function as a black-box propose BOExplain, novel ...

Terrain navigation is an application where inference be tween conceptually di erent sensors is performed re cursively on line In this work the Bayesian framework of statistical inference is applied to this recursive esti mation problem Three algorithms for approximative Bayesian estimation are evaluated in simulations one deterministic algorithm and two stochastic The deter ministic method solv...