A very natural approach to regression problems is to place a prior on the kinds of function that we expect, and then after observing the data to obtain a posterior.

Markov Chain Monte Carlo based Bayesian data analysis has now become the method of choice for analyzing and interpreting data in almost all disciplines of science. In astronomy, over the last decade, we have also seen a steady increase in the number of papers that employ Monte Carlo based Bayesian analysis. New, efficient Monte Carlo based methods are continuously being developed and explored. In this review, we first explain the basics of Bayesian theory and discuss how to set up data analysis problems within this framework. Next, we provide an overview of various Monte Carlo based methods for performing Bayesian data analysis.

So, what are Markov chain Monte Carlo (MCMC) methods? In this article, I will explain that short answer, without any math. A parameter of interest is just some number that summarizes a phenomenon we're interested in. In general we use statistics to estimate parameters. For example, if we want to learn about the height of human adults, our parameter of interest might be average height in in inches.

So, what are Markov chain Monte Carlo (MCMC) methods? In this article, I will explain that short answer, without any math. A parameter of interest is just some number that summarizes a phenomenon we're interested in. In general we use statistics to estimate parameters. For example, if we want to learn about the height of human adults, our parameter of interest might be average height in in inches.

Markov Chain Monte Carlo (MCMC) methods such as Gibbs sampling are finding widespread use in applied statistics and machine learning. These often lead to difficult computational problems, which are increasingly being solved on parallel and distributed systems such as compute clusters. Recent work has proposed running iterative algorithms such as gradient descent and MCMC in parallel asynchronously for increased performance, with good empirical results in certain problems. Unfortunately, for MCMC this parallelization technique requires new convergence theory, as it has been explicitly demonstrated to lead to divergence on some examples. Recent theory on Asynchronous Gibbs sampling describes why these algorithms can fail, and provides a way to alter them to make them converge. In this article, we describe how to apply this theory in a generic setting, to understand the asynchronous behavior of any MCMC algorithm, including those implemented using parameter servers, and those not based on Gibbs sampling.

In this paper, we introduce an approach to automated story generation using Markov Chain Monte Carlo (MCMC) sampling. This approach uses a sampling algorithm based on Metropolis-Hastings to generate a probability distribution which can be used to generate stories via random sampling that adhere to criteria learned by recurrent neural networks. We show the applicability of our technique through a case study where we generate novel stories using an acceptance criteria learned from a set of movie plots taken from Wikipedia. This study shows that stories generated using this approach adhere to this criteria 85%-86% of the time.

Recent work has exploited boundedness of data in the unsupervised learning of new types of generative model. For nonnegative data it was recently shown that the maximum-entropy generative model is a Nonnegative Boltzmann Distribution not a Gaussian distribution, when the model is constrained to match the first and second order statistics of the data. Learning for practical sized problems is made difficult by the need to compute expectations under the model distribution. The computational cost of Markov chain Monte Carlo methods and low fidelity of naive mean field techniques has led to increasing interest in advanced mean field theories and variational methods. Here I present a secondorder mean-field approximation for the Nonnegative Boltzmann Machine model, obtained using a "high-temperature" expansion. The theory is tested on learning a bimodal 2-dimensional model, a high-dimensional translationally invariant distribution, and a generative model for handwritten digits.

Recent work has exploited boundedness of data in the unsupervised learning of new types of generative model. For nonnegative data it was recently shown that the maximum-entropy generative model is a Nonnegative Boltzmann Distribution not a Gaussian distribution, when the model is constrained to match the first and second order statistics of the data. Learning for practical sized problems is made difficult by the need to compute expectations under the model distribution. The computational cost of Markov chain Monte Carlo methods and low fidelity of naive mean field techniques has led to increasing interest in advanced mean field theories and variational methods. Here I present a secondorder mean-field approximation for the Nonnegative Boltzmann Machine model, obtained using a "high-temperature" expansion. The theory is tested on learning a bimodal 2-dimensional model, a high-dimensional translationally invariant distribution, and a generative model for handwritten digits.

Recent work has exploited boundedness of data in the unsupervised learning of new types of generative model. For nonnegative data it was recently shown that the maximum-entropy generative model is a Nonnegative BoltzmannDistribution not a Gaussian distribution, when the model is constrained to match the first and second order statistics of the data. Learning for practical sized problems is made difficult by the need to compute expectations under the model distribution. The computational costof Markov chain Monte Carlo methods and low fidelity of naive mean field techniques has led to increasing interest in advanced mean field theories and variational methods. Here I present a secondorder mean-fieldapproximation for the Nonnegative Boltzmann Machine model, obtained using a "high-temperature" expansion. The theory is tested on learning a bimodal 2-dimensional model, a high-dimensional translationally invariant distribution, and a generative model for handwritten digits.

If data collection is costly, there is much to be gained by actively selecting particularly informative data points in a sequential way. In a Bayesian decision-theoretic framework we develop a query selection criterion which explicitly takes into account the intended use of the model predictions. By Markov Chain Monte Carlo methods the necessary quantities can be approximated to a desired precision. As the number of data points grows, the model complexity is modified by a Bayesian model selection strategy. The properties of two versions of the criterion ate demonstrated in numerical experiments.