Related papers: An introduction to computational complexity in Mar…
In these lectures, given in '96 summer schools in Beg-Rohu (France) and Budapest, I discuss the fundamental principles of thermodynamic and dynamic Monte Carlo methods in a simple light-weight fashion. The keywords are MARKOV CHAINS,…
Applications that require substantial computational resources today cannot avoid the use of heavily parallel machines. Embracing the opportunities of parallel computing and especially the possibilities provided by a new generation of…
Adaptive Markov chain Monte Carlo (MCMC) algorithms, which automatically tune their parameters based on past samples, have proved extremely useful in practice. The self-tuning mechanism makes them `non-Markovian', which means that their…
Sampling from complicated probability distributions is a hard computational problem arising in many fields, including statistical physics, optimization, and machine learning. Quantum computers have recently been used to sample from…
In this paper, we address technical difficulties that arise when applying Markov chain Monte Carlo (MCMC) to hierarchical models designed to perform clustering in the space of latent parameters of subject-wise generative models.…
Due to its constrained support, the Dirichlet distribution is uniquely suited to many applications. The constraints that make it powerful, however, can also hinder practical implementations, particularly those utilizing Markov Chain Monte…
Markov chains are a class of probabilistic models that have achieved widespread application in the quantitative sciences. This is in part due to their versatility, but is compounded by the ease with which they can be probed analytically.…
We provide explicit nonasymptotic estimates for the rate of convergence of empirical means of Markov chains, together with a Gaussian or exponential control on the deviations of empirical means. These estimates hold under a "positive…
The concepts of probability, statistics and stochastic theory are being successfully used in structural engineering. Markov Chain modelling is a simple stochastic process model that has found its application in both describing stochastic…
Modern imaging methods rely strongly on Bayesian inference techniques to solve challenging imaging problems. Currently, the predominant Bayesian computation approach is convex optimisation, which scales very efficiently to high dimensional…
An introduction to the basics of Monte Carlo is given. The topics covered include, sample space, events, probabilities, random variables, mean, variance, covariance, characteristic function, chebyshev inequality, law of large numbers,…
Markov chain Monte Carlo (MCMC) algorithms have become powerful tools for Bayesian inference. However, they do not scale well to large-data problems. Divide-and-conquer strategies, which split the data into batches and, for each batch, run…
We provide a self-contained introduction into Weihrauch complexity and its applications to computable analysis. This includes a survey on some classification results and a discussion of the relation to other approaches.
While Robert and Rousseau (2010) addressed the foundational aspects of Bayesian analysis, the current chapter details its practical aspects through a review of the computational methods available for approximating Bayesian procedures.…
Sequential Monte Carlo Samplers are a class of stochastic algorithms for Monte Carlo integral estimation w.r.t. probability distributions, which combine elements of Markov chain Monte Carlo methods and importance sampling/resampling…
The widespread use of Markov Chain Monte Carlo (MCMC) methods for high-dimensional applications has motivated research into the scalability of these algorithms with respect to the dimension of the problem. Despite this, numerous problems…
The literature in social network analysis has largely focused on methods and models which require complete network data; however there exist many networks which can only be studied via sampling methods due to the scale or complexity of the…
We present an intuitive, conceptual, but semi-rigorous introduction to the celebrated Markov Chain Monte Carlo method using a simple model of population dynamics as our motivation and focusing on a few elementary distributions.…
Markov chain Monte Carlo methods are a powerful tool for sampling equilibrium configurations in complex systems. One problem these methods often face is slow convergence over large energy barriers. In this work, we propose a novel method…
We introduce a novel time-homogeneous Markov embedding of a class of time inhomogeneous Markov chains widely used in the context of Monte Carlo sampling algorithms which allows us to answer one of the most basic, yet hard, question about…