Search results for " Markov chain"

showing 2 items of 52 documents

Recursion at the crossroads of sequence modeling, random trees, stochastic algorithms and martingales

2013

This monograph synthesizes several studies spanning from dynamical systems in the statistical analysis of sequences, to analysis of algorithms in random trees and discrete stochastic processes. These works find applications in various fields ranging from biological sequences to linear regression models, branching processes, through functional statistics and estimates of risk indicators for insurances. All the established results use, in one way or another, the recursive property of the structure under study, by highlighting invariants such as martingales, which are at the heart of this monograph, as tools as well as objects of study.

modèles auto-régressifs[MATH.MATH-PR] Mathematics [math]/Probability [math.PR]estimation and prediction errorstochastic gradient algorithmschaîne de Markov à mémoire variable[STAT.TH] Statistics [stat]/Statistics Theory [stat.TH]Digital search treesvariable length Markov chainstrong laws for discrete martingalessuffix trietemps d'occurrences de motifsoptimisation stochastique.dynamical systemtrie des suffixesstochastic optimization.erreur d'estimation et de prédictionArbres digitaux de rechercheauto-regressive modelssystème dynamiquelois fortes de martingales discrètesalgorithmes de gradient stochastiques[MATH.MATH-ST] Mathematics [math]/Statistics [math.ST]occurrences time
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Can the adaptive Metropolis algorithm collapse without the covariance lower bound?

2011

The Adaptive Metropolis (AM) algorithm is based on the symmetric random-walk Metropolis algorithm. The proposal distribution has the following time-dependent covariance matrix at step $n+1$ \[ S_n = Cov(X_1,...,X_n) + \epsilon I, \] that is, the sample covariance matrix of the history of the chain plus a (small) constant $\epsilon>0$ multiple of the identity matrix $I$. The lower bound on the eigenvalues of $S_n$ induced by the factor $\epsilon I$ is theoretically convenient, but practically cumbersome, as a good value for the parameter $\epsilon$ may not always be easy to choose. This article considers variants of the AM algorithm that do not explicitly bound the eigenvalues of $S_n$ away …

stabiiliusMetropolis-algoritmiAdaptive Markov chain Monte Carlostochastic approximationstokastinen approksimaatiostabilityadaptiivinen Markov chain Monte CarloMetropolis algorithm
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