Search results for " metropolis"
showing 10 items of 15 documents
Group Metropolis Sampling
2017
Monte Carlo (MC) methods are widely used for Bayesian inference and optimization in statistics, signal processing and machine learning. Two well-known class of MC methods are the Importance Sampling (IS) techniques and the Markov Chain Monte Carlo (MCMC) algorithms. In this work, we introduce the Group Importance Sampling (GIS) framework where different sets of weighted samples are properly summarized with one summary particle and one summary weight. GIS facilitates the design of novel efficient MC techniques. For instance, we present the Group Metropolis Sampling (GMS) algorithm which produces a Markov chain of sets of weighted samples. GMS in general outperforms other multiple try schemes…
Group Importance Sampling for particle filtering and MCMC
2018
Bayesian methods and their implementations by means of sophisticated Monte Carlo techniques have become very popular in signal processing over the last years. Importance Sampling (IS) is a well-known Monte Carlo technique that approximates integrals involving a posterior distribution by means of weighted samples. In this work, we study the assignation of a single weighted sample which compresses the information contained in a population of weighted samples. Part of the theory that we present as Group Importance Sampling (GIS) has been employed implicitly in different works in the literature. The provided analysis yields several theoretical and practical consequences. For instance, we discus…
A Review of Multiple Try MCMC algorithms for Signal Processing
2018
Many applications in signal processing require the estimation of some parameters of interest given a set of observed data. More specifically, Bayesian inference needs the computation of {\it a-posteriori} estimators which are often expressed as complicated multi-dimensional integrals. Unfortunately, analytical expressions for these estimators cannot be found in most real-world applications, and Monte Carlo methods are the only feasible approach. A very powerful class of Monte Carlo techniques is formed by the Markov Chain Monte Carlo (MCMC) algorithms. They generate a Markov chain such that its stationary distribution coincides with the target posterior density. In this work, we perform a t…
Adaptive independent sticky MCMC algorithms
2018
In this work, we introduce a novel class of adaptive Monte Carlo methods, called adaptive independent sticky MCMC algorithms, for efficient sampling from a generic target probability density function (pdf). The new class of algorithms employs adaptive non-parametric proposal densities which become closer and closer to the target as the number of iterations increases. The proposal pdf is built using interpolation procedures based on a set of support points which is constructed iteratively based on previously drawn samples. The algorithm's efficiency is ensured by a test that controls the evolution of the set of support points. This extra stage controls the computational cost and the converge…
Grapham: Graphical models with adaptive random walk Metropolis algorithms
2008
Recently developed adaptive Markov chain Monte Carlo (MCMC) methods have been applied successfully to many problems in Bayesian statistics. Grapham is a new open source implementation covering several such methods, with emphasis on graphical models for directed acyclic graphs. The implemented algorithms include the seminal Adaptive Metropolis algorithm adjusting the proposal covariance according to the history of the chain and a Metropolis algorithm adjusting the proposal scale based on the observed acceptance probability. Different variants of the algorithms allow one, for example, to use these two algorithms together, employ delayed rejection and adjust several parameters of the algorithm…
The metropolis in retrospect : from the trading metropolis to the global metropolis.
2005
SummaryMetropolization is not a new phenomenon: metropolises have been around for centuries. The prime and permanent function of a metropolis is the coordination of economic activities at a world scale. This function has been applied to different activities in history, depending on technological conditions and economic organization, and consequently it generated different forms of metropolises. The resulting continuities and discontinuities in the metropolises' evolution can be understood in terms of agglomeration economies. In the pre-industrial period, the trading metropolis coordinates long range trade. The industrial revolutions generate new needs for coordination of production and give…
A la deriva entre cartells de cinema: una narrativa personal sobre París
2020
INTRODUCCIÓ. Les ciutats enquadrades des del cinema han construït una cultura visual amb la qual s’identifiquen els seus consumidors; imatges emblemàtiques que configuren una memòria col·lectiva. Però aquestes metròpolis només existeixen en la ficció. La realitat té poc o gens a veure amb aquestes visualitats. En aquesta investigació s’ofereix un relat alternatiu sobre la ciutat de París. MÈTODE. A partir d’una metodologia de recerca basada en l’art, s’empra la deriva com a mètode d’observació i anàlisi crítica de l’entorn urbà. L’objectiu és percebre París d’una manera alternativa a l’imaginari urbà creat pel cinema, a partir de la recerca de cartells de cinema que es troben en aquesta ciu…
On the stability and ergodicity of adaptive scaling Metropolis algorithms
2011
The stability and ergodicity properties of two adaptive random walk Metropolis algorithms are considered. The both algorithms adjust the scaling of the proposal distribution continuously based on the observed acceptance probability. Unlike the previously proposed forms of the algorithms, the adapted scaling parameter is not constrained within a predefined compact interval. The first algorithm is based on scale adaptation only, while the second one incorporates also covariance adaptation. A strong law of large numbers is shown to hold assuming that the target density is smooth enough and has either compact support or super-exponentially decaying tails.
Contributed discussion on article by Pratola
2016
The author should be commended for his outstanding contribution to the literature on Bayesian regression tree models. The author introduces three innovative sampling approaches which allow for efficient traversal of the model space. In this response, we add a fourth alternative.
Pursuits of the Dioecese of Wrocław for Exemption - from thr Beginning of the 14th Century to 1821
2022
Istniejąca od 1000 roku w związku metropolitalnym z Gnieznem diecezja wrocławska, na mocy bulli papieża Piusa VII De salute animarum z16 lipca 1821 roku, stała się diecezją egzymowaną, tj. podległą bezpośrednio pod Stolicę Apostolską. Mijająca 200. rocznica tegoż wydarzenia jest dobrą okazją, aby prześledzić, w jaki sposób dążenia do zerwania zależności kościelnej od związku metropolitalnego z Gnieznem były wypadkową dziejów politycznych śląskiej dzielnicy. W artykule przedstawiono dążenia diecezji wrocławskiej do uzyskania egzempcji, których początki datowane są na okres dominacji czeskiej na Śląsku w I połowie XIV wieku, a uwieńczone zostały prawnymi określeniami w bulli z 1821 roku. Auto…