Search results for "Importance sampling"
showing 4 items of 24 documents
Cross Correlations in Scaling Analyses of Phase Transitions
2008
Thermal or finite-size scaling analyses of importance sampling Monte Carlo time series in the vicinity of phase transition points often combine different estimates for the same quantity, such as a critical exponent, with the intent to reduce statistical fluctuations. We point out that the origin of such estimates in the same time series results in often pronounced cross-correlations which are usually ignored even in high-precision studies, generically leading to significant underestimation of statistical fluctuations. We suggest to use a simple extension of the conventional analysis taking correlation effects into account, which leads to improved estimators with often substantially reduced …
Importance sampling correction versus standard averages of reversible MCMCs in terms of the asymptotic variance
2017
We establish an ordering criterion for the asymptotic variances of two consistent Markov chain Monte Carlo (MCMC) estimators: an importance sampling (IS) estimator, based on an approximate reversible chain and subsequent IS weighting, and a standard MCMC estimator, based on an exact reversible chain. Essentially, we relax the criterion of the Peskun type covariance ordering by considering two different invariant probabilities, and obtain, in place of a strict ordering of asymptotic variances, a bound of the asymptotic variance of IS by that of the direct MCMC. Simple examples show that IS can have arbitrarily better or worse asymptotic variance than Metropolis-Hastings and delayed-acceptanc…
Importance sampling type estimators based on approximate marginal Markov chain Monte Carlo
2020
We consider importance sampling (IS) type weighted estimators based on Markov chain Monte Carlo (MCMC) targeting an approximate marginal of the target distribution. In the context of Bayesian latent variable models, the MCMC typically operates on the hyperparameters, and the subsequent weighting may be based on IS or sequential Monte Carlo (SMC), but allows for multilevel techniques as well. The IS approach provides a natural alternative to delayed acceptance (DA) pseudo-marginal/particle MCMC, and has many advantages over DA, including a straightforward parallelisation and additional flexibility in MCMC implementation. We detail minimal conditions which ensure strong consistency of the sug…
Event generation and statistical sampling for physics with deep generative models and a density information buffer
2021
Simulating nature and in particular processes in particle physics require expensive computations and sometimes would take much longer than scientists can afford. Here, we explore ways to a solution for this problem by investigating recent advances in generative modeling and present a study for the generation of events from a physical process with deep generative models. The simulation of physical processes requires not only the production of physical events, but to also ensure that these events occur with the correct frequencies. We investigate the feasibility of learning the event generation and the frequency of occurrence with several generative machine learning models to produce events l…