Variance reduction by truncated multimodal importance sampling

1994 ◽  
Vol 13 (4) ◽  
pp. 267-283 ◽  
Author(s):  
Gongkang Fu
Keyword(s):  
Importance Sampling ◽  
Variance Reduction

scholarly journals On the optimal importance process for piecewise deterministic Markov process

2019 ◽  
Vol 23 ◽  
pp. 893-921
Author(s):  
H. Chraibi ◽  
A. Dutfoy ◽  
T. Galtier ◽  
J. Garnier
Keyword(s):  
Importance Sampling ◽  
Simulation Study ◽  
Variance Reduction ◽  
Sampling Method ◽  
Piecewise Deterministic Markov Process ◽  
Importance Sampling Method ◽  
Markovian Processes ◽  
Component Systems ◽  
Reference Measure ◽  
Reduction Methods

In order to assess the reliability of a complex industrial system by simulation, and in reasonable time, variance reduction methods such as importance sampling can be used. We propose an adaptation of this method for a class of multi-component dynamical systems which are modeled by piecewise deterministic Markovian processes (PDMP). We show how to adapt the importance sampling method to PDMP, by introducing a reference measure on the trajectory space. This reference measure makes it possible to identify the admissible importance processes. Then we derive the characteristics of an optimal importance process, and present a convenient and explicit way to build an importance process based on theses characteristics. A simulation study compares our importance sampling method to the crude Monte-Carlo method on a three-component systems. The variance reduction obtained in the simulation study is quite spectacular.

scholarly journals Variance Reduction in Black-box Variational Inference by Adaptive Importance Sampling

2018 ◽  
Author(s):  
Ximing Li ◽  
Changchun Li ◽  
Jinjin Chi ◽  
Jihong Ouyang
Keyword(s):  
Monte Carlo ◽  
Importance Sampling ◽  
Variance Reduction ◽  
Black Box ◽  
Variational Inference ◽  
Experimental Results ◽  
Moment Matching ◽  
Proposal Distribution ◽  
Inference Algorithms ◽  
Better Than

Overdispersed black-box variational inference employs importance sampling to reduce the variance of the Monte Carlo gradient in black-box variational inference. A simple overdispersed proposal distribution is used. This paper aims to investigate how to adaptively obtain better proposal distribution for lower variance. To this end, we directly approximate the optimal proposal in theory using a Monte Carlo moment matching step at each variational iteration. We call this adaptive proposal moment matching proposal (MMP). Experimental results on two Bayesian models show that the MMP can effectively reduce variance in black-box learning, and perform better than baseline inference algorithms.

Variance Reduction for Simulating Transient GI/G/1 Behavior

1996 ◽  
Vol 10 (2) ◽  
pp. 197-205 ◽  
Author(s):  
Søren Asmussen ◽  
Chia-Li Wang
Keyword(s):  
Monte Carlo ◽  
Importance Sampling ◽  
Waiting Time ◽  
Variance Reduction ◽  
Identity Importance ◽  
Expected Waiting Time

A variety of methods for reducing the variance on Monte Carlo estimators of the expected waiting time Wn of the nth customer in a GI/G/1 queue are studied. The ideas involve Spitzer's identity, importance sampling, and sums with stratified or controlled randomized length.

scholarly journals The Convergence Rate and Asymptotic Distribution of the Bootstrap Quantile Variance Estimator for Importance Sampling

2012 ◽  
Vol 44 (3) ◽  
pp. 815-841 ◽  
Author(s):  
Jingchen Liu ◽  
Xuan Yang
Keyword(s):  
Convergence Rate ◽  
Importance Sampling ◽  
Value At Risk ◽  
Variance Reduction ◽  
Asymptotic Distributions ◽  
Regularity Conditions ◽  
Variance Estimator ◽  
Asymptotically Normal ◽  
Empirical Distributions ◽  
Relative Standard

Importance sampling is a widely used variance reduction technique to compute sample quantiles such as value at risk. The variance of the weighted sample quantile estimator is usually a difficult quantity to compute. In this paper we present the exact convergence rate and asymptotic distributions of the bootstrap variance estimators for quantiles of weighted empirical distributions. Under regularity conditions, we show that the bootstrap variance estimator is asymptotically normal and has relative standard deviation of orderO(n−1/4).

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