Random Input Sampling for Complex Models Using Markov Chain Monte Carlo

TL;DR

This paper introduces a novel Markov Chain Monte Carlo method to efficiently sample input variables for complex models, ensuring the output matches prescribed statistics, demonstrated on stochastic differential equations.

Contribution

It proposes a modified Metropolis-Hastings algorithm for sampling inputs in complex models where input distributions are implicitly defined by output statistics.

Findings

Effective sampling of input variables for complex models

Generation of sample paths for stochastic differential equations

Improved accuracy in modeling stochastic systems

Abstract

Many random processes can be simulated as the output of a deterministic model accepting random inputs. Such a model usually describes a complex mathematical or physical stochastic system and the randomness is introduced in the input variables of the model. When the statistics of the output event are known, these input variables have to be chosen in a specific way for the output to have the prescribed statistics. Because the probability distribution of the input random variables is not directly known but dictated implicitly by the statistics of the output random variables, this problem is usually intractable for classical sampling methods. Based on Markov Chain Monte Carlo we propose a novel method to sample random inputs to such models by introducing a modification to the standard Metropolis-Hastings algorithm. As an example we consider a system described by a stochastic differential equation (sde) and demonstrate how sample paths of a random process satisfying this sde can be generated with our technique.