Monte Carlo integration of $$C^r$$ functions with adaptive variance reduction: an asymptotic analysis

Monte Carlo Integration and Variance Reduction

Variance Reduction for Monte Carlo Implementation of Adaptive Sensor Management

Adaptive sensor management (scheduling) is usually formulated as a finite horizon POMDP and implemented using sequential Monte Carlo. In Monte Carlo, variance reduction is important for the reliable performance of the sensor scheduler. In this paper, we propose a Control Variate method for variance reduction when the sensor is scheduled using the Kullbach Leibler criterion.

Adaptive Stratified Sampling for Monte-Carlo integration of Differentiable functions

We consider the problem of adaptive stratified sampling for Monte Carlo integration of a differentiable function given a finite number of evaluations to the function. We construct a sampling scheme that samples more often in regions where the function oscillates more, while allocating the samples such that they are well spread on the domain (this notion shares similitude with low discrepancy). ...

Variance Analysis for Monte Carlo Integration: A Representation-Theoretic Perspective

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Variance Analysis for Monte Carlo Integration: Representation-Theoretic Perspective

In this report, we revisit the work of Pilleboue et al. [2015], providing a representation-theoretic derivation of the closed-form expression for the expected value and variance in homogeneous Monte Carlo integration. We show that the results obtained for the variance estimation of Monte Carlo integration on the torus, the sphere, and Euclidean space can be formulated as specific instances of a...