Event Details

Reusing Information in Monte Carlo: From Control Variates to Green Simulation

Monte Carlo simulation is often treated as a sequence of independent computational tasks: run a simulation, estimate a quantity, discard the output, and start again when the next question arises. This talk takes a different view: simulation output, auxiliary variables, constraints, and historical runs are all forms of information that can potentially be reused.

The first part of the talk revisits control variates as a general principle for converting side information into variance reduction. Starting from the classical case where the mean of an auxiliary variable is known, I will discuss geometric and weighted-distribution interpretations that extend naturally beyond mean estimation to nonlinear statistical quantities such as risk measures and stochastic optimization. I will also describe recent work on moving beyond equality constraints, where one-sided or interval information leads to projection-type control variates and boundary-dependent variance reduction.

The second part turns to green simulation: the idea of reusing outputs from previous simulation experiments to answer new questions. Here the side information is no longer a known moment or constraint, but historical sample paths generated under related, but not identical, input conditions. I will discuss likelihood-ratio and surrogate-based recycling ideas, the resulting bias–variance tradeoff, and open questions about how to decide which past simulations should be reused, corrected, or discarded. The overall theme is that efficient simulation is not just about generating more random numbers, but about learning how to reuse information safely.