Variance Reduction for Population Growth Simulation Models

Most variance reduction techniques encountered in simulations are designed to operate with stationary models. However, many simulations are nonstationary in character, population growth models being an example. One way to facilitate statistical inference in a nonstationary simulation is to interchange the order of replication collection and time evolution. That is, at each time point several replications are performed to enable a user to estimate parameters at that point in time. This paper describes three variance reduction models that use this interchange between collection and evolution to induce negative correlation between replications, thereby producing estimates with smaller variances. Model 1 describes a procedure that occasionally relies on the solution of a linear program to develop an optimal sampling plan. Model 2 offers an alternative that applies when the populations in strata are large. Model 3 applies when survival probabilities are functions of an exogenous random variable such as rainfall. A female elephant population simulation illustrates the success one can expect with Model 1.