Dynamic Sampling Allocation Under Finite Simulation Budget for Feasibility Determination

Monte Carlo simulation is a commonly used tool for evaluating the performance of complex stochastic systems. In practice, simulation can be expensive, especially when comparing a large number of alternatives, thus motivating the need to intelligently allocate simulation replications. Given a finite set of alternatives whose means are estimated via simulation, we consider the problem of determining the subset of alternatives that have means smaller than a fixed threshold. A dynamic sampling procedure that possesses not only asymptotic optimality, but also desirable finite-sample properties is proposed. Theoretical results show that there is a significant difference between finite-sample optimality and asymptotic optimality. Numerical experiments substantiate the effectiveness of the new method. Summary of Contribution: Simulation is an important tool to estimate the performance of complex stochastic systems. We consider a feasibility determination problem of identifying all those among a finite set of alternatives with mean smaller than a given threshold, in which the means are unknown but can be estimated by sampling replications via stochastic simulation. This problem appears widely in many applications, including call center design and hospital resource allocation. Our work considers how to intelligently allocate simulation replications to different alternatives for efficiently finding the feasible alternatives. Previous work focuses on the asymptotic properties of the sampling allocation procedures, whereas our contribution lies in developing a finite-budget allocation rule that possesses both asymptotic optimality and desirable finite-budget properties.

Efficient Sampling Allocation Procedures for Optimal Quantile Selection

We propose a dynamic sampling allocation and selection paradigm for finding the alternative with the optimal quantile in a Bayesian framework. Myopic allocation policies (MAPs), analogous to existing methods in classic ranking and selection for selecting the alternative with the optimal mean, and computationally efficient selection policies are derived for selecting the alternative with the optimal quantile. Under certain conditions, we prove that the proposed MAPs and selection procedures are consistent, which means that the best quantile would be eventually correctly selected as the sample size goes to infinity. Numerical experiments demonstrate that the proposed schemes can significantly improve the performance.

A protocol for online documentation of spider biodiversity inventories applied to a Mexican tropical wet forest (Araneae, Araneomorphae)

Spider community inventories have relatively well-established standardized collecting protocols. Such protocols set rules for the orderly acquisition of samples to estimate community parameters and to establish comparisons between areas. These methods have been tested worldwide, providing useful data for inventory planning and optimal sampling allocation efforts. The taxonomic counterpart of biodiversity inventories has received considerably less attention. Species lists and their relative abundances are the only link between the community parameters resulting from a biotic inventory and the biology of the species that live there. However, this connection is lost or speculative at best for species only partially identified (e. g., to genus but not to species). This link is particularly important for diverse tropical regions were many taxa are undescribed or little known such as spiders. One approach to this problem has been the development of biodiversity inventory websites that document the morphology of the species with digital images organized as standard views. Their main contributions are the dissemination of phenotypic data for species difficult to identify or new with the assignment of species codes, allowing species comparisons between areas regardless of their taxonomic status. The present paper describes a protocol to produce these websites almost automatically. This protocol was successfully applied to 237 species from a tropical primary forest in Mexico. The time and infrastructure required for the documentation of these species are discussed. Taxonomic information in terms of identification challenges, possible new species, and potential nomenclatural issues is described. In addition, the conventional community parameters (e. g., inventory completeness, species richness estimations, sampling intensity) are also calculated and compared through time and between methods. An optimized version for sampling allocation effort per season is presented and compared with protocols optimized for other tropical forests.