18,956 research outputs found
Ranking and Selection under Input Uncertainty: Fixed Confidence and Fixed Budget
In stochastic simulation, input uncertainty (IU) is caused by the error in
estimating the input distributions using finite real-world data. When it comes
to simulation-based Ranking and Selection (R&S), ignoring IU could lead to the
failure of many existing selection procedures. In this paper, we study R&S
under IU by allowing the possibility of acquiring additional data. Two
classical R&S formulations are extended to account for IU: (i) for fixed
confidence, we consider when data arrive sequentially so that IU can be reduced
over time; (ii) for fixed budget, a joint budget is assumed to be available for
both collecting input data and running simulations. New procedures are proposed
for each formulation using the frameworks of Sequential Elimination and Optimal
Computing Budget Allocation, with theoretical guarantees provided accordingly
(e.g., upper bound on the expected running time and finite-sample bound on the
probability of false selection). Numerical results demonstrate the
effectiveness of our procedures through a multi-stage production-inventory
problem
Beyond binomial and negative binomial: adaptation in Bernoulli parameter estimation
Estimating the parameter of a Bernoulli process arises in many applications, including photon-efficient active imaging where each illumination period is regarded as a single Bernoulli trial. Motivated by acquisition efficiency when multiple Bernoulli processes (e.g., multiple pixels) are of interest, we formulate the allocation of trials under a constraint on the mean as an optimal resource allocation problem. An oracle-aided trial allocation demonstrates that there can be a significant advantage from varying the allocation for different processes and inspires the introduction of a simple trial allocation gain quantity. Motivated by achieving this gain without an oracle, we present a trellis-based framework for representing and optimizing stopping rules. Considering the convenient case of Beta priors, three implementable stopping rules with similar performances are explored, and the simplest of these is shown to asymptotically achieve the oracle-aided trial allocation. These approaches are further extended to estimating functions of a Bernoulli parameter. In simulations inspired by realistic active imaging scenarios, we demonstrate significant mean-squared error improvements up to 4.36 dB for the estimation of p and up to 1.86 dB for the estimation of log p.https://arxiv.org/abs/1809.08801https://arxiv.org/abs/1809.08801First author draf
- …