Browsing by Author "Pasupathy, R."

Now showing 1 - 3 of 3
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    An Algorithm for Fast Generation of Bivariate Poisson Random Vectors
    Shin, K.; Pasupathy, R. (INFORMS, 2010)
    We present the "trivariate reduction extension" (TREx)-an exact algorithm for the fast generation of bivariate Poisson random vectors. Like the normal-to-anything (NORTA) procedure, TREx has two phases: a preprocessing phase when the required algorithm parameters are identified, and a generation phase when the parameters identified during the preprocessing phase are used to generate the desired Poisson vector. We prove that the proposed algorithm covers the entire range of theoretically feasible correlations, and we provide efficient-computation directives and rigorous bounds for truncation error control. We demonstrate through extensive numerical tests that TREx, being a specialized algorithm for Poisson vectors, has a preprocessing phase that is uniformly a hundred to a thousand times faster than a fast implementation of NORTA. The generation phases of TREx and NORTA are comparable in speed, with that of TREx being marginally faster. All code is publicly available.
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    C-NORTA: A Rejection Procedure for Sampling from the Tail of Bivariate NORTA Distributions
    Ghosh, Samik; Pasupathy, R. (INFORMS, 2012)
    We propose C-NORTA, an exact algorithm to generate random variates from the tail of a bivariate NORTA random vector. (A NORTA random vector is specified by a pair of marginals and a rank or product-moment correlation, and it is sampled using the popular NORmal-To-Anything procedure.) We first demonstrate that a rejection-based adaptation of NORTA on such constrained random vector generation problems may often be fundamentally intractable. We then develop the C-NORTA algorithm, relying on strategic conditioning of the NORTA vector, followed by efficient approximation and acceptance/rejection steps. We show that, in a certain precise asymptotic sense, the sampling efficiency of C-NORTA is exponentially larger than what is achievable through a naive application of NORTA. Furthermore, for at least a certain class of problems, we show that the acceptance probability within C-NORTA decays only linearly with respect to a defined rarity parameter. The corresponding decay rate achievable through a naive adaptation of NORTA is exponential. We provide directives for efficient implementation.
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    Optimal Sampling Laws for Stochastically Constrained Simulation Optimization on Finite Sets
    Hunter, S. R.; Pasupathy, R. (INFORMS, 2013)
    Consider the context of selecting an optimal system from among a finite set of competing systems, based on a "stochastic" objective function and subject to multiple "stochastic" constraints. In this context, we characterize the asymptotically optimal sample allocation that maximizes the rate at which the probability of false selection tends to zero. Since the optimal allocation is the result of a concave maximization problem, its solution is particularly easy to obtain in contexts where the underlying distributions are known or can be assumed. We provide a consistent estimator for the optimal allocation and a corresponding sequential algorithm fit for implementation. Various numerical examples demonstrate how the proposed allocation differs from competing algorithms.