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- W33382332 abstract "Monte Carlo simulation methods are becoming increasingly important for solving difficult optimization problems. Monte Carlo methods are often used when it is infeasible to determine an exact result via a deterministic algorithm, such as with NP or #P problems. Several recent Monte Carlo techniques employ the idea of importance sampling; examples include the Cross-Entropy method and sequential importance sampling. The Cross-Entropy method is a relatively new Monte Carlo technique that has been successfully applied to a wide range of optimization and estimation problems since introduced by R. Y. Rubinstein in 1997. However, as the problem size increases, the Cross-Entropy method, like many heuristics, can take an exponentially increasing amount of time before it returns a solution. For large problems this can lead to an impractical amount of running time. A main aim of this thesis is to develop the Cross-Entropy method for large-scale parallel computing, allowing the running time of a Cross-Entropy program to be significantly reduced by the use of additional computing resources. The effectiveness of the parallel approach is demonstrated via a number of numerical studies. A second aim is to apply the Cross-Entropy method and sequential importance sampling to biological problems, in particular the multiple change-point problem for DNA sequences. The multiple change-point problem in a general setting is the problem of identifying, given a particular sequence of numbers/characters, a point along that sequence where some property of interest changes abruptly. An example in a biological setting, is identifying points in a DNA sequence where there is a significant change in the proportion of the nucleotides G and C with respect to the nucleotides A and T. We show that both sequential importance sampling and the Cross-Entropy approach yield significant improvements in time and/or accuracy over existing techniques." @default.
- W33382332 created "2016-06-24" @default.
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- W33382332 date "2008-10-01" @default.
- W33382332 modified "2023-09-26" @default.
- W33382332 title "Parallel and Sequential Monte Carlo Methods with Applications" @default.
- W33382332 hasPublicationYear "2008" @default.
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