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Monte Carlo Strategies in Scientific Computing
by:Jun S. Liu
A large number of scientists and engineers employ Monte Carlo simulation and related global optimization techniques (such as simulated annealing) as an essential tool in their work. For such scientists, there is a need to keep up to date with several recent advances in Monte Carlo methodologies such as cluster methods, data- augmentation, simulated...
A large number of scientists and engineers employ Monte Carlo simulation and related global optimization techniques (such as simulated annealing) as an essential tool in their work. For such scientists, there is a need to keep up to date with several recent advances in Monte Carlo methodologies such as cluster methods, data- augmentation, simulated tempering and other auxiliary variable methods. There is also a trend in moving towards a population-based approach. All these advances in one way or another were motivated by the need to sample from very complex distribution for which traditional methods would tend to be trapped in local energy minima. It is our aim to provide a self-contained and up to date treatment of the Monte Carlo method to this audience. The Monte Carlo method is a computer-based statistical sampling approach for solving numerical problems concerned with a complex system. The methodology was initially developed in the field of statistical physics during the early days of electronic computing (1945-55) and has now been adopted by researchers in almost all scientific fields. The fundamental idea for constructing Markov chain based Monte Carlo algorithms was introduced in the 1950s. This idea was later extended to handle more and more complex physical systems. In the 1980s, statisticians and computer scientists developed Monter Carlo-based algorithms for a wide variety of integration and optimization tasks. In the 1990s, the method began to play an important role in computational biology. Over the past fifty years, reasearchers in diverse scientific fields have studied the Monte Carlo method and contributed to its development. Today, a large number of scientisits and engineers employ Monte Carlo techniques as an essential tool in their work. For such scientists, there is a need to keep up-to-date with recent advances in Monte Carlo methodologies.
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