Monte Carlo MethodsSpringer Science & Business Media, 7 de març 2013 - 178 pàgines This monograph surveys the present state of Monte Carlo methods. we have dallied with certain topics that have interested us Although personally, we hope that our coverage of the subject is reasonably complete; at least we believe that this book and the references in it come near to exhausting the present range of the subject. On the other hand, there are many loose ends; for example we mention various ideas for variance reduction that have never been seriously appli(:d in practice. This is inevitable, and typical of a subject that has remained in its infancy for twenty years or more. We are convinced Qf:ver theless that Monte Carlo methods will one day reach an impressive maturity. The main theoretical content of this book is in Chapter 5; some readers may like to begin with this chapter, referring back to Chapters 2 and 3 when necessary. Chapters 7 to 12 deal with applications of the Monte Carlo method in various fields, and can be read in any order. For the sake of completeness, we cast a very brief glance in Chapter 4 at the direct simulation used in industrial and operational research, where the very simplest Monte Carlo techniques are usually sufficient. We assume that the reader has what might roughly be described as a 'graduate' knowledge of mathematics. The actual mathematical techniques are, with few exceptions, quite elementary, but we have freely used vectors, matrices, and similar mathematical language for the sake of conciseness. |
Continguts
| 1 | |
Short resumé of statistical terms | 10 |
Random pseudorandom and quasirandom numbers | 25 |
Direct simulation | 43 |
General principles of the Monte Carlo method | 50 |
Conditional Monte Carlo | 76 |
Solution of linear operator equations | 85 |
Radiation shielding and reactor criticality | 97 |
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Monte Carlo Methods John Michael Hammersley,David Christopher Handscomb Visualització de fragments - 1965 |
Monte Carlo Methods John Michael Hammersley,David Christopher Handscomb Previsualització no disponible - 1964 |
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analysis antithetic variates applied approximation bond calculate Camb Chapter Chem co-ordinates collision Comp constant control variate correlation crude Monte Carlo define denote density function depends digits direct simulation distribution function efficiency eigenvalues energy equation equidistributed equidistributed sequence esti estimand evaluate example F. T. WALL finite formula importance sampling independent integral J. M. HAMMERSLEY labour large number lattice linear Markov chain Math mathematical mean molecules Monte Carlo estimation Monte Carlo experiment Monte Carlo methods neutrons normal distribution observations Oper parent distribution particle Phys physical possible probabilistic problem Proc procedure proportional pseudorandom pseudorandom numbers quasirandom random numbers random variable ratio rectangularly distributed result satisfy self-avoiding walks sequence sphere standard error statistical stochastic stratified sampling Suppose techniques theoretical theory unbiased estimator unblocked values variance variance-covariance matrix vector weight