by Sze Tsz-leung. / Thesis (M.Phil.)--Chinese University of Hong Kong, 1993. / Includes bibliographical references (leaves 91). / Chapter Chapter 1 --- Introduction / Chapter 1.1 --- Basic concepts of Monte Carlo integration --- p.1 / Chapter 1.1.1 --- Importance sampling --- p.4 / Chapter 1.1.2 --- Control variate --- p.5 / Chapter 1.1.3 --- Antithetic variate --- p.6 / Chapter 1.1.4 --- Stratified sampling --- p.7 / Chapter 1.1.5 --- Biased Estimator --- p.10 / Chapter 1.2 --- Some special methods in Monte Carlo integration --- p.11 / Chapter 1.2.1 --- Haber´ةs modified Monte Carlo quadrature I --- p.11 / Chapter 1.2.2 --- Haber's modified Monte Carlo quadrature II --- p.11 / Chapter 1.2.3 --- Weighted Monte Carlo integration --- p.12 / Chapter 1.2.4 --- Adaptive importance sampling --- p.13 / Chapter Chapter 2 --- New methods / Chapter 2.1 --- The use of Newton Cotes quadrature formulae in stage one --- p.17 / Chapter 2.1.1 --- Using one-dimensional trapezoidal rule --- p.17 / Chapter 2.1.2 --- Using two-dimensional or higher dimensional product trapezoidal rule --- p.21 / Chapter 2.1.3 --- Extension to higher order one-dimensional Newton Cotes formulae --- p.32 / Chapter 2.2 --- The use of Guass quadrature rule in stage one --- p.45 / Chapter 2.3 --- Some variations of the new methods --- p.56 / Chapter 2.3.1 --- Using probability points in both stages --- p.56 / Chapter 2.3.2 --- Importance sampling --- p.59 / Chapter 2.3.2.1 --- Triangular distribution --- p.60 / Chapter 2.3.2.2 --- Beta distribution --- p.64 / Chapter Chapter 3 --- Examples / Chapter 3.1 --- Example one: using trapezoidal rule as basic rule --- p.73 / Chapter 3.1.1 --- One-dimensional case --- p.73 / Chapter 3.1.2 --- Two-dimensional case --- p.80 / Chapter 3.2 --- Example two: Using Simpson's 3/8 rule as basic rule --- p.85 / Chapter 3.3 --- Example three： Using Guass rule as basic rule --- p.86 / Chapter Chapter 4 --- Conclusion and discussions --- p.88 / Reference --- p.91
| Identifer | oai:union.ndltd.org:cuhk.edu.hk/oai:cuhk-dr:cuhk_319111 |
| Date | January 1993 |
| Contributors | Sze, Tsz-leung., Chinese University of Hong Kong Graduate School. Division of Statistics. |
| Publisher | Chinese University of Hong Kong |
| Source Sets | The Chinese University of Hong Kong |
| Language | English |
| Detected Language | English |
| Type | Text, bibliography |
| Format | print, 91 leaves ; 30 cm. |
| Rights | Use of this resource is governed by the terms and conditions of the Creative Commons “Attribution-NonCommercial-NoDerivatives 4.0 International” License (http://creativecommons.org/licenses/by-nc-nd/4.0/) |
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