Markov Chain Monte Carlo Innovations And Applications 1st Edition by Kendall Wilfrid S ISBN 9812564276 9789812564276

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ISBN 10: 9812564276 
ISBN 13: 9789812564276
Author: Kendall Wilfrid S

Markov Chain Monte Carlo Innovations And Applications 1st Table of contents:

1 Introduction
2 Probability Distributions and Sampling
3 Random Numbers and Fortran Code
3.1 How to Get and Run the Fortran Code
4 Confidence Intervals and Heapsort
5 The Central Limit Theorem and Binning
6 Gaussian Error Analysis for Large and Small Samples
6.1 χ2 Distribution, Error of the Error Bar, F-Test
6.2 The Jackknife Approach
7 Statistical Physics and Potts Models
8 Sampling and Re-weighting
9 Importance Sampling and Markov Chain Monte Carlo
9.1 Metropolis and Heat Bath Algorithm for Potts Models
9.2 The O(3) σ Model and the Heat Bath Algorithm
9.3 Example Runs
10 Statistical Errors of Markov Chain Monte Carlo Data
10.1 Autocorrelations
10.2 Integrated Autocorrelation Time and Binning
10.3 Illustration: Metropolis Generation of Normally Distributed Data
11 Self-Consistent versus Reasonable Error Analysis
12 Comparison of Markov Chain MC Algorithms
13 Multicanonical Simulations
13.1 How to Get the Weights?
14 Multicanonical Example Runs (2d Ising and Potts Models)
14.1 Energy and Specific Heat Calculation
14.2 Free Energy and Entropy Calculation
14.3 Time Series Analysis
Acknowledgments
References
An Introduction to Monte Carlo Methods in Statistical Physics D. P. Landau
Contents
1 Introduction
2 How Monte Carlo Methods can be Used in Statistical Physics
2.1 The “Classical” Method: Metropolis Sampling
2.2 Choice of Boundary Conditions
2.2.1 Periodic boundary conditions (pbc)
2.2.2 Antiperiodic boundary conditions
2.2.3 Free edge boundary conditions
2.3 Random Number Generators!
3 Analyzing the Data
3.1 Finite Size E.ects
3.1.1 Finite size scaling and critical exponents
3.2 Finite Sampling Time Effects
3.2.1 Statistical error
3.2.2 Biased sampling error
3.3 Histogram Reweighting
3.4 How to Find the Free Energy
4 Some “Advanced” Monte Carlo Algorithms
4.1 “Optimized” Metropolis
4.2 Cluster Flipping Algorithms
4.3 Probability Changing Cluster Algorithm
4.4 The N-Fold Way and Extensions
4.5 Phase Switch Monte Carlo
4.6 Multicanonical Monte Carlo
4.7 “Wang-Landau” Sampling
5 Summary and Perspective
Acknowledgement
References
Notes on Perfect Simulation W.S. Kendall
Contents
Introduction
Useful Reading
1 CFTP: The Classic Case
1.1 Coupling and Convergence: The Binary Switch
1.2 Random Walk CFTP
1.3 The CFTP Theorem
1.4 The Falling Leaves of Fontainebleau
1.5 Ising CFTP
1.6 Point Process CFTP
1.7 CFTP in Space and Time
1.8 Some Complements
2 CFTP and Regeneration
2.1 Small Sets
2.2 Murdoch-Green Small-set CFTP
2.3 Slice Sampler CFTP
2.4 Multi-shift Sampler
2.5 Catalytic CFTP
2.6 Read-once CFTP
2.7 Some Complements
3 Dominated CFTP
3.1 Queues
3.2 Uniform and Geometric Ergodicity
3.3 Classic CFTP and Uniform Ergodicity
3.4 Dominated CFTP
3.5 Non-linear Birth-death Processes
3.6 Point Processes
3.7 A General Theorem for domCFTP
3.8 Some Complements
4 Theory and Connections
4.1 Siegmund Duality
4.2 Fill’s Method
4.3 FMMR and CFTP
4.4 Effciency and the Price of Perfection
4.5 Dominated CFTP and Foster-Lyapunov conditions
4.6 Backward-forward Algorithm
4.7 Some Complements
References
Sequential Monte Carlo Methods and Their Applications R. Chen
Contents
1 Introduction
2 Stochastic Dynamic Systems
2.1 Generalized State Space Models
2.2 The Growth Principle
3 A General Framework of Sequential Monte Carlo
3.1 Importance Sampling
3.2 The SMC Framework
4 Design Issues (I): Propagation
4.1 Propagation in State Space Models
4.2 Delay Strategy (Look Ahead)
4.2.1 Delayed weight method
4.2.2 Delayed sample method: (exact)
4.2.3 Delayed pilot sampling method
5 Design Issues (II): Resampling
5.1 The Priority Score
5.2 The Sampling Method
5.3 Resampling Schedule
5.4 Rejection Control
6 Design Issues (III): Marginalization
6.1 Conditional Dynamic Linear Models
6.2 Mixture Kalman Filters (MKF)
7 Design Issues (IV): Inferences
8 Applications
8.1 Target Tracking
8.1.1 Random (Gaussian) accelerated target in clutter
8.1.2 Random (Non-Gaussian) accelerated target in a clean environment
8.1.3 Maneuvered target in a clean environment:
8.1.4 Other tracking problems
8.2 Signal Processing
8.2.1 Fading channels
8.2.2 Blind deconvolution
8.3 Stochastic Volatility Models
8.4 Self-Avoiding Walks on Lattice
8.5 Counting 0-1 Tables
8.6 Other Applications
Acknowledgments
References
MCMC in the Analysis of Genetic Data on Pedigrees E. A. Thompson
Contents
1 Introduction
2 Pedigrees, Inheritance, and Genetic Models
3 The Structure of a Genetic Model
4 Exact Computations on Pedigrees: Peeling Algorithms
5 MCMC on Pedigree Structures
6 Genetic Mapping and the Location Lod Score
7 Monte Carlo Likelihood on Pedigrees
8 An Illustrative Example
9 Conclusion

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Tags: Kendall Wilfrid S, Markov Chain, Carlo Innovations