Data processing: structural design – modeling – simulation – and em – Modeling by mathematical expression
Reexamination Certificate
2006-07-04
2006-07-04
Jones, Hugh (Department: 2128)
Data processing: structural design, modeling, simulation, and em
Modeling by mathematical expression
Reexamination Certificate
active
07072811
ABSTRACT:
The method of the present invention is to modify an initial target distribution it π by combining it with a point mass concentrated on an “artificial atom” α which is outside the state-space X. A Markov chain may then be constructed using any known technique (for example, using the Metropolis-Hastings Algorithm) with the new target distribution. For this chain, the state α is Harris-recurrent (i.e. with probability one, it occurs infinitely many times). By the Markov property, the times at which the new chain hits α are regeneration times. To recover an ergodic chain with limiting distribution π, it is sufficient simply to delete every occurrence of the state α from the new chain. The points immediately after the (deleted) occurrences of the state α are then regeneration times in a Markov chain with limiting distribution π.
REFERENCES:
Brockwell et al.; “Practical regeneration for markov chain monte carlo simulation”; pp. 1-23; Aug. 2001; incorporated document, obtained from www.stat.cmu.edu/www/cmu-stats/tr/.
regenmcmc.cc; program listing incorporated by reference; Aug. 2001; pp. 1-14; obtained from http://lib.stat.cmu/general.
Crane, M.A. et al., An Introduction to the Regenerative Method for Simulation Analysis, vol. 4 of Lecture Notes in Control and Information Sciences, Springer, 1977.
Mykland, P. et al., Regeneration in Markov chain samplers, Journal of the American Statistical Association, 90:233-241, 1995.
Ripley, B.D., Stochastic Simulation, Wiley, 1987, only pages ix-xi and 157-161.
Brockwell Anthony E.
Kadane Joseph B.
Carnegie Mellon University
Jones Hugh
Pencoske Edward L.
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