Loading...
Please wait, while we are loading the content...
Similar Documents
Convergence properties of perturbed Markov chains
| Content Provider | Semantic Scholar |
|---|---|
| Author | Roberts, Gareth O. Rosenthal, Jeffrey S. Schwartz, Peter O. |
| Copyright Year | 1998 |
| Abstract | Markov chain Monte Carlo algorithms – such as Gibbs sampler and MetropolisHastings – are now widely used in statistics (Gelfand and Smith, 1990; Smith and Roberts, 1993), physical chemistry (Sokal, 1989), and computer science (Sinclair, 1992; Neal, 1993). To explore a complicated probability distribution π(·), a Markov chain P (x, ·) is defined such that π(·) is stationary for the Markov chain. Hopefully, the Markov chain will converge in distribution to π(·), allowing for inferences to be drawn. One potential shortcoming is that the Markov chain is not run analytically but rather by computer simulation. This creates several potential limitations: computers have finite precision and finite range; they use pseudo-randomness rather than true randomness; and they sometimes use algorithms which involve approximations. Thus, rather than running the original chain P (x, ·), the computer is in fact running a slightly perturbed chain P̃ (x, ·). This difference is potentially serious, as it might alter the chain’s convergence properties, convergence rate, and stationary distribution. It is reasonable to ask whether these changes |
| File Format | PDF HTM / HTML |
| Alternate Webpage(s) | http://probability.ca/jeff/ftpdir/sens.pdf |
| Alternate Webpage(s) | http://www.probability.ca/jeff/ftpdir/sens.pdf |
| Alternate Webpage(s) | http://markov.utstat.toronto.edu/jeff/ftpdir/sens.pdf |
| Language | English |
| Access Restriction | Open |
| Subject Keyword | Algorithm Approximation Chemistry, Physical Computer science Computer simulation Computers Converge Gibbs sampling Markov chain Monte Carlo Monte Carlo method Pseudo brand of pseudoephedrine Pseudorandomness Randomness Rate of convergence Sampling (signal processing) Sokal Score Stationary process |
| Content Type | Text |
| Resource Type | Article |
