Creating Unbiased Monte Carlo Schemes from Biased Ones: Theory and Applications
Event details
| Date | 28.04.2015 |
| Hour | 12:00 › 13:00 |
| Speaker | Peter GLYNN (Stanford University) |
| Location | |
| Category | Conferences - Seminars |
In many Monte Carlo settings, one wishes to compute the expectation of a random object which can not be generated in finite time. In such settings, it is often the case that one can instead compute approximations to the random object, where the computer time required to generate the approximation is increasing in the quality of the approximation. An example of such a problem context is that of stochastic differential equations (SDEs), where the approximation is typically obtained via an appropriate discretization of the equation. Of course, when such approximations are used, the resulting estimators are generally biased. We show that in the presence of an appropriate coupling of the sequence of approximations, one can create new estimators that are unbiased. These new unbiased estimators often enjoy much better rates of convergence than do the underlying biased schemes. Furthermore, because the expectation can then be computed by averaging independent unbiased samples, the wide range of output analysis methods available in the presence of conventional Monte Carlo are applicable. In the SDE setting, such unbiased schemes are closely related to multi-level Monte Carlo. We discuss this new class of unbiased estimators in the SDE setting, that of Markov chain Monte Carlo, and several other problem contexts.
Links
Practical information
- Informed public
- Free
Organizer
- CRAG-CDM Seminar, with the support of the EPFL Center on Risk Analysis and Governance (CRAG) http://crag.epfl.ch