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SUMMARY:Creating Unbiased Monte Carlo Schemes from Biased Ones: Theory and
  Applications
DTSTART:20150428T120000
DTEND:20150428T130000
DTSTAMP:20260916T003931Z
UID:926c4a069f377476aced8159630d5577d46878c6a612fa73e2d4c8b5
CATEGORIES:Conferences - Seminars
DESCRIPTION:Peter GLYNN (Stanford University)\nIn many Monte Carlo setting
 s\, 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 c
 omputer time required to generate the approximation is increasing in the q
 uality of the approximation. An example of such a problem context is that 
 of stochastic differential equations (SDEs)\, where the approximation is t
 ypically 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 t
 he expectation can then be computed by averaging independent unbiased samp
 les\, the wide range of output analysis methods available in the presence 
 of conventional Monte Carlo are applicable. In the SDE setting\, such unbi
 ased schemes are closely related to multi-level Monte Carlo. We discuss th
 is new class of unbiased estimators in the SDE setting\, that of Markov ch
 ain Monte Carlo\, and several other problem contexts.
LOCATION:UNIL\, Extranef\, room 126 https://planete.unil.ch/plan/?local=EX
 T-126
STATUS:CONFIRMED
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