Abstract:
An adaptive backward sampling modification of independent Metropolis
algorithm
is suggested in order to estimate the location parameter of a certain class
of bivariate truncated posteriors.
This problem is related to the estimation of location of a point source of
radiation on a 2-D plane, while the quanta of scattered radiation are shot
through a circular slot and detected on a parallel plane \cite{Shemyakin:1985}.
Depending on the scattering law and prior localization, traditional
Metropolis-Hastings algorithm may mix very slowly. Backward sampling and
proposal adaptations \cite{Shemyakin:2007} are used to reveal the
problems and improve the rate of convergence.
Numerical examples are provided.
\bibitem{Shemyakin:1985}
A. Shemyakin.
\newblock A problem of estimating coordinates of a radiation source.
\newblock {\em Theory Probab. Appl.}, Vol. 30, 128-140, 1985.
\bibitem{Shemyakin:2007}
A. Shemyakin.
\newblock An adaptive backward coupling Metropolis algorithm for
truncated distributions.
\newblock{\em Model Assisted Statistics and Applications}.,
IOS Press, Vol. 2, 1-7, 2007.