Multi-dimensional Integrals by Stochastic Integral Method

Gupta, Avinash Kumar (2014) Multi-dimensional Integrals by Stochastic Integral Method. Masters thesis, Indian Institute of Science Education & Research Kolkata.

PDF (MS dissertation of Avinash Kumar Gupta) Avinash_Kumar_Gupta_09MS083.pdf - Submitted Version Restricted to Repository staff only Download (1MB)

Abstract

To model stochastic processes different statistics have been developed. In Bayesian statistics for example, the state of the system is defined in terms of degrees of belief. The methods developed for handling stochastic processes proved to be very useful in statistics in general. The Bayesian methodology is very powerful for problem like parameter inference, model selection. But the computation time has also been a big disappointment. The simple brute force method is too obsolete to be used for higher dimensional system problem. A very recent development of a computational method called ‘Nested sampling’ by a physicist John Skilling in the year 2004 has proved itself to be more effective than all other sampling technique. Nested sampling method works in Bayesian statistics and calculates evidence and posterior distribution as a function of likelihood and posterior mass. Nested sampling method itself uses the method of Monte Carlo imposing a hard constraint over the likelihood. Today Nested Sampling algorithm has proved itself to be very useful for Model selection for physical systems, multi-dimensional integral, and parameter estimation for a stochastic system. One of the present uses of this algorithm is in parameter estimation of compact binary inspiralling system, where data from ground based gravitational wave detectors is analyzed.

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