Unit:
Κατεύθυνση Στατιστική και Επιχειρησιακή ΈρευναLibrary of the School of Science
Author:
Κωνσταντίνου Μαρία-Ζαφειρούλα
Supervisors info:
Μελιγκοτσίδου Λουκία Λέκτορας (Επιβλέπουσα), Μπουρνέτας Απόστολος Αναπλ. Καθηγ., Σιάννης Φώτης Λέκτορας
Original Title:
Ακολουθιακές μέθοδοι monte carlo με εφαρμογή στη μπευζιανή στατιστική
Translated title:
Sequential Monte carlo methods with applications to the bayesian statistics
Summary:
In this paper we refer to the Bayesian statistics and we describe the basic
steps of the Bayesian approach both for problems of a parameter and for
multi-parameter problems. The steps of the algorithm Gibbs for multi-parameter
problems are also mentioned. We describe basic Monte Carlo techniques such as
the rejection method, the method of antithetic variables, the method of control
variables, the stratified sampling and importance sampling. Particular
attention is given to methods associated with importance sampling and an
example is given of a Bayesian missing data problem and how it can be solved
using the importance sampling. Wedescribe the sequential Monte Carlo methods
such as SAW method, the growth method, the sequential imputationfor statistical
missing data problems and how these methods are linked. These methods are
advanced techniques, which improve the previous Monte Carlo methods because
they minimize disadvantages and help solve multidimensional problems. They give
better simulations which can be used as a basis for new techniques, help
immensely in solving missing data problems, give best approaches and have great
advantages in many areas of science in general.
Specifically in this paper we deal with Monte Carlo methods to solve
statistical missing data problems under the light of the Bayesian approach.
Specifically we deal with the problem of estimating the covariance matrix of
missing data using three different Monte Carlo methods, 1) importance sampling,
2)Gibbs and 3)SIS.
Keywords:
Sequential, Importance , Sampling, Missing, Data
