The Library

Monotonicity properties of the Monte Carlo EM algorithm and connections with simulated likelihood

Tools

Papaspiliopoulos, Omiros and Sermaidis, Giorgos (2007) Monotonicity properties of the Monte Carlo EM algorithm and connections with simulated likelihood. Working Paper. Coventry: University of Warwick. Centre for Research in Statistical Methodology. Working papers, Vol.2007 (No.24).

Preview

PDF
WRAP_Papaspilioupoulos_07-24w.pdf - Published Version - Requires a PDF viewer such as GSview, Xpdf or Adobe Acrobat Reader
Download (329Kb)

Official URL: http://www2.warwick.ac.uk/fac/sci/statistics/crism...

Abstract

In this note we show that the Monte Carlo EM algorithm, appropriately constructed with importance re-weighting, monotonically increases a corresponding simulated likelihood. This is result is formally proved but also intuitively explained by a formulation of the problem using auxiliary variables.

Item Type:

Working or Discussion Paper (Working Paper)

Subjects:

Q Science > QA Mathematics

Divisions:

Faculty of Science > Statistics

Library of Congress Subject Headings (LCSH):

Distribution (Probability theory), Monte Carlo method, Monotonic functions, Missing observations (Statistics)

Series Name:

Working papers

Publisher:

University of Warwick. Centre for Research in Statistical Methodology

Place of Publication:

Coventry

Official Date:

2007

Dates:

Date	Event
2007	Published

Volume:

Vol.2007

Number:

No.24

Number of Pages:

Status:

Not Peer Reviewed

Access rights to Published version:

Open Access

Funder:

Greek State Scholarships Foundation (IKY)

References:

Beskos, A., Papaspiliopoulos, O. & Roberts, G. O. (2007). Monte Carlo max-
imum likelihood estimation for discretely observed diffusion processes. Ann. Statist.
To appear.
Chan, K. S. & Ledolter, J. (1995). Monte Carlo EM estimation for time series models
involving counts. J. Amer. Statist. Assoc. 90 242{252.
Dempster, A. P., Laird, N. M. & Rubin, D. B. (1977). Maximum likelihood from
incomplete data via the EM algorithm. J. Roy. Statist. Soc. Ser. B 39 1{38. With
discussion.
Fort, G. & Moulines, E. (2003). Convergence of the Monte Carlo expectation maxi-
mization for curved exponential families. Ann. Statist. 31 1220{1259.
Geyer, C. J. (1994). On the convergence of Monte Carlo maximum likelihood calcula-
tions. J. Roy. Statist. Soc. Ser. B 56 261{274.
Jank, W. (2006). The EM algorithm, its stochastic implementation and global
optimization: Some challenges and opportunities for OR. Available from
http://www.smith.umd.edu/faculty/wjank/GA-EM-SaulGass.pdf.
Levine, R. A. & Casella, G. (2001). Implementations of the Monte Carlo EM algo-
rithm. J. Comput. Graph. Statist. 10 422{439.
McCulloch, C. E. (1997). Maximum likelihood algorithms for generalized linear mixed
models. J. Amer. Statist. Assoc. 92 162{170.
Quintana, F., Liu, J. & del Pino, G. (1999). Monte Carlo EM with importance
reweighting and its applications in random e®ects models. Computational Statistics &
Data Analysis 29 429{444.
Wei, G. C. G. & Tanner, M. A. (1990). A Monte Carlo implementation of the EM
algorithm and the poor man's data augmentation algorithms. J. Amer. Statist. Assoc.
85 699{704.
Wu, C. F. J. (1983). On the convergence properties of the EM algorithm. Ann. Statist.
11 95{103.