Multidimensional rare event probability estimation algorithm

Leonidas Sakalauskas, Ingrida Vaičiulytė


This work contains Monte–Carlo Markov Chain algorithm for estimation of multi-dimensional rare events frequencies. Logits of rare event likelihood we are modeling with Poisson distribution, which parameters are distributed by multivariate normal law with unknown parameters – mean vector and covariance matrix. The estimations of unknown parameters are calculated by the maximum likelihood method. There are equations derived, those must be satisfied with model’s maximum likelihood parameters estimations. Positive definition of evaluated covariance matrixes are controlled by calculating ratio between matrix maximum and minimum eigenvalues.


Abramowitz, M.; Stegun, I. A. (1964). Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables. New York: Dover Publications.

Altaleb, Anas; Chauveau, Didier (2002). Bayesian analysis of the Logit model and comparison of two. Metropolis–Hastings strategies. Computational Statistics and Data Analysis, 39: 137–152.

Bradley, P. C.; Thomas, A. L. (2000). Bayes and Empirical Bayes Methods for Data Analysis. New York: Chapman and Hall.

Chen, Fang (2009). Bayesian modeling using the MCMC procedure [interaktyvus]. [žiūrėta 2013 m. gegužės 4 d.]. Prieiga per internetą:

Clayton, David; Kaldor, John (1987). Empirical Bayes estimates of age-standardized relative risks for use in disease mapping, Biometrics, 43(3): 671–681.

Dennis J. E.; Schnabel, R. B. (1996). Numerical methods for unconstrained optimization and nonlinear equations. Philadelphia: Classics in Applied Mathematics.

Kantorovich, L. V.; Akilov, G. P. (1982). Functional Analysis. Oxford: Pergamon Press.

Liseo, Brunero; Loperfido, Nicola (2003). A Bayesian interpretation of the multivariate skew-normal distribution. Statistics & Probability Letters, 61(4): 395–401.

Pearce, D. W. (2006). Aiškinamasis ekonomikos anglų–lietuvių kalbų žodynas. Lithuania: Vilnius, TEV.

Sakalauskas, Leonidas (2000). Nonlinear stochastic optimization by Monte–Carlo estimators. Informatica, 11(4): 455–468.

Tsutakawa, Robert K.; Shoop, Gary L., Marienfeld, Carl J. (1985). Empirical Bayes estimation of cancer mortality rates. Statistics in Medicine, 4(2): 201–212.

Full Text: PDF


  • There are currently no refbacks.

Creative Commons License
This work is licensed under a Creative Commons Attribution 3.0 License.

eISSN: 2029-9966

Creative Commons License