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In this project we develop for regression models trans-dimensional genetic algorithms for the exploration of large model spaces. Our algorithms can be used in two different ways. The first possibility is to search the best model according to some criteria such as AIC or BIC. The second possibility is to use our algorithms to explore the model space, search for the most probable models and estimate their posterior probabilities. This is accomplished by the use of genetic operators embedded in a reversible jump Markov chain Monte Carlo algorithm in the model space with several chains. As these chains run simultaneously and learn from each other via the genetic operators, our algorithm efficiently explores the large model space and easily escapes local maxima regions common in the presence of highly correlated regressors. We illustrate the power of our trans-dimensional genetic algorithms with applications to two real data sets.


To Do list

  1. Develop methods to assess convergence. This is not straightforward as the chains are not independent.
  2. Apply these ideas in other classes of problems.


[2000, article]
Liang, F., & Wong, W. H. (2000). Evolutionary Monte Carlo: applications to C_p model sampling and change point problem. Statistica Sinica, 317-342.
[1998, techreport]
Holmes, C. C., & Mallick, B. K. (1998). Parallel Markov chain Monte Carlo Sampling: An Evolutionary Based Approach Imperial College, London.
[1996, article]
Chatterjee, S., Laudato, M., & Lynch, L. A. (1996). Genetic Algorithms and their Statistical Applications: an Introduction. Computational Statistics and Data Analysis, 22, 633-651.

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