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Monte Carlo Methods of Inference for Implicit Statistical Models
Open accessAbstract
SUMMARY: A prescribed statistical model is a parametric specification of the distribution of a random vector, whilst an implicit statistical model is one defined at a more fundamental level in terms of a generating stochastic mechanism. This paper develops methods of inference which can be used for implicit statistical models whose distribution theory is intractable. The kernel method of probability density estimation is advocated for estimating a log-likelihood from simulations of such a model. The development and testing of an algorithm for maximizing this estimated log-likelihood function is described. An illustrative example involving a stochastic model for quantal response assays is given. Possible applications of the maximization algorithm to ad hoc methods of parameter estimation are noted briefly, and illustrated by an example involving a model for the spatial pattern of displaced amacrine cells in the retina of a rabbit.
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Citations
Cites
Variable Kernel Estimates of Multivariate Densities
Breiman, L., Meisel, W., & Purcell, E. (1977) · Technometrics · doi:10.1080/00401706.1977.10489521 · Cited by 488
Cited by
A Monte Carlo Implementation of the EM Algorithm and the Poor Man's Data Augmentation Algorithms
Wei, G. C. G., & Tanner, M. A. (1990) · Journal of the American Statistical Association · doi:10.1080/01621459.1990.10474930 · Cited by 1,453
Markov chain Monte Carlo without likelihoods
Marjoram, P., Molitor, J., Plagnol, V., & Tavaré, S. (2003) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.0306899100 · Cited by 1,199
The frontier of simulation-based inference
Cranmer, K., Brehmer, J., & Louppe, G. (2020) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.1912789117 · Cited by 1,032
Approximate Bayesian computation (ABC) gives exact results under the assumption of model error
Wilkinson, R. D. (2013) · Statistical Applications in Genetics and Molecular Biology · doi:10.1515/sagmb-2013-0010 · Cited by 247
SMITH, T., KILLEEN, G. F., MAIRE, N., ROSS, A., MOLINEAUX, L., TEDIOSI, F., HUTTON, G., UTZINGER, J., DIETZ, K., & TANNER, M. (2006) · The American Journal of Tropical Medicine and Hygiene · doi:10.4269/ajtmh.2006.75.2_suppl.0750001 · Cited by 225
Metadata
- Authors
- Diggle, P. J., & Gratton, R. J.
- Venue
- Journal of the Royal Statistical Society Series B: Statistical Methodology
- Publisher
- Oxford University Press (OUP)
- Published
- 1984-01-01
- Volume
- 46
- Issue
- 2
- Pages
- 193-212
- ISSN
- 1369-7412 (ISSN-L)
- 1467-9868
- OpenAlex
- W114923250
- Cited by
- 427
- References
- 1
- FWCI
- 4.80
- Type
- journal article
- Language
- en
- Open access
- bronze
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- Diggle, P. J., & Gratton, R. J. (1984). Monte Carlo Methods of Inference for Implicit Statistical Models. Journal of the Royal Statistical Society Series B: Statistical Methodology. https://doi.org/10.1111/j.2517-6161.1984.tb01290.x
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