Laplace Approximation
Laplace-approksimationen er en klassisk analytisk teknik, der erstatter en intractable posterior-fordeling med en multivariat Gaussisk fordeling centreret ved posterior-mode, idet krumningen af log-posterior ved denne mode anvendes til at fastsætte kovariansen. Formelt udarbejdet for Bayesiansk statistik af Tierney og Kadane (1986) i deres skelsættende artikel i Journal of the American Statistical Association, udgør den et hurtigt, deterministisk alternativ til Markov chain Monte Carlo og danner den matematiske kerne af Integrated Nested Laplace Approximations (INLA).
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Method map
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Kilder
- Tierney, L. & Kadane, J. B. (1986). Accurate approximations for posterior moments and marginal densities. Journal of the American Statistical Association, 81(393), 82–86. DOI: 10.1080/01621459.1986.10478240 ↗
- MacKay, D. J. C. (2003). Information Theory, Inference, and Learning Algorithms. Cambridge University Press. ISBN: 978-0521642989
- Rue, H., Martino, S. & Chopin, N. (2009). Approximate Bayesian inference for latent Gaussian models by using integrated nested Laplace approximations. Journal of the Royal Statistical Society: Series B, 71(2), 319–392. DOI: 10.1111/j.1467-9868.2008.00700.x ↗
Sådan citerer du denne side
ScholarGate. (2026, June 3). Laplace Approximation to the Posterior. ScholarGate. https://scholargate.app/da/bayesian/laplace-approximation
Which method?
Set this method beside its closest kin and read them side by side — the library lays the books on the table; the choice is yours.
- Bayesiansk regressionBayesiansk↔ compare
- Forventningsudbredelse (EP)Bayesiansk↔ compare
- Markov Chain Monte Carlo (MCMC)Bayesiansk↔ compare
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