Details

Autor(en) / Beteiligte

• Liesenfeld, Roman
• Richard, Jean-Francois

Titel

Monte Carlo Methods and Bayesian Computation: Importance Sampling

Ist Teil von

• International Encyclopedia of the Social & Behavioral Sciences, 2015, Vol.15, p.758-762

Auflage

Second Edition

Ort / Verlag

Elsevier Ltd

Erscheinungsjahr

2015

Link zum Volltext

Beschreibungen/Notizen

• Monte Carlo simulation methods can be used to numerically evaluate expectations of functions of random variables (e.g., posterior moments of parameters of interest) for which no analytical expressions are available. They consist of generating random draws from the relevant distribution and replacing expectations by arithmetic means across such draws. Under appropriate technical conditions, the (statistical) accuracy of Monte Carlo estimates is inversely proportional to the number of draws. In cases where a sampling density is not available, which produces sufficiently accurate estimates, one will try to construct an auxiliary sampling density, which is called an importance function. The ratio between the integrand and the selected importance function defines the corresponding remainder function. The initial expectation is then estimated by the arithmetic mean of realizations of the remainder function under random draws from the importance function. An efficient importance function is one which closely resembles the initial integrand under an appropriate metric and, thereby, produces accurate Monte Carlo estimates under as few draws as possible. The article discusses several methods for constructing efficient importance functions at a sufficient level of generality.