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{{short description|Distribution estimation technique}}
'''Importance sampling''' is a [[Monte Carlo method]] for evaluating properties of a particular [[probability distribution|distribution]], while only having samples generated from a different distribution than the distribution of interest. Its introduction in statistics is generally attributed to a paper by [[Teun Kloek]] and [[Herman K. van Dijk]] in 1978,<ref>{{cite journal |first=T. |last=Kloek |first2=H. K. |last2=van Dijk |title=Bayesian Estimates of Equation System Parameters: An Application of Integration by Monte Carlo |journal=[[Econometrica]] |volume=46 |issue=1 |year=1978 |pages=1–19 |doi=10.2307/1913641 }}</ref> but its precursors can be found in [[Monte Carlo method in statistical physics|statistical physics]] as early as 1949.<ref>{{cite journal |first=G. |last=Goertzle |authorlink=Gerald Goertzel |title=Quota Sampling and Importance Functions in Stochastic Solution of Particle Problems |journal=Technical Report ORNL-434, Oak Ridge National Laboratory |year=1949 |hdl=2027/mdp.39015086443671 }}</ref><ref>{{cite journal |last=Kahn |first=H. |authorlink=Herman Kahn |last2=Harris |first2=T. E. |authorlink2=Theodore E. Harris |year=1949 |title=Estimation of Particle Transmission by Random Sampling |journal=Monte Carlo Method |volume=12 |series=Applied Mathematics Series |pages=27–30 |publisher=National Bureau of Standards. }}</ref> Importance sampling is also related to [[umbrella sampling]] in [[computational physics]]. Depending on the application, the term may refer to the process of sampling from this alternative distribution, the process of inference, or both.
== Basic theory ==
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