# Likelihood

Likelihood[dist,{x1,x2,}]

gives the likelihood function for observations x1, x2, from the distribution dist.

Likelihood[proc,{{t1,x1},{t2,x2},}]

gives the likelihood function for the observations xi at time ti from the process proc.

Likelihood[proc,{path1,path2,}]

gives the likelihood function for observations from path1, path2, from the process proc.

# Details • The likelihood function Likelihood[dist,{x1,x2,}] is given by , where is the probability density function at xi, PDF[dist,xi].
• For a scalarvalued process proc the likelihood function Likelihood[proc,{{t1,x1},{t2,x2},}] is given by Likelihood[SliceDistribution[proc,{t1,t2,}],{{x1,x2,}}].
• For a vector-valued process proc the likelihood function Likelihood[proc,{{t1,{x1,,z1},{t2,{x2,,z2}},}] is given by Likelihood[SliceDistribution[proc,{t1,t2,}],{{x1,,z1,x2,,z2,}}].
• The likelihood function for a collection of paths Likelihood[proc,{path1,path2,}] is given by iLikelihood[proc,pathi].

# Examples

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## Basic Examples(4)

Get the likelihood function for a normal distribution:

 In:= Out= Compute a likelihood for numeric data:

 In:= In:= Out= Plot likelihood contours as a function of and on a log scale:

 In:= Out= Compute the likelihood for multivariate data:

 In:= In:= Out= Compute the likelihood for a process:

 In:= In:= Out= ## Neat Examples(2)

Introduced in 2010
(8.0)
|
Updated in 2014
(10.0)