Likelihood

Likelihood[dist,{x1,x2,}]
gives the likelihood function for observations , , from the distribution dist.

Likelihood[proc,{{t1,x1},{t2,x2},}]
gives the likelihood function for the observations at time from the process proc.

Likelihood[proc,{path1,path2,}]
gives the likelihood function for observations from , , from the process proc.

DetailsDetails

  • The likelihood function Likelihood[dist,{x1,x2,}] is given by , where is the probability density function at , 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 .

ExamplesExamplesopen allclose all

Basic Examples  (4)Basic Examples  (4)

Get the likelihood function for a normal distribution:

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Compute a likelihood for numeric data:

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

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Compute the likelihood for multivariate data:

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Compute the likelihood for a process:

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