# LogLikelihood

LogLikelihood[dist,{x1,x2,}]

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

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

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

LogLikelihood[proc,{path1,path2,}]

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

# Details

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

# Examples

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## Basic Examples(4)

Get the loglikelihood function for a normal distribution:

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Compute a loglikelihood for numeric data:

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Plot loglikelihood contours as a function of and :

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Compute the loglikelihood for multivariate data:

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Compute the log-likelihood for a process:

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