Such features are also used as part of the likelihood function, which makes use of the observed data.
22.
The unbiased particle estimator of the likelihood functions presented in this article is used today in Bayesian statistical inference.
23.
For a data set with " N " observations the likelihood function for a type I Tobit is
24.
Unlike EM, such methods typically require the evaluation of first and / or second derivatives of the likelihood function.
25.
This is done through the calculation shown below, where P ( D | H ) is the likelihood function.
26.
They are also a measure of the curvature of the log likelihood function ( see section on Maximum likelihood estimation ).
27.
To do this, the equation is first rewritten as a likelihood function in terms of " ? ":
28.
The article also contains a proof of the unbiased properties of a particle approximations of likelihood functions and unnormalized conditional probability measures.
29.
Y _ 1 and Y _ 2 in the log-likelihood function are observed variables being equal to one or zero.
30.
Note that the likelihood function depends only on what actually happened, and not on what " could " have happened.
