A likelihood function arises from a conditional probability distribution considered as a function of its distributional parameterization argument, conditioned on the data argument.
32.
The precision to which one can estimate the estimator of a parameter ? is limited by the Fisher Information of the log likelihood function.
33.
However, for more complex models, an analytical formula might be elusive or the likelihood function might be computationally very costly to evaluate.
34.
From a philosophical perspective, the loss function in a regularization setting plays a different role than the likelihood function in the Bayesian setting.
35.
When the likelihood function depends on many parameters, depending on the application, we might be interested in only a subset of these parameters.
36.
Where \ theta \ mapsto L ( \ theta \ mid x ) is the likelihood function, and \ sup is the supremum function.
37.
One can arrive at the same conclusion by noticing that the expression for the curvature of the likelihood function is in terms of the geometric variances
38.
Let the likelihood function be considered fixed; the likelihood function is usually well-determined from a statement of the data-generating process.
39.
Let the likelihood function be considered fixed; the likelihood function is usually well-determined from a statement of the data-generating process.
40.
There are adherents to several different statistical philosophies of inference, such as Bayes theorem versus the likelihood function, or positivism versus critical rationalism.
