maximum likelihood estimation | parameter estimation | Probability and Statistics| U/Grad|MPhil| PhD

Описание: Maximum Likelihood Estimator
(MLE) provides a point estimate.

The sample is assumed to consist
of independent random variables.

We construct a joint pmf/pdf,
also known as the likelihood
function, by taking the product
of individual pmf/pdf of
observations (due to them
being independent rvs,
we take the product of their
individual pmf/pdf)

We maximize this joint
distribution (likelihood function)
with respect to the unknown
parameter.

We set the first-order derivative
of the likelihood function, with
respect to the unknown parameter,
to zero. Solving it gives the MLE
estimate of the parameter.

MLE of Bernoulli Parameter

MLE of Poisson Parameter