Explain maximum likelihood estimation.

666    Asked by SnehaPandey in Data Science , Asked on Nov 28, 2019
Answered by Sneha Pandey

Maximum likelihood estimation is a method of estimating the parameters of a model given observations, by finding the parameter values that maximize the likelihood of making the observations, this means finding parameters that maximize the probability p of event 1 and (1-p) of non-event 0, as we know:

probability (event + non-event) = 1

Let a sample (0, 1, 0, 0, 1, 0) be drawn from a binomial distribution. Now let us calculate the maximum likelihood estimate of μ.

Given the fact that for binomial distribution P(X=1) = μ and P(X=0) = 1- μ where μis the parameter:


Since maximizing likelihood is the same as the maximizing log of likelihood so, log is applied to both sides of the equation for mathematical convenience


Determining the maximum value of μ by equating derivative to zero:


Hence it has been proven that at value μ = 1/3, it is maximizing the likelihood.


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