Maximum Likelihood Estimation of Phase

1. How do you calculate maximum likelihood estimation?
2. When should I use maximum likelihood estimation?
3. What does the maximum likelihood estimation tell us?
4. What is the maximum likelihood estimator of θ?

How do you calculate maximum likelihood estimation?

Definition: Given data the maximum likelihood estimate (MLE) for the parameter p is the value of p that maximizes the likelihood P(data |p). That is, the MLE is the value of p for which the data is most likely. 100 P(55 heads|p) = ( 55 ) p55(1 − p)45. We'll use the notation p for the MLE.

When should I use maximum likelihood estimation?

We can use MLE in order to get more robust parameter estimates. Thus, MLE can be defined as a method for estimating population parameters (such as the mean and variance for Normal, rate (lambda) for Poisson, etc.) from sample data such that the probability (likelihood) of obtaining the observed data is maximized.

What does the maximum likelihood estimation tell us?

Maximum likelihood estimation is a statistical method for estimating the parameters of a model. In maximum likelihood estimation, the parameters are chosen to maximize the likelihood that the assumed model results in the observed data.

What is the maximum likelihood estimator of θ?

A maximum likelihood estimator (MLE) of the parameter θ, shown by ˆΘML is a random variable ˆΘML=ˆΘML(X1,X2,⋯,Xn) whose value when X1=x1, X2=x2, ⋯, Xn=xn is given by ˆθML.