Mle

What Mle is

Maximum likelihood estimation (MLE) is a statistical procedure that uses sample data to estimate the parameters of a population distribution. It is an iterative process where the estimates of the parameters are improved on each iteration until the estimates converge on the optimal values.

The steps of MLE are as follows:

1. Specify the distribution of the population.

2. Specify the likelihood function, which expresses the probability of obtaining the sample data given the parameters of the population distribution.

3. Set the initial values for the parameters of the population distribution.

4. Compute the maximum likelihood estimator (MLE) by maximizing the likelihood function with respect to the parameters of the population distribution.

5. Check the convergence of the MLE.

6. Calculate the standard errors and confidence intervals for the parameters of the population distribution.

Examples

1. MLE is used to estimate the parameters of a probability distribution given a set of observed data. For example, MLE can be used to estimate the mean and variance of a Gaussian distribution given a set of observed data points.

2. MLE is used to fit a regression model to a given set of data. For example, MLE can be used to fit a linear regression model to a set of observed data points.

3. MLE is used to estimate the parameters of a mixture model given a set of observed data. For example, MLE can be used to estimate the proportions and parameters of a mixture of two Gaussian distributions given a set of observed data points.

Related Topics

• ESTIMATOR

• LINEAR

• MEAN

• PROBABILITY

• SET

• POPULATION

• VARIANCE

• ESTIMATION

• REGRESSION

• DISTRIBUTION

• SAMPLE

• CONVERGE