Maxium Likelihood Estimate (MLE)

1. from wikipedia:

Maximum likelihood estimation (MLE) is a popular statistical method used to make inferences about parameters of the underlying probability distribution from a given data set. That is to say, you have a sample of data

X_{1}, \dots, X_{n} \!

and some kind of model for data, and you want to estimate parameters of the distribution.

2. from http://www.itl.nist.gov/div898/handbook/eda/section3/eda3652.htm
Maximum likelihood estimation begins with the mathematical expression known as a likelihood function of the sample data. Loosely speaking, the likelihood of a set of data is the probability of obtaining that particular set of data given the chosen probability model. This expression contains the unknown parameters. Those values of the parameter that maximize the sample likelihood are known as the maximum likelihood estimates.

the dis/advantages are discussed, as well as the software.

3. about smoothed maximum likelihood estimates.
One purpose of the smoothed estimates is too account for sparseness in counts for distributions with a lot of history by backing off to less sparse estimates.
(McDonald, R. (2005). Extracting Relations from Unstructured Text, Department of Computer and Information Science, University of Pennsylvania.)