# Maximum Likelihood Estimation Task

A Maximum Likelihood Estimation Task is a point estimation task that requires a maximum-likelihood estimate (that maximizes the (log‐)likelihood of the data).

## References

### 2015

1. Lange, Kenneth L.; Little, Roderick J. A.; Taylor,Jeremy M. G. (1989). "Robust Statistical Modeling Using the t Distribution". Journal of the American Statistical Association 84 (408): 881–896. doi:10.2307/2290063. JSTOR 2290063.
2. Sijbers, Jan; den Dekker, A.J. (2004). "Maximum Likelihood estimation of signal amplitude and noise variance from MR data". Magnetic Resonance in Medicine 51 (3): 586–594. doi:10.1002/mrm.10728. PMID 15004801.
3. Sijbers, Jan; den Dekker, A.J.; Scheunders, P.; Van Dyck, D. (1998). "Maximum Likelihood estimation of Rician distribution parameters". IEEE Transactions on Medical Imaging 17 (3): 357–361. doi:10.1109/42.712125. PMID 9735899.

### 2011

• (Wikipedia, 2009) ⇒ http://en.wikipedia.org/wiki/Maximum_likelihood
• In statistics, maximum-likelihood estimation (MLE) is a method of estimating the parameters of a statistical model. When applied to a data set and given a statistical model, maximum-likelihood estimation provides estimates for the model's parameters.

The method of maximum likelihood corresponds to many well-known estimation methods in statistics. For example, one may be interested in the heights of adult female giraffes, but be unable due to cost or time constraints, to measure the height of every single giraffe in a population. Assuming that the heights are normally (Gaussian) distributed with some unknown mean and variance, the mean and variance can be estimated with MLE while only knowing the heights of some sample of the overall population. MLE would accomplish this by taking the mean and variance as parameters and finding particular parametric values that make the observed results the most probable (given the model).

In general, for a fixed set of data and underlying statistical model, the method of maximum likelihood selects values of the model parameters that produce a distribution that gives the observed data the greatest probability (i.e., parameters that maximize the likelihood function). Maximum-likelihood estimation gives a unified approach to estimation, which is well-defined in the case of the normal distribution and many other problems. However, in some complicated problems, difficulties do occur: in such problems, maximum-likelihood estimators are unsuitable or do not exist.