Talk:Maximum likelihood

I removed this from the article, until it can be made more NPOV and more encyclopedic. Currently reads more like a list of observations than true encyclopedic content and needs more explanation. --Lexor|Talk 07:25, 5 Aug 2004 (UTC)

Maximum likelihood is one of the main methods used by frequentist (i.e. non-Bayesian) statisticians. Bayesian arguments against the ML and other point estimation methods are that

• all the information contained in the data is in the likelihood function, so why use just the maximum?Bayesian methods use ALL of the likelihood function and this is why they are optimal.

• ML methods have good asymptotic properties (consistency and attainment of the Cramer-Rao lower bound) but there is nothing to recommend them for analysis of small samples

• the method doesn't work so well with distributions that have many modes or unusual shapes. Apart from the practical difficulties of getting stuck in local modes, there is the difficulty of interpreting the output, which consists of a point estimate plus standard error. Suppose you have a distribution for a quantity that can only take positive values, and your ML estimate for the mean comes out at 1.0 with a standard error of 3? Bayesian methods gives you the entire posterior distribution as output, so you can make sense of it and then decide what summaries are appropriate.

This whole article reads like an 80's highschool textbook. As a matter of fact, a lot wikipedia's articles on difficult to understand subjects read like they're out of an 80's highschool textbook, making them only useful to people who have already know the subject back to front, making the entire wikipedia project a failure.

Clarity issues in a statistics article (a subject that is less than clear) should not be used to make the inference that "the entire wikipedia project a failure" Rschulz 23:56, 1 Mar 2005 (UTC)

This article was never intended to be accessible to secondary school students generally (although certainly there are those among them who would understand it). I would consider this article successful if mathematicians who know probability theory but do not know statistics can understand it. And I think by that standard it is fairly successful, although more examples and more theory could certainly be added. If someone can make this particular topic comprehensible to most people who know high-school mathematics, through first-year calculus or perhaps through the prerequisites to first-year calculus, I would consider that a substantially greater achievement. But that would tak more work. Michael Hardy 00:40, 10 Jan 2005 (UTC)

As a university student learning statistics, I think this article needs improvement. It would be good if a graph of the likelihood of different parameter values for p was added (with the maximum pointed out) to the example. This addition would require adding some specific data to the example. Also, the example should be separated from the discussion about MLE, to make sure people understand that the binominal distribution is only used for this case. The reasons why it is good to take the log of likelihood are not discussed. Further the discussion about what makes a good estimator (and how MLE is related to other estimators) could be expanded. Rschulz 23:56, 1 Mar 2005 (UTC)

a user in CA Good article, don't be so hard on the author(s), of course could be better, but most of us have day jobs, but I would change the notation, as this was confusing " The value (lower-case) x/n observed in a particular case is an estimate; the random variable (Capital) X/n is an estimator." seems to conflict with the excellent example at the end for finding maximum likelihood x/n in a bionomial distribution of x voters in a sample of n (without replacement). Now, next question, can anybody explain the Viterbi algorithm to a high-schooler? 01 March 2004

I don't see the conflict. The lower-case x in the example at the end is not a random variable, but an observed realization. Michael Hardy 22:50, 2 Mar 2005 (UTC)