# Questions tagged [maximum-likelihood]

a method of estimating parameters of a statistical model by choosing the parameter value that optimizes the probability of observing the given sample.

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### Maximum Likelihood Estimation (MLE) in layman terms

Could anyone explain to me in detail about maximum likelihood estimation (MLE) in layman's terms? I would like to know the underlying concept before going into mathematical derivation or equation.
3answers
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### What is “restricted maximum likelihood” and when should it be used?

I have read in the abstract of this paper that: "The maximum likelihood (ML) procedure of Hartley aud Rao is modified by adapting a transformation from Patterson and Thompson which partitions the ...
7answers
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### Examples where method of moments can beat maximum likelihood in small samples?

Maximum likelihood estimators (MLE) are asymptotically efficient; we see the practical upshot in that they often do better than method of moments (MoM) estimates (when they differ), even at small ...
2answers
23k views

### What is the difference between a partial likelihood, profile likelihood and marginal likelihood?

I see these terms being used and I keep getting them mixed up. Is there a simple explanation of the differences between them?
2answers
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### Basic question about Fisher Information matrix and relationship to Hessian and standard errors

Ok, this is a quite basic question, but I am a little bit confused. In my thesis I write: The standard errors can be found by calculating the inverse of the square root of the diagonal elements of ...
9answers
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### Advanced statistics books recommendation

There are several threads on this site for book recommendations on introductory statistics and machine learning but I am looking for a text on advanced statistics including, in order of priority: ...
3answers
64k views

### What is the difference in Bayesian estimate and maximum likelihood estimate?

Please explain to me the difference in Bayesian estimate and Maximum likelihood estimate?
2answers
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### Likelihood - Why multiply?

I am studying about maximum likelihood estimation and I read that the likelihood function is the product of the probabilities of each variable. Why is it the product? Why not the sum? I have been ...
4answers
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### Estimating parameters of Student's t-distribution

What are the maximum-likelihood estimators for the parameters of Student's t-distribution? Do they exist in closed form? A quick Google search didn't give me any results. Today I am interested in the ...
2answers
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### Which distributions have closed-form solutions for maximum likelihood estimation?

Which distributions have closed-form solutions for the maximum likelihood estimates of the parameters from a sample of independent observations?
6answers
15k views

### What is the 'fundamental' idea of machine learning for estimating parameters?

The 'fundamental' idea of statistics for estimating parameters is maximum likelihood. I am wondering what is the corresponding idea in machine learning. Qn 1. Would it be fair to say that the '...
3answers
5k views

### Why maximum likelihood and not expected likelihood?

Why is it so common to obtain maximum likelihood estimates of parameters, but you virtually never hear about expected likelihood parameter estimates (i.e., based on the expected value rather than the ...
1answer
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### Weibull distribution parameters $k$ and $c$ for wind speed data

Hi can the same be shown to obtain shape and scale parameter for modified maximum likelihood method
1answer
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### What are the disadvantages of the profile likelihood?

Consider a vector of parameters $(\theta_1, \theta_2)$, with $\theta_1$ the parameter of interest, and $\theta_2$ a nuisance parameter. If $L(\theta_1, \theta_2 ; x)$ is the likelihood constructed ...
5answers
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### Using lmer for prediction

Hello I have two problems that sound like natural candidates for multilevel/mixed models, which I have never used. The simpler, and one that I hope to try as an introduction, is as follows: The data ...
2answers
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### Why is maximum likelihood estimation considered to be a frequentist technique

Frequentist statistics for me is synonymous for trying to make decision that are good for all possible samples. I.e., a frequentist decision rule $\delta$ should always try to minimize the frequentist ...
1answer
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### Properties of logistic regressions

We're working with some logistic regressions and we have realized that the average estimated probability always equals the proportion of ones in the sample; that is, the average of fitted values ...
2answers
15k views