Linked Questions

1 vote
0 answers

In maximum likelihood estimation, can you maximize $p(x|\theta)$ rather than $L(\theta)$? [duplicate]

Why do you have to define a likelihood function then say you are maximising the likelihood function? Why can't you just maximize $p(x|\theta)$, which is an expression in $\theta$ ? What is technically ...
liyuan's user avatar
  • 123
1 vote
0 answers

Conflicting "facts" about the likelihood employed in Bayes theorem [duplicate]

Consider the following "facts" about Bayes theorem and likelihood: Bayes theorem, written generically as $P(A|B) = \frac{ P(B|A) P(A) }{ P(B) }$ involves conditional and marginal probabilities. ...
basicidea's user avatar
  • 177
678 votes
12 answers

What is the difference between "likelihood" and "probability"?

The wikipedia page claims that likelihood and probability are distinct concepts. In non-technical parlance, "likelihood" is usually a synonym for "probability," but in statistical usage there is a ...
Douglas S. Stones's user avatar
133 votes
14 answers

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.
StatsUser's user avatar
  • 1,819
29 votes
6 answers

Why do people use $\mathcal{L}(\theta|x)$ for likelihood instead of $P(x|\theta)$?

According to the Wikipedia article Likelihood function, the likelihood function is defined as: $$ \mathcal{L}(\theta|x)=P(x|\theta), $$ with parameters $\theta$ and observed data $x$. This equals $p(...
danijar's user avatar
  • 990
31 votes
3 answers

Is there any difference between Frequentist and Bayesian on the definition of Likelihood?

Some sources say likelihood function is not conditional probability, some say it is. This is very confusing to me. According to most sources I have seen, the likelihood of a distribution with ...
CyberPlayerOne's user avatar
17 votes
2 answers

Relation between MAP, EM, and MLE

I am a beginner in machine learning. I can do programming fine but the theory confuses me a lot of the times. What is the relation between Maximum Likelihood Estimation (MLE), Maximum A posteriori (...
Sie Tw's user avatar
  • 439
9 votes
3 answers

When (and why) do Bayesians reject valid Bayesian methods? [closed]

From what I have read and from answers to other questions I have asked here, many so-called frequentist methods correspond mathematically (I don't care if they correspond philosophically, I only care ...
Chill2Macht's user avatar
  • 6,369
10 votes
2 answers

Why not to use Bayes theorem in the form $p(\theta | x) = \frac{L(\theta | x) p(\theta)}{p(x)}$?

There are a lot of questions (like this) about some ambiguity with Bayesian formula in continuous case. $$p(\theta | x) = \frac{p(x | \theta) \cdot p(\theta)}{p(x)}$$ Oftentimes, confusion arises ...
iot's user avatar
  • 275
5 votes
2 answers

What's the difference between prior and marginal probabilities?

Let's say I have a distribution for a random variable S: s | P(S=s) --+------- 0 | .28 1 | .72 That's a prior, right? It ...
jds's user avatar
  • 1,714
4 votes
1 answer

why maximize likelihood, rather than maximizing the inverse of the likelihood? [duplicate]

Let $X$ be a vector of sample data, and $W$ is a vector of parameters of a model based on that data, and we want to estimate a vector $W^*$ that is, informally speaking, "as close to $W$ as possible". ...
user56834's user avatar
  • 2,877
7 votes
2 answers

What does "parameterized by" mean?

Sometimes I have seen likelihood written as $L(\mu,\sigma |y)$ and sometimes as $L(y|\mu,\sigma)$. I have been told that in the first case it means that there is a pre-assumed model depicting the ...
Kirsten's user avatar
  • 803
7 votes
2 answers

Weighted arithmetic mean weight choice in a simplified Bayes estimator

A Bayesian estimator as defined in the Wikipedia article Practical example of Bayes estimators balances the prior knowledge of the entire data set with the knowledge of the subset. This is usually ...
Chris's user avatar
  • 1,249
7 votes
1 answer

Relation between: Likelihood, conditional probability and failure rate

Crosspost from math.stacksexchange. Though it might fit better here. My question is about the possibility of showing equivalence between the hazard rate, the conditional probability (of failure) and ...
tmo's user avatar
  • 205
3 votes
1 answer

Likelihood in bayes and likelihood function

Bayesian inference is very confusing. I want to clarify about the notation in bayes theorem and the use of the likelihood function(or is it not?) as a part of it. From my early frequentist days, I ...
tintinthong's user avatar

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