Linked Questions

674 votes
12 answers
495k views

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
80k views

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
14 votes
12 answers
12k views

Why can you not find the probability of a specific value for the normal distribution? [duplicate]

I am learning about the normal distribution and was watching this video. At 6:28, the question imposed is what is the probability of an ice-cream weighing exactly 120 grams (using the normal ...
Christopher U's user avatar
26 votes
5 answers
10k views

What does "likelihood is only defined up to a multiplicative constant of proportionality" mean in practice?

I'm reading a paper where the authors are leading from a discussion of maximum likelihood estimation to Bayes' Theorem, ostensibly as an introduction for beginners. As a likelihood example, they ...
kmm's user avatar
  • 557
26 votes
2 answers
19k views

In using the cbind() function in R for a logistic regression on a $2 \times 2$ table, what is the explicit functional form of the regression equation?

Suppose I have a $2 \times 2$ table that looks like: ...
user321627's user avatar
  • 4,342
12 votes
5 answers
2k views

Is the exact value of any likelihood meaningless?

While reading about likelihood, I have heard that "the exact value of any likelihood is meaningless" why? So, because of that we may use the likelihood ratio. So, my question is, why the ...
Alice's user avatar
  • 640
11 votes
6 answers
1k views

What is likelihood actually?

I have been pretty confused about maximum likelihood as expressed by my question here. But this question is not about MLE. It occurs to me my confusion may have been because the likelihood function ...
Kirsten's user avatar
  • 793
9 votes
2 answers
2k views

Why we always put log() before the joint pdf when we use MLE(Maximum likelihood Estimation)?

Maybe this question is simple, but I really need some help. When we use the Maximum Likelihood Estimation(MLE) to estimate the parameters, why we always put the log() before the joint density? To use ...
user17670's user avatar
  • 327
7 votes
5 answers
854 views

Intuition for why likelihood function sometimes *is* a PDF

The likelihood function is not in general a PDF (there have been many questions on this). e.g. if we take the binomial likelihood, $$P(Evidence \mid \theta) = f(\theta) = {n \choose k} \theta^k (1-\...
tmkadamcz's user avatar
  • 191
1 vote
1 answer
117 views

Should we really search for the model for which the probability of the data is maximal?

I try to figure out what a Bayesian approach to Machine Learning is. I start from a model that for any given features-vector and target calculate probability density: $ P (y, x_1, x_2, \dots, x_n, c_1,...
Roman's user avatar
  • 594
0 votes
0 answers
81 views

How does simulation help check if model assumptions are met? [duplicate]

I am trying to understand how simulation can be used to check if (regression) model assumptions are met. For example here is a linear regression model: $$y = \beta_0 + \beta_1x + \epsilon$$ I ...
Uk rain troll's user avatar