Linked Questions

115
votes
12answers
69k 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.
31
votes
5answers
2k views

Wikipedia entry on likelihood seems ambiguous

I have a simple question regarding "conditional probability" and "Likelihood". (I have already surveyed this question here but to no avail.) It starts from the Wikipedia page on likelihood. They say ...
27
votes
3answers
15k views

Why Normalizing Factor is Required in Bayes Theorem?

Bayes theorem goes $$ P(\textrm{model}|\textrm{data}) = \frac{P(\textrm{model}) \times P(\textrm{data}|\textrm{model})}{P(\textrm{data})} $$ This is all fine. But, I've read somewhere: Basically, ...
22
votes
2answers
20k views

Normalizing constant in Bayes theorem

I read that in Bayes rule, the denominator $\Pr(\textrm{data})$ of $$\Pr(\text{parameters} \mid \text{data}) = \frac{\Pr(\textrm{data} \mid \textrm{parameters}) \Pr(\text{parameters})}{\Pr(\text{...
6
votes
2answers
3k views

Normalizing constant irrelevant in Bayes theorem?

I've been reviewing Bayesian literature in an attempt to utilize Bayesian inference for hypothesis testing when I have very well established priors, but there's one thing I cannot get my head around: ...
8
votes
3answers
2k views

Intuition of Bayesian normalizing constant

In the commonly mentioned mammography screening problem with a screening likelihood of 80%, a prior of 10% and a false positive rate of 50%, or its variants, it is easy to explain that the conditional ...
3
votes
1answer
1k views

Dropping the normalization constant in Bayesian inference

Could anyone please explain to me (or provide a situation) where one would drop the normalising constant (or marginal probability term) from Bayes rule when performing Bayesian Inference? New to ...
1
vote
1answer
300 views

What is the meaning of maximum likelihood estimation? [duplicate]

From what I understand, MLE for a model helps us find out what parameters in the model will suit the data most. Thus, in linear regression, we try to find $L(\theta)$ as $\prod_{i=1}^{m}p(y|x;\theta)$...
2
votes
1answer
159 views

Why does $P(\theta_1\mid D, \theta_2) \propto P(D \mid \theta_1, \theta_2)P(\theta_1)$ hold?

Suppose that in a Bayesian framework we have observed data $D$, using independent prior distributions on the parameters of the model, denoted by $\theta_1, \theta_2$. Then, the joint posterior ...
1
vote
1answer
122 views

In a Bayesian Model, if we know that the prior, likelihood, and posterior are all distributions, is the normalizing constant a distribution as well?

In a Bayesian model, we normally have that: $$ p(\boldsymbol\mu|\boldsymbol X) = \dfrac{p(\boldsymbol X|\boldsymbol \mu)p(\boldsymbol \mu)}{p( \boldsymbol X)} $$ Now suppose that $\boldsymbol \mu \...