Linked Questions

3
votes
1answer
2k views

Why ignore the denominator of bayes rule? [duplicate]

I am a new beginner in stats. I have specifically diverted my attention towards this because, I wish to understand the concept of Deep Bayesian Learning, so I am starting with the basics. The question ...
2
votes
2answers
500 views

Why is the normalization necesary in Bayesian inference? [duplicate]

In this post it reads that: normalization can be intractable when applying Bayes’ Theorem And in this answer it says that: it does not depend on the parameters since these have been ...
152
votes
6answers
82k views

Can a probability distribution value exceeding 1 be OK?

On the Wikipedia page about naive Bayes classifiers, there is this line: $p(\mathrm{height}|\mathrm{male}) = 1.5789$ (A probability distribution over 1 is OK. It is the area under the bell curve ...
6
votes
2answers
770 views

What does it mean intuitively to know a pdf “up to a constant”?

I've seen this mentioned numerous times, most recently in motivating the MCMC method and description of the Metropolis-Hastings algorithm. The text (Simulation and the Monte Carlo Method, Second ...
8
votes
3answers
1k 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 ...
2
votes
1answer
4k views

With the Naive Bayes classifier, why do we have to normalize the probabilities after calculating the probabilities of each hypothesis?

In the Naive Bayes classifier, why do we have to normalize the probabilities after calculating the probabilities of each hypothesis?
2
votes
1answer
2k views

Bayesian posterior: is multiplying likelihood by prior (rather than simulation) an acceptable approach?

Ken Rice has a helpful introductory set of slides available online called 'Bayesian Statistics (a very brief introduction)'. http://faculty.washington.edu/kenrice/BayesIntroClassEpi515kmr2016.pdf On ...
5
votes
1answer
801 views

Confusion in Gibbs sampling

I am self-studying Gibbs sampling from a book. The book introduces metropolis hastings algortihm to generate representative values from a posterior distribution. So we know $p(D | \theta) p(\theta)$ ...
3
votes
3answers
272 views

Bayes in English

I am not a statistician or mathematician but am trying to learn. My question: In Bayes Theorem, $p(C|X)=p(X|C)p(C)/p(X)$, what are the English terms for $p(X|C)$ and $p(C)/p(X)$? In other words, is ...
2
votes
2answers
191 views

Bayes' theorem forms

In Bayes' theorem, what kinds of situations would lead us to chose the alternate form (#2) over the basic form (#1)? $P(A|B) = \frac{P(B|A)P(A)}{P(B)}$ $P(A|B) = \frac{P(B|A)P(A)}{P(B|A)P(A)+P(B|\...
3
votes
1answer
190 views

Derivation of Logistic regression

I am trying to understand the derivation of logistic regression. Some books like the famous Elements of Statistical Learning just give you the formula without too ...
0
votes
1answer
292 views

posterior is proportional to joint?

The posterior $$ P(M|D) = \frac{P(D|M) P(M)}{P(D)} $$ I think in my first class it said that $P(D)$ is a fixed thing, so it is permissible to ignore it for optimization purpose and use $$ P(M|D)...
0
votes
2answers
176 views

Return value of uniform distributions for MCMC simulations

I am confused about how what value should be returned from a uniform distribution when using MCMC simulations. The proper normal distribution is define as $$ p(\theta) = \left\{ \begin{array}{cc} 1/...
2
votes
1answer
175 views

A confusion about Bayes's theorem

I am reading a paper on the differences between bayesian outlook and frequentist outlook. The exact pic from the paper is: I have read a decent amount about what likelihood is and how it is not a ...