Linked Questions

5 votes
1 answer
5k 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 ...
Animesh Karnewar's user avatar
2 votes
2 answers
2k 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 ...
Lerner Zhang's user avatar
  • 6,810
0 votes
2 answers
762 views

Is the density of the unnormalised posterior distribution the same as the density for normalised posterior? [duplicate]

The posterior distribution is proportional to the likelihood times the prior distribution $p(\theta|D) \propto p(D|\theta)p(\theta)$. Computing $p(D|\theta)p(\theta)$ would give the un-normalised ...
calveeen's user avatar
  • 1,116
0 votes
1 answer
422 views

How is the "proportional" calculated in Bayes theorem? [duplicate]

I am struggling with the Wikipedia entry on Likelihood. In an example it mentions $L(P_H = 0.5 |HH) = 0.25$ It mentions that Bayes' theorem implies that the posterior probability is proportional to ...
Kirsten's user avatar
  • 803
185 votes
6 answers
126k 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 ...
babelproofreader's user avatar
9 votes
3 answers
2k views

What is the "grid" in Bayesian grid approximations?

I tried looking for my specific question, but I only found partially related questions here, here, and here. I think my question is much simpler than what was asked and answered in these queries. I'm ...
Shawn Hemelstrand's user avatar
9 votes
2 answers
3k 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 ...
Dingo Kilo's user avatar
8 votes
3 answers
3k 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 ...
Haynes's user avatar
  • 113
2 votes
1 answer
10k 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?
MenorcanOrange's user avatar
4 votes
2 answers
1k views

Why *only* denominator(marginal likelihood) is difficult in Bayesian Inference, cant we keep track of it while calculating numerator

First, this question might give impression that it is related to several question but other don't explain the confusion regarding nominator part. For 2D, Given we have two parameters $\theta$ and $\...
A.B's user avatar
  • 217
2 votes
1 answer
4k 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 ...
jamse's user avatar
  • 123
6 votes
1 answer
2k 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 $p(D | \theta) p(\theta)$ ...
abkds's user avatar
  • 227
1 vote
1 answer
2k 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)...
isolatedstudent's user avatar
2 votes
2 answers
357 views

Likelihood and Prior density scales

I have a question about priors and likelihoods and their visualisation. A Bernoulli likelihood is $$\theta^{N_1}(1 - \theta)^{N_0}$$ where $N_1$ and $N_0$ are number of success and failures, ...
Zlo's user avatar
  • 137
2 votes
2 answers
557 views

Inference: How is the Laplace approximation actually useful to us compared with MLE and MAP?

I was reading a few different sources (including the "Machine Learning and Pattern Recognition" book by Bishop) about the Laplace integral approximation method for inference. However, I am ...
Rocky the Owl's user avatar

15 30 50 per page