Posterior and Likelihood probabilities meaning

Question

I am a computer scientist, so I have a background at maths (however limited). I am reading about posterior distribution from here http://en.wikipedia.org/wiki/Posterior_distribution .

It says there:

The posterior probability is the probability of the parameters θ given the evidence X: p(θ|x).

It contrasts with the likelihood function, which is the probability of the evidence given the parameters: p(x|θ).

My question is firstly can you provide me with a very simple example to understand better these concepts? And in addition in machine learning, what we want isn't the probability p(Class|x)?

Thanks a lot

There are many many examples out there already, which you can easily find by googling. — jerad, Jan 26 '14 at 20:22
If you define the 'parameter' $\theta$ as being $P(Class | x)$ then it's clear that that's what you actually want. A fairly complete exposition with an ML slant is [Bishop's book](http://research.microsoft.com/en-us/um/people/cmbishop/prml/) and a very short piece that helpfully related posteriors to likelihood functions in a classification context is [Jordan 1995](http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.54.27) — conjugateprior, Jan 26 '14 at 22:57

score 0 · Answer 1 · answered Jan 26 '14 at 20:40

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Likelihood is something that you design. Using Likelihood and prior you compute posterior and use it for inference.

Watch this for details: http://videolectures.net/mlss09uk_bishop_ibi/

answered Jan 26 '14 at 20:40

Daniel

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Thank you! "Using Likelihood and prior you compute posterior and use it for inference.", was, what I was looking for. – orustammanapov Feb 15 '21 at 12:31

Posterior and Likelihood probabilities meaning

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