Normal prior Normal likelihood Normal posterior distribution

A normally distributed prior is the conjugate prior for a Normal likelihood function. This video works through the derivation of the parameters of the resulting posterior distribution.
These short videos work through mathematical details used in the Multivariate Statistical Modelling module at UWE.

[@houdamrad1273]

Hey , I am looking for how to calculate the interval of the gamma density distribution when setting the priors in Bayesian estimation. For beta(a,b) the mean of X= E(X)=a/(a+b) and variance is V(X)=(a+b)/(a+b+1)(a+b)^2, as we define the mean and varaince from the common values in the literature I return and calculate a and b. Please for gamma (a,b) distribution with E(X)=0.74 and std(X)=0.0056 how to find a and b? Many thanks in advance.

[@HakiConqueror]

Thank-you so much for the clear explanation.

[@sohamkupale8293]

Thank you so much for this amazing video!!!!!

[@saulocortes7758]

you saved me with this explanation

[@joseayala3469]

Great, please could anyone recomend me additional material (books, demostrations :) ), i need practice too much...

[@musefakedir2712]

oh! amazing please finish it. thank you vary much!

[@lradhakrishnarao902]

It is great video. I am trying to solve a variant of this. David Barber's 8th chaper 28th question, where, the format is same, but given as yi.

[@lradhakrishnarao902]

I have solved it. Today, I have understood, that likelihood has to be computed on likelihood of the bayes condition, even if prior is give. I was not aware of this concept.

[@bagussetiaji4382]

thank you :)

[@AbrarAhmed10]

Thank You so much :D :D :D

[@fjumi3652]

why is it mu - ybar in the likelihood and not ybar - mu?

[@meenakshigautam4249]

please calculate bayes factor for this

[@aaronschlegel9808]

Does the video seem to end abruptly to you? Or was that the end of the derivation?

[@dennisdryden9504]

I wonder too

[@tylorcrusoe421]

No, that was the entire derivation.

[@liqitai5189]

very good

[@selangorplkuazman2380]

great!gamma conjugate wif poisson n beta cjugate wif binom.What else??

[@shabnamkohistani20]

5. Today, Sasha checked their weight several times with different scales observing (in
kilograms): 92, 82, 83, 86, 86, 90, 83, 84, 89, 85. Assume that the data is normal
with variance σ
2 = 9 and a prior distribution for the true weight µ ∼ N(80, 100).
(a) What is the posterior distribution?
(b) Compute the credible interval of 95% for µ a priori and a posteriori.
(c) Compare both intervals with the frequentist 95% confidence interval. Can you
conclude that I was optimistic?

[@yitaklee9043]

Hey, it should be n*y_bar^2/sigma^2 in the constant term. I know this is not important haha but just a reminder lol

[@parashorea]

my brain hurts