Jan 25, 2022 · An a priori distribution is what you know of a population before taking a sample. The distribution a posteriori is what you can infer after drawing a sample (for example by estimating an …

By conjugacy, the posterior is $\text {Beta} (a+1+n\bar {X}, b+1+n-n\bar {X})$, as derived by @lightfish. However, Beta distribution has relatively flexible shape, with several situations to consider for the …

May 26, 2020 · Also, I've used that we have a normal distribution for the likelihood and a normal distribution for the prior, and we know that the posterior is going to be a normal distribution again due …

Feb 9, 2019 · The posterior mode is just the maximizing value of the posterior, so this is essentially just a calculus problem. You have already correctly derived the posterior kernel:

Dec 20, 2015 · I've been immersing myself into Bayesian statistics in school and I'm having a very difficult time grasping argmax and maximum a posteriori. A quick explanation of this can be found: …

Feb 28, 2018 · thanks for the explanation, it is bayesian stat I am talking about. So, $\pi$ can be used to designate prior or posterior distribution, and does not necessary need to be conjugate?

May 23, 2024 · In a certain population, 1% of people have a particular rare disease. A diagnostic test for this disease is known to be 95% accurate when a person has the disease and 90% accurate when a …

Nov 16, 2020 · Having studied this, I would remark that there is quite a lot going on with the EM algorithm if it's unfamiliar. Yours is an interesting question - some of the presentations I have seen on …

Nov 16, 2020 · Then a posterior distribution can be found by updating the prior distribution with the likelihood of observing the random variable as that given value and the probability it actually takes on …

Feb 27, 2014 · The arithmetic - geometric mean inequality states that $$\\frac{x_1+ \\ldots + x_n}{n} \\geq \\sqrt[n]{x_1 \\cdots x_n}$$ I'm looking for some original proofs of this inequality. I can find the …