All Questions
5 questions
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Expectation and variance of the posterior distribution example: seeking elaboration on normalising constant
I have the following example:
Assume that we have an observation $Y$ from a Binomial distribution with parameter $n = 20$ and success probability $p: [Y \sim \mathrm{Bin}(20, p)]$.
Further assume ...
- 2,204
3
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1
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274
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Is an improper prior/posterior equivalent to an undefined PDF?
A "proper" prior or posterior distribution is defined as a distribution for which the PDF integrates to 1 (or in practice, if we're working with a known distribution, one for which the PDF without ...
- 3,800
7
votes
1
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453
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Fastest way to solve Bayes estimator problem
The below problem is from an old PhD qualifying exam in our department. My own solution below is time-consuming and quite possibly wrong. It also relies on recognizing a less common distribution, so I ...
- 4,601
1
vote
1
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394
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Find posterior distribution
Let $X_{1},..,X_{n}$ be a sample from a poisson$({\lambda})$ distribution. Let the prior be ${\pi}({\lambda})=1/{\sqrt{\lambda}}$. Find the posterior distribution.
My work: We have $f(x|{\lambda})=\...
- 351
1
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1
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47
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Derive the conditional pdf of data on prior parameters
In Bayesian statistics I see this derivation often.
Given the likelihood function $f(X|\theta)$ and the prior $f( \theta |a, b)$, the author will derive $f(X|a,b)$. The steps in between are ...
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