Linked Questions

0 votes
0 answers
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References for the conjugate prior to the beta distribution? [duplicate]

The Wikipedia article about "Conjugate Prior" has a table containing information about Likelihood Distributions with their Conjugate Priors. In the "Continuous Likelihood" table, ...
Gilga's user avatar
  • 1
103 votes
7 answers
181k views

Calculating the parameters of a Beta distribution using the mean and variance

How can I calculate the $\alpha$ and $\beta$ parameters for a Beta distribution if I know the mean and variance that I want the distribution to have? Examples of an R command to do this would be most ...
Dave Kincaid's user avatar
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3 votes
1 answer
3k views

How to select hyperprior distribution for Beta distribution parameter?

I have a parameter $\theta$ whose value should lie between $(0,1)$. Therefore, I am assuming the prior distribution of $\theta$ to be a beta distribution with hyper-priors $\alpha$ and $\beta$ ie. $P(\...
Spandyie's user avatar
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5 votes
1 answer
1k views

Conjugate beta / interpretation of the "continuous binomial" signal

Note: this question has significantly evolved, thanks to inspiring comments by Tim. Assume there is some "truth" $x\in[0,1]=Beta(1,1)$ that is signaled with some precision. I assume that the ...
Joanna F's user avatar
  • 123
1 vote
1 answer
457 views

Beta-Binomial mixture vs Beta-Binomial multilevel model?

I first read about the Beta PDF in the context that it was conjugate to the Binomial distribution; a Beta prior with a Binomial likelihood returns a Beta posterior. So this sounds to me like a ...
jbuddy_13's user avatar
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6 votes
1 answer
355 views

Random number generation for conjugate distribution of beta distribution

I try to generate random numbers from the conjugate distribution of beta distribution. It is as follows $$ p(α,β∣a,b,d)∝ \frac{e^{-a \alpha} e^{-b \beta}}{(\beta(\alpha,\beta))^d} \:\:\:\:,\:\:\: \...
Ilayda's user avatar
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2 votes
1 answer
314 views

Bayesian priors and probability distributions

Book "Bayesian Statistics the Fun Way: Understanding Statistics and Probability with Star Wars, Lego, and Rubber Ducks", chapter 9 "Bayesian priors and working with probability ...
Sweet Potato's user avatar
5 votes
0 answers
295 views

I'm not asking for a conjugate prior. Is there a distribution $p(x|y)$ that satisfies $\int p(x|y)Beta(y|a,b) dy = Beta(x| a', b')$?

I know the result of integrating a Gaussian against another Gaussian is still Gaussian, $$\int N(x|\mu_y,\sigma_y)N(y|\mu,\sigma) dy = N(x|\mu',\sigma')\quad.$$ Can I get the same form for Beta ...
dontloo's user avatar
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1 vote
2 answers
43 views

Binomial Update with Uncertain Ground Truth

I have a problem in which I'm trying to maintain a binomial distribution likelihood function. The wrinkle is that I have uncertainty about the results of an individual trial. For example, each trial's ...
Thomas Cleberg's user avatar
2 votes
0 answers
28 views

Drawing random numbers with quadrature

In a comment on this question, the user 'probabilityislogic' says "No, not MCMC this thing! Quadrature this thing! only 2 parameters - quadrature is the "gold standard" for small ...
Wilbur's user avatar
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