# Tag Info

### What is the appropriate model for underdispersed count data?

The best --- and standard ways to handle underdispersed Poisson data is by using a generalized Poisson, or perhaps a hurdle model. Three parameter count models can also be used for underdispersed data;...
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### Taking into account the uncertainty of p when estimating the mean of a binomial distribution

There are several problems with your approach. First, you want to use confidence intervals for something that they were not designed for. If $p$ varies, then confidence interval will not show you how ...
• 140k
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### Why is there -1 in beta distribution density function?

This is a story about degrees of freedom and statistical parameters and why it is nice that the two have a direct simple connection. Historically, the "$-1$" terms appeared in Euler's studies of the ...
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### What is the intuition behind beta distribution?

Most of the answers here seem to cover two approaches: Bayesian and the order statistic. I'd like to add a viewpoint from the binomial, which I think the easiest to grasp. The intuition for a beta ...
• 859
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### Limit of beta-binomial distribution is binomial

There are at least two ways of seeing this. The urn interpretation of the distribution can be shown to be The beta-binomial distribution can also be motivated via an urn model for positive ...
• 4,573
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### Property of two independent Beta distribution

It does not seem to be a correct conjecture. It seems your condition is that the mode for $X$ is greater than the mode for $Y$. Since in non-symmetric Beta distributions, the mode is not equal to the ...
• 40.6k
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### Hyper-parameter estimation for Beta-Binomial Empirical Bayes

The hierarchical model You don't actually even need the marginal probability mass function $m()$, you actually only need the marginal moments of $Y$. In this tutorial, Casella (1992) is assuming the ...
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### What is the distribution of a sum of identically distributed Bernoulli random varibles if each pair has the same correlation?

Have you seen this paper: Kadane, 2016, Sums of Possibly Associated Bernoulli Variables: The Conway-Maxwell-Binomial Distribution? In this paper, you can see that the conditions assumed in your ...
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### Poisson-binomial vs. Beta-binomial

My question stemmed from my own ignorance at the time, but I thought I'd post the answer in case anyone else has the same misunderstanding I did. When I posed the question I erroneously understood ...
• 71
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### What is the appropriate model for underdispersed count data?

It seems that the solution provided by Joseph Hilbe within the vgam package is no longer available. From the manual of the package: The genpoisson() has been simplified to genpoisson0 by only ...

### How do I specify a Bayesian Beta binomial model, with predictor variables, for R2jags?

It is not really a "how to code it in JAGS" problem, but it is about defining the appropriate model for your data. If you want to include predictor variables for your data, this means you need a ...
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### How do I carry out a significance test with Tarone's Z-statistic?

If you would like another explanation of the procedure, you can read the original paper by Tarone (1979), but the blog actually gives a longer and clearer explanation than the original paper. In any ...
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### Does order of events matter in Bayesian update?

In Bayesian inference, terms like "observation" and "event" are just conveniences; there is no fundamental importance to them, so don't get hung up on them. In particular, there is no physical ...
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There are just two things you need to know for this. First one: definition of the Beta function. $$B(x,y) := \int_0^1 t^{x-1}(1-t)^{y-1}\,\text dt.$$ Second thing: the identity that $$B(x,y) = \... • 20.6k 3 votes Accepted ### how to analyze overdispersed binary data If you analyse the data using an ordinary generalised linear model this is what you get: ... • 11.3k 3 votes Accepted ### Correct usage/understanding of Bayes Factor when comparing two proportions The Bayes factor for testing H_0:\ p\le q when X\sim\mathcal{N}(n,p) and Y\sim\mathcal{N}(m,p) is$$\mathfrak{B}_{01}(x,y)=\dfrac{\int_{p\le q} f_X(x|p)f_Y(y|q)\pi(p,q)\text{d}p\text{d}q}{\int_{p\...
In order for this to be the case, the random variables must be exchangeable. Your example is a little different since $p>1/2$ isn't an event. An event should be in the support of the likelihood. ...