# 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;...
Accepted

### 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 ...
Accepted

### 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 ...

### What is the intuition behind beta distribution?

So far the preponderance of answers covered the rationale for Beta RVs being generated as the prior for a sample proportions, and one clever answer has related Beta RVs to order statistics. Beta ...
Accepted

### 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 ...

### 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 ...
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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 ...
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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 ...

### What is the intuition behind beta distribution?

My intuition says that it "weighs" both the current proportion of success "$x$" and current proportion of failure "$(1-x)$": $f(x;\alpha,\beta) = \text{constant}\cdot x^{\alpha-1}(1-x)^{\beta-1}$. ...
Accepted

### 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 ...

### Relationship between Binomial and Beta distributions

Summary: It is often said that Beta distribution is a distribution on distributions! But what is means? It essentially means that you may fix $n,k$ and think of $\mathbb P[Bin(n,p)\geqslant k]$ as a ...

### 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 ...

### 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 ...

### 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 ...
Accepted

### What is the intuition behind beta distribution?

In the cited example the parameters are alpha = 81 and beta = 219 from the prior year [81 hits in 300 at bats or (81 and 300 - 81 = 219)] I don't know what they call the prior assumption of 81 hits ...
If you're willing to assign a prior Beta distribution on $p_1$ and $p_2$, you could do a Bayesian analysis. The model would be \begin{align} p_1&\sim \operatorname{Beta}(\alpha_1,\beta_1) \\ p_2&...