626 views

### Show that $\frac{X}{X+Y}\sim Beta(\alpha,\beta)$ [duplicate]

Let IG denote Inverse-Gamma distribution Inverse-Gamma. If $X\sim IG(\alpha,1)$ and $Y\sim IG(\beta,1)$. Show that $\frac{X}{X+Y}\sim Beta(\alpha,\beta)$ I tried with jacobian transformation ...
804 views

### Understanding parameters of Beta distribution [duplicate]

I've heard that the $\alpha$ and $\beta$ parameters of the Beta distribution intuitively represent the number of successes and failures, respectively. 1) If so, what's the purpose of subtracting $1$ ...
52 views

### Estimate probability from sample frequency in a binomial distribution [duplicate]

If I get $s$ successes out of $n$ trials in a binomial distribution, what is the probability $p$ of getting a success in each individual trial? Presumably $p = s/n$, but what if $s = 0$ or $s = n$? ...
78k views

### Can a probability distribution value exceeding 1 be OK?

On the Wikipedia page about naive Bayes classifiers, there is this line: $p(\mathrm{height}|\mathrm{male}) = 1.5789$ (A probability distribution over 1 is OK. It is the area under the bell curve ...
169k views

### Help me understand Bayesian prior and posterior distributions

In a group of students, there are 2 out of 18 that are left-handed. Find the posterior distribution of left-handed students in the population assuming uninformative prior. Summarize the results. ...
28k views

### What exactly is the alpha in the Dirichlet distribution?

I'm fairly new to Bayesian statistics and I came across a corrected correlation measure, SparCC, that uses the Dirichlet process in the backend of it's algorithm. I have been trying to go through the ...
5k views

### Choosing between uninformative beta priors

I am looking for uninformative priors for beta distribution to work with a binomial process (Hit/Miss). At first I thought about using $\alpha=1, \beta=1$ that generate an uniform PDF, or Jeffrey ...
6k views

### Bayesian batting average prior

I wanted to ask a question inspired by an excellent answer to the query about the intuition for the beta distribution. I wanted to get a better understanding of the derivation for the prior ...
18k views

### How to choose prior in Bayesian parameter estimation

I know 3 methods to do parameter estimation, ML, MAP and Bayes approach. And for MAP and Bayes approach, we need to pick priors for parameters, right? Say I have this model $p(x|\alpha,\beta)$, in ...
852 views

### Whence the beta distribution?

As I'm sure everyone here knows already, the PDF of the Beta distribution $X \sim B(a,b)$ is given by $f(x) = \frac{1}{B(a,b)}x^{a-1}(1-x)^{b-1}$ I've been hunting all over the place for an ...
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### Since the beta distribution is similar in form to the binomial, why do we need the beta distribution?

It appears that the binomial distribution is very similar in form to the beta distribution and that I can re-parametrize constants on either pdf to make them look the same. So, why do we need the beta ...
5k views

### Properly interpret the alpha / beta parameters in the Beta Distribution

For quite a while I believed that the proper interpretation of a Beta distribution with $\alpha$ and $\beta$ is: "what is the most likely $P$ given $\alpha -1$ success (heads), and $\beta -1$ of ...
I have a dataset and I made the QQ-plot against the $N(0,1)$ distribution. The plot is included below. My statistics is rusty to say the least (meaning what little knowledge I had is now rusted away!)...