Linked Questions

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0answers
105 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 $s = n$? ...
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0answers
32 views

Why are beta distributions commonly chosen for priors? [duplicate]

Is there any specific reason why a Beta distribution would be chosen as a prior, other than that it is conjugate for the Binomial?
506
votes
14answers
205k views

What is the intuition behind beta distribution?

Disclaimer: I'm not a statistician but a software engineer. Most of my knowledge in statistics comes from self-education, thus I still have many gaps in understanding concepts that may seem trivial ...
141
votes
3answers
203k 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. ...
87
votes
4answers
31k views

What is an “uninformative prior”? Can we ever have one with truly no information?

Inspired by a comment from this question: What do we consider "uninformative" in a prior - and what information is still contained in a supposedly uninformative prior? I generally see the prior in ...
33
votes
3answers
8k views

Do Bayesian priors become irrelevant with large sample size?

When performing Bayesian inference, we operate by maximizing our likelihood function in combination with the priors we have about the parameters. Because the log-likelihood is more convenient, we ...
4
votes
2answers
2k views

Haldane's prior Beta(0,0) - Part 1

This article$^1$ on p.16 specifies Haldane's prior as: $$p(\theta) = \frac{1}{θ(1−θ)}$$. However, other$^2$ source on p.6 specifies Haldane's prior as proportional to $\frac{1}{θ(1−θ)}$, i.e. $$p(\...
2
votes
2answers
2k views

How to define prior for beta-binomial A/B test

I would like to run an A/B test using a Bayesian beta-binomial model whereby I would state probabilities such as $P(p_B>p_A)$ in place of using a traditional T-test. I've read that the prior should ...
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1answer
334 views

Bayesian inference - a use case

I've been recently studying Bayesian inference with PyMC3. I understand the flexibility that comes with multiple possible options for initial distribution choices, yet I can't seem to understand why ...
3
votes
2answers
126 views

Discrepancy between binomial and beta in R?

I'm getting a result I cannot explain when using beta distribution. I've got a result which came from a binomial distribution: 2 successes in 6 trials. I would think the maximum likelihood estimator ...
1
vote
1answer
699 views

bayesian update of continuous beliefs

I know that the very similar question has been asked many times, but I hope that somebody can explain the mechanics in simple terms. Let's say there is a population of N=1000 people. A certain share <...
3
votes
1answer
292 views

Finding posterior probability mass function of binomial parameter

Question: Suppose a lot containing 1000 items is received from a supplier containing parameter (unknown) defective items. The past experiences with this supplier suggest that 5% of items in a lot are ...
0
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1answer
337 views

How to calculate the probability of the parameters?

I am reading the Wikipedia article on posterior probability and I note the expression: $$P(\theta|X) = \frac{P(X|\theta)P(\theta)}{P(X)}$$ I understand that $\theta$ represents the parameters of the ...
3
votes
3answers
120 views

How can Bayesians express true ignorance about a parameter and still perform inference? The binomial case

How do I capture a claim of ignorance about a parameter in a Bayesian analysis? For instance, suppose I observed a binomial random variable $X\sim Bin(n, p)$. Say $X = 5$ and $n = 10$. I want to make ...
1
vote
3answers
144 views

Confusion about Bayesian statistics. Does the probability for heads change from .5 to 1, after observing heads?

P(A): The coin has a 50 percent chance of being Heads. P(A|X): You look at the coin, observe a Heads has landed, denote this information X, and trivially assign probability 1.0 to Heads and 0.0 to ...

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