Linked Questions

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0answers
79 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
28 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?
471
votes
13answers
187k 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 ...
133
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3answers
183k 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. ...
75
votes
4answers
25k 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 ...
26
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3answers
7k 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 ...
2
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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
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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
271 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 ...
1
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1answer
543 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 <...
0
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1answer
171 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 ...
1
vote
3answers
92 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 ...
1
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1answer
49 views

Confidence boundaries for an AB test [closed]

Given an AB-test, I have two variants running over a certain timeperiod gathering data. I split the time period up in smaller frames and cumulative add the population for the given variant as well as ...
1
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1answer
39 views

Probability with Limited Data

I have a theoretical question which has been bugging me, involving prediction based on limited data. Say you go to the horse track and see that horse A has just won its race with horse B. The two ...