Linked Questions

0
votes
0answers
49 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 $s = n$? ...
0
votes
0answers
25 views

Bayes: posterior density, mean and mode [duplicate]

The likelihood function is $f(n_1|\alpha,n) = [\frac{n!}{n_1!(n-n_1)!}]\alpha^{n_1}(1-\alpha)^{n-n_1}$ The prior for $\alpha$ $g(\alpha)=(\alpha(1-\alpha))^{-1}$ for $\alpha$ between 0 and 1. ...
440
votes
11answers
170k 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 ...
73
votes
4answers
21k 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 ...
50
votes
3answers
66k views

What is the difference in Bayesian estimate and maximum likelihood estimate?

Please explain to me the difference in Bayesian estimate and Maximum likelihood estimate?
15
votes
1answer
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 ...
11
votes
2answers
16k views

Bayesian logit model - intuitive explanation?

I must confess that I previously haven't heard of that term in any of my classes, undergrad or grad. What does it mean for a logistic regression to be Bayesian? I'm looking for an explanation with a ...
13
votes
3answers
794 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 ...
5
votes
1answer
14k views

How do I choose parameters for my beta prior?

Suppose today I'm going to flip a coin. I believe that 9 of 10 flips will come up heads. I flip the coin and 8 of 10 are heads. Is my distribution of belief beta(9+8, 1+2) beta(1+9+8, 1+1+2) beta(...
1
vote
1answer
2k views

Posterior vs conditional probability

When talking about events, there is the following formula called Bayes' rule, where $A$ and $B$ are random events: $$P(A|B)=\frac{P(B|A)P(A)}{P(B)}$$ Now let's say that for now only $A$ happened. I ...
5
votes
2answers
199 views

Estimation derived from ignorance

Is something wrong with the following reasoning? Mostly I wonder how could one derive uniformly random arrival from ignorance. But even if that derivation is invalid generally, it seems reasonable ...
6
votes
1answer
320 views

Comparing two groups with binomially distributed data

Below (in R), I have two INDEPENDENT groups of scores that are binomially distributed. These two groups of scores are known to have different probability of success (i,e., $p_1 \neq p_2$). Let's ...
1
vote
2answers
315 views

Conditional probabilities/expectations

A coin minting machine randomly produces unbalanced coins so that the probability of getting a head in tossing a coin is a random variably $Y$. Supposed $Y$ has a pdf $f(y) = 2y$ for $0 <= y <= ...
0
votes
1answer
174 views

Find a posterior distribution [closed]

I came across this task that I have no idea how to solve, because I'm not very good at statistics, so I was wondering if someone could help me understand it. 7 scientists with very different ...
3
votes
1answer
175 views

Estimating probability or frequency with low N?

I am trying to estimate the probability of an event using a low number of observations. The naive estimator $\hat{p} =\frac{\text{number of positive observations}}{\text{total number of observations}}...

15 30 50 per page