Questions tagged [bayesian]

The approach and interpretation of probability associated with Bayes' theorem; usually used as opposed to the frequentist approach. It can be seen as an extension of logic that enables reasoning with propositions whose truth or falsity is uncertain. A Bayesian probabilist starts with some prior probability, and evaluates the evidence in favour of a hypothesis by combining the prior with the likelihood function of the observed data.

1838 questions
35
votes
3 answers

Bayes rule with multiple conditions

I am wondering how I would apply Bayes rule to expand an expression with multiple variables on either side of the conditioning bar. In another forum post, for example, I read that you could expand $P(a,z \mid b)$ using Bayes rule like this (see…
maogenc
  • 1,085
  • 2
  • 18
  • 21
28
votes
8 answers

Facebook Question (Data Science)

Out of curiosity, here's a question from Glassdoor (Facebook Data Science Interview) You're about to get on a plane to Seattle. You want to know if you should bring an umbrella. You call 3 random friends of yours who live there and ask each…
Vincent
  • 425
  • 1
  • 4
  • 6
18
votes
2 answers

Cat dead or alive?

You put a cat into a toxic box, it might be dead or alive after an hour. Two witches $A$ and $B$ have the ability to predict the status of the cat with the accuracy of $p_1$ and $p_2$, respectively.Suppose their prediction are independent. Both…
fizis
  • 943
  • 7
  • 20
15
votes
5 answers

Bayes, two tests in a row

I came up with a standard Bayesian example as to point out my confusion. There is an epidemic. A person has a probability $\frac{1}{100}$ to have the disease. The authorities decide to test the population, but the test is not completely reliable:…
Vincent Warmerdam
  • 297
  • 1
  • 2
  • 8
15
votes
5 answers

Bayes Theorem Example in Nate Silver's The Signal and the Noise

In his book The Signal and the Noise, Nate Silver presents this example application of Bayes's Theorem on pp. 247-248: Consider a somber example: the September 11 attacks. Most of us would have assigned almost no probability to terrorists…
David
  • 584
  • 3
  • 13
13
votes
3 answers

What is the most general formalism for machine learning?

Most of the literature I can find in the field of machine learning is extremely practical, listing many techniques you can use like neural networks, SVMs, random forests, and so on. There are lots of suggestions on implementations and what…
13
votes
2 answers

Bayesian posterior with truncated normal prior

Suppose we observe one draw from the random variable $X$, which is distributed with normal distribution $\mathcal{N}(\mu,\sigma^2)$. The variance $\sigma^2$ is known, $\mu$ isn't. We want to estimate $\mu$. Suppose further that the prior…
13
votes
3 answers

What is the meaning of "mean-field"?

In lots of Bayesian papers, people use variational approximation. In lots of them they call it "mean-field variational approximation". Does anyone know what is the meaning of mean-field in this context?
Daniel
  • 2,390
  • 1
  • 19
  • 31
13
votes
1 answer

Is Edwin Jaynes correct about statistics?

I've recently been reading Edwin Jaynes's book, Probability Theory: The Logic of Science, and I was struck by Jaynes's hostile view of what he dubs "orthodox statistics." He repeatedly claims that much of statistics is a giant mess, and argues that…
SilasLock
  • 578
  • 2
  • 15
13
votes
1 answer

Is Entropy = Information circular or trivial?

I have seen several "maximum entropy distributions" used in the mathematical and statistical literature, often with the justification that they are "minimally informed" beyond the assumptions and data used to construct them. However, it seems that…
12
votes
6 answers

Probability of getting heads given that first flip was a head?

What's the probability of getting heads on the second toss given that the first toss was a head. (Trying to refresh my probability a bit). I've seen this analyzed like this: HH 1/4 HT 1/4 TH 1/4 TT 1/4 So since we are given information (Head on…
Ole
  • 247
  • 1
  • 2
  • 10
11
votes
2 answers

Bayesian Inference in Measure Theory

What's the deal. How does this work, or can you point me to some references? I tried $\mu(A|B) = \mu(A \cap B) / \mu(B)$ and got stuck on $\mu(B) = 0$. Edit: Sorry for being lazy. My background is the basics of measure theory (working on it):…
usul
  • 3,464
  • 2
  • 22
  • 25
10
votes
2 answers

Is there an introduction to probability and statistics that balances frequentist and bayesian views?

Perhaps, roughly, I might be described as advanced undergraduate regarding mathematics. However, I have not learned statistics and have only learned elementary probability. Does there exist a book or monograph that introduces probability and…
joeA
  • 1,439
  • 2
  • 14
  • 19
10
votes
2 answers

Probability of number of people who know a rumor

Suppose that among a group of $n$ people, some unknown number of people $K$ know a rumor. If someone knows the rumor, there is a probability $p$ that they will tell it to us if we ask. If they don't know the rumor they will always say they don't…
Max
  • 226
  • 1
  • 9
9
votes
2 answers

Why do many textbooks on Bayes' Theorem include the frequency of the disease in examples on the reliability of medical tests?

A "standard" example of Bayes Theorem goes something like the following: In any given year, 1% of the population will get disease X. A particular test will detect the disease in 90% of individuals who have the disease but has a 5% false positive…
1
2 3
99 100