Questions tagged [bayesian]

Bayesian inference is a method of statistical inference that relies on treating the model parameters as random variables and applying Bayes' theorem to deduce subjective probability statements about the parameters or hypotheses, conditional on the observed dataset.

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410
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14answers
259k views

Bayesian and frequentist reasoning in plain English

How would you describe in plain English the characteristics that distinguish Bayesian from Frequentist reasoning?
285
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9answers
161k views

What's the difference between a confidence interval and a credible interval?

Joris and Srikant's exchange here got me wondering (again) if my internal explanations for the difference between confidence intervals and credible intervals were the correct ones. How you would ...
261
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11answers
178k views

How would you explain Markov Chain Monte Carlo (MCMC) to a layperson?

Maybe the concept, why it's used, and an example.
227
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38answers
136k views

What is the best introductory Bayesian statistics textbook?

Which is the best introductory textbook for Bayesian statistics? One book per answer, please.
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15answers
76k views

Amazon interview question—probability of 2nd interview

I got this question during an interview with Amazon: 50% of all people who receive a first interview receive a second interview 95% of your friends that got a second interview felt they had a good ...
143
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3answers
210k 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. ...
128
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14answers
27k views

What's wrong with XKCD's Frequentists vs. Bayesians comic?

This xkcd comic (Frequentists vs. Bayesians) makes fun of a frequentist statistician who derives an obviously wrong result. However it seems to me that his reasoning is actually correct in the sense ...
116
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10answers
7k views

ASA discusses limitations of $p$-values - what are the alternatives?

We already have multiple threads tagged as p-values that reveal lots of misunderstandings about them. Ten months ago we had a thread about psychological journal that "banned" $p$-values, now American ...
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12answers
11k views

Who Are The Bayesians?

As one becomes interested in statistics, the dichotomy "Frequentist" vs. "Bayesian" soon becomes commonplace (and who hasn't read Nate Silver's The Signal and the Noise, anyway?). In talks and ...
92
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8answers
12k views

Are there any examples where Bayesian credible intervals are obviously inferior to frequentist confidence intervals

A recent question on the difference between confidence and credible intervals led me to start re-reading Edwin Jaynes' article on that topic: Jaynes, E. T., 1976. `Confidence Intervals vs Bayesian ...
87
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4answers
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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 ...
87
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11answers
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Why should I be Bayesian when my model is wrong?

Edits: I have added a simple example: inference of the mean of the $X_i$. I have also slightly clarified why the credible intervals not matching confidence intervals is bad. I, a fairly devout ...
83
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14answers
17k views

When (if ever) is a frequentist approach substantively better than a Bayesian?

Background: I do not have an formal training in Bayesian statistics (though I am very interested in learning more), but I know enough--I think--to get the gist of why many feel as though they are ...
81
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2answers
23k views

XKCD's modified Bayes theorem: actually kinda reasonable?

I know this is from a comic famous for taking advantage of certain analytical tendencies, but it actually looks kind of reasonable after a few minutes of staring. Can anyone outline for me what this "...
77
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2answers
42k views

Bayes regression: how is it done in comparison to standard regression?

I got some questions about the Bayesian regression: Given a standard regression as $y = \beta_0 + \beta_1 x + \varepsilon$. If I want to change this into a Bayesian regression, do I need prior ...
71
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11answers
10k views

Is there any *mathematical* basis for the Bayesian vs frequentist debate?

It says on Wikipedia that: the mathematics [of probability] is largely independent of any interpretation of probability. Question: Then if we want to be mathematically correct, shouldn't we ...
69
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5answers
24k views

Why is the Jeffreys prior useful?

I understand that the Jeffreys prior is invariant under re-parameterization. However, what I don't understand is why this property is desired. Why wouldn't you want the prior to change under a change ...
69
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8answers
8k views

What is a good, convincing example in which p-values are useful?

My question in the title is self explanatory, but I would like to give it some context. The ASA released a statement earlier this week “on p-values: context, process, and purpose”, outlining various ...
67
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7answers
6k views

Where did the frequentist-Bayesian debate go?

The world of statistics was divided between frequentists and Bayesians. These days it seems everyone does a bit of both. How can this be? If the different approaches are suitable for different ...
66
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7answers
4k views

How much to pay? A practical problem

This is not a home work question but real problem faced by our company. Very recently (2 days ago) we ordered for manufacturing of 10000 product labels to a dealer. Dealer is independent person. He ...
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8answers
6k views

Are bayesians slaves of the likelihood function?

In his book "All of Statistics", Prof. Larry Wasserman presents the following Example (11.10, page 188). Suppose that we have a density $f$ such that $f(x)=c\,g(x)$, where $g$ is a known (nonnegative, ...
63
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3answers
91k 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?
63
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9answers
5k views

List of situations where a Bayesian approach is simpler, more practical, or more convenient

There have been many debates within statistics between Bayesians and frequentists. I generally find these rather off-putting (although I think it has died down). On the other hand, I've met several ...
61
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11answers
16k views

Examples of Bayesian and frequentist approach giving different answers

Note: I am aware of philosophical differences between Bayesian and frequentist statistics. For example "what is the probability that the coin on the table is heads" doesn't make sense in ...
61
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2answers
34k views

What does the inverse of covariance matrix say about data? (Intuitively)

I'm curious about the nature of $\Sigma^{-1}$. Can anybody tell something intuitive about "What does $\Sigma^{-1}$ say about data?" Edit: Thanks for replies After taking some great courses, I'd ...
57
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2answers
36k views

What is the difference between a particle filter (sequential Monte Carlo) and a Kalman filter?

A particle filter and Kalman filter are both recursive Bayesian estimators. I often encounter Kalman filters in my field, but very rarely see the usage of a particle filter. When would one be used ...
56
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1answer
18k views

Can someone explain the concept of 'exchangeability'?

I see the concept of 'exchangeability' being used in different contexts (e.g., bayesian models) but I have never understood the term very well. What does this concept mean? Under what circumstances ...
54
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10answers
9k views

Who are frequentists?

We already had a thread asking who are Bayesians and one asking if frequentists are Bayesians, but there was no thread asking directly who are frequentists? This is a question that was asked by @...
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2answers
4k views

Why is a Bayesian not allowed to look at the residuals?

In the article "Discussion: Should Ecologists Become Bayesians?" Brian Dennis gives a surprisingly balanced and positive view of Bayesian statistics when his aim seems to be to warn people about it. ...
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6answers
5k views

Eliciting priors from experts

How should I elicit prior distributions from experts when fitting a Bayesian model?
48
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7answers
7k views

Why would someone use a Bayesian approach with a 'noninformative' improper prior instead of the classical approach?

If the interest is merely estimating the parameters of a model (pointwise and/or interval estimation) and the prior information is not reliable, weak, (I know this is a bit vague but I am trying to ...
48
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6answers
8k views

Bayesian statistics tutorial

I am trying to get upto speed in Bayesian Statistics. I have a little bit of stats background (STAT 101) but not too much - I think I can understand prior, posterior, and likelihood :D. I don't want ...
48
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3answers
6k views

Is it possible to interpret the bootstrap from a Bayesian perspective?

Ok, this is a question that keeps me up at night. Can the bootstrap procedure be interpreted as approximating some Bayesian procedure (except for the Bayesian bootstrap)? I really like the Bayesian "...
47
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8answers
18k views

What are the cons of Bayesian analysis?

What are some practical objections to the use of Bayesian statistical methods in any context? No, I don't mean the usual carping about choice of prior. I'll be delighted if this gets no answers.
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8answers
34k views

Bayesian vs frequentist Interpretations of Probability

Can someone give a good rundown of the differences between the Bayesian and the frequentist approach to probability? From what I understand: The frequentists view is that the data is a repeatable ...
47
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4answers
21k views

Bayesian equivalent of two sample t-test?

I'm not looking for a plug and play method like BEST in R but rather a mathematical explanation of what are some Bayesian methods I can use to test the difference between the mean of two samples.
45
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8answers
7k views

Would a Bayesian admit that there is one fixed parameter value?

In Bayesian data analysis, parameters are treated as random variables. This stems from the Bayesian subjective conceptualization of probability. But do Bayesians theoretically acknowledge that there ...
45
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6answers
5k views

How seriously should I think about the different philosophies of statistics?

I've just finished a module where we covered the different approaches to statistical problems – mainly Bayesian vs frequentist. The lecturer also announced that she is a frequentist. We covered some ...
45
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1answer
11k views

Variational inference versus MCMC: when to choose one over the other?

I think I get the general idea of both VI and MCMC including the various flavors of MCMC like Gibbs sampling, Metropolis Hastings etc. This paper provides a wonderful exposition of both methods. I ...
44
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3answers
95k views

Difference between naive Bayes & multinomial naive Bayes

I've dealt with Naive Bayes classifier before. I've been reading about Multinomial Naive Bayes lately. Also Posterior Probability = (Prior * Likelihood)/(Evidence). The only prime difference (while ...
42
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1answer
19k views

What are posterior predictive checks and what makes them useful?

I understand what the posterior predictive distribution is, and I have been reading about posterior predictive checks, although it isn't clear to me what it does yet. What exactly is the posterior ...
41
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2answers
44k 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 ...
40
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3answers
8k views

What kind of information is Fisher information?

Suppose we have a random variable $X \sim f(x|\theta)$. If $\theta_0$ were the true parameter, the the likelihood function should be maximized and the derivative equal to zero. This is the basic ...
40
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3answers
3k views

What is the Wine/Water Paradox in Bayesian statistics, and what is its resolution?

I have just heard about the Wine/Water Paradox in Bayesian statistics, but didn't understand it very well (see Mikkelson 2004 for an introduction). Can you explain in simple terms what the paradox is ...
40
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4answers
17k views

What are the factors that cause the posterior distributions to be intractable?

In Bayesian statistics, it is often mentioned that the posterior distribution is intractable and thus approximate inference must be applied. What are the factors that cause this intractability?
40
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5answers
59k views

What exactly is a Bayesian model?

Can I call a model wherein Bayes' Theorem is used a "Bayesian model"? I am afraid such a definition might be too broad. So what exactly is a Bayesian model?
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7answers
18k views

Combining probabilities/information from different sources

Lets say I have three independent sources and each of them make predictions for the weather tomorrow. The first one says that the probability of rain tomorrow is 0, then the second one says that the ...
38
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2answers
39k views

Why is the Dirichlet distribution the prior for the multinomial distribution?

In LDA topic model algorithm, I saw this assumption. But I don't know why chose Dirichlet distribution? I don't know if we can use Uniform distribution over Multinomial as a pair?
38
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6answers
4k views

What is the connection between credible regions and Bayesian hypothesis tests?

In frequentist statistics, there is a close connection between confidence intervals and tests. Using inference about $\mu$ in the $\rm N(\mu,\sigma^2)$ distribution as an example, the $1-\alpha$ ...

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