Linked Questions

102 votes
31 answers

Is there a way to remember the definitions of Type I and Type II Errors?

I'm not a statistician by education, I'm a software engineer. Yet statistics comes up a lot. In fact, questions specifically about Type I and Type II error are coming up a lot in the course of my ...
53 votes
9 answers

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 ...
17 votes
2 answers

Relation between MAP, EM, and MLE

I am a beginner in machine learning. I can do programming fine but the theory confuses me a lot of the times. What is the relation between Maximum Likelihood Estimation (MLE), Maximum A posteriori (...
4 votes
2 answers

Can someone explain why Bayesian networks are called "Bayesian"

I have been reading Jensen's book on Bayesian Networks and Decision Graphs as well as the Deep Learning book by Bengio, et. al. I am trying to understand why undirected graphs are referred to as ...
1 vote
2 answers

Bayesian : Comparing means of two posterior samples/ Help a Frequentist Out

UPDATE Thanks for the many thoughtful responses and questions! I've made edits here to clarify further. and also respond to each respondent individually. Original Post I have two sets of posterior ...
7 votes
2 answers

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
2 answers

Bayesian vs. frequentist estimation

I don't really understand the connection between bayesian to "normal" frequentist estimation. Suppose we want to estimate the expected value of a population given a sample. In frequentist statisics ...
5 votes
2 answers

Bayesian and frequentist optimization and intervals

I realize the methodology pursued by the Frequentist and Bayesian camps generally differ. However, one method of estimation that they do share is optimization of a certain function: Frequentists ...
20 votes
2 answers

How to apply Bayes' theorem to the search for a fisherman lost at sea

The article The Odds, Continually Updated mentions the story of a Long Island fisherman who literally owes his life to Bayesian Statistics. Here's the short version: There are two fishermen on a ...
1 vote
0 answers

Does bayesians' critique to frequentists apply to themselves too?

I've been reading about bayesians versus frequentists, including articles in this forum (like this one). Key is of course the issue of "priors". The bayesian critique being that frequentists ...
9 votes
1 answer

Bayesian Bootstrap interpretation

I am using Bayesian Bootstrap for some analysis. Given dataset $X=\{x_1, \dots, x_N\}$, we generate bootstrapped samples $X_1,\dots, X_K$ by sampling from the $X$, with replacement. In classical ...
11 votes
5 answers

Why would perfectly similar data have 0 mutual information?

I'm not a statistic major, so my knowledge of statistics is quite limited but I've found myself in need of learning about and using mutual information. I believe I understand the concept and formula, ...
16 votes
5 answers

Is there more to probability than Bayesianism?

As a student in physics, I have experienced the "Why I am a Bayesian" lecture perhaps half a dozen times. It is always the same -- the presenter smugly explains how the Bayesian interpretation is ...
4 votes
2 answers

Why would considering $\theta$ to be a random variable not be 'Bayesian'?

I am currently studying the textbook In All Likelihood -- Statistical Modelling and Inference Using Likelihood by Yudi Pawitan. Section Inverse probability: the Bayesians of chapter 1 says the ...
10 votes
3 answers

Bayesian AB testing

I am running an AB Test on a page that receives only 5k visits per month. It would take too long to reach traffic levels necessary to measure a +-1% difference between the test and control. I have ...

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