In the frequentist approach to inference, statistical procedures are assessed by their performance over a hypothetical long run of repetitions of a process deemed to have generated the data.

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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 ...
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0answers
20 views

Is there any way to convert from a posterior probability to p-value, or the opposite?

I have results of a study from associations of a variant with a phenotype in the form of posterior probabilities but I was wondering if there is any way to convert these to p-values, even making ...
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1answer
271 views

Concrete examples of a frequentist approach that is superior to a Bayesian one [closed]

Can you help me understand the frequentist point of view in the bayesian vs frequentist debate? I have read a lot and all the sources I found are either filled with complex equations or written from a ...
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19 views

p-value of observation in non-parametric distribution

The question is really naive but i'm stucked in... I'll eliminate all the biological details and experiments and quote just the problem at hand. I would like to know how to proceed. If the data (or ...
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1answer
33 views

Different methods, different confidence intervals

A definition of a confidence interval could be: A confidence interval for the parameter θ, with confidence level or confidence coefficient γ, is an interval with random endpoints ($u(X)$, ...
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42 views

Bayesian interpretation of the repeated sampling principle

My question is philosophical rather than practical, and I will try to explain it through an example: Consider a Kaggle competition. All these contests have a similar structure: A "train dataset" is ...
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16 views

Are there any statistical fallacies that go with E-values?

I am presently learning how to use bioinformatics tools and among the first things to encounter was the notion of an E-value, explained on NCBI's help page for sequence alignment tool BLAST. As far as ...
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38 views

Is there a conceivable frequentist counter to the Bayesian calculation of life in other planets?

This paper in the Proceedings of the Natural Academy of Sciences of the United States of America attempts to give a Bayesian probability of life outside planet Earth. Their approach is based on a ...
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1answer
54 views

Mathematical prove that the posterior probability that a CI contains the true parameter is $\{0,1\}$

There are great posts on confidence intervals, a subject that was brought up recently on this question, leading to an endogamous and circular surfing between CV classics, such as this one and this one ...
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38 views

Statistical Inference Under Misspecification

The classical treatment of statistical inference relies on the assumption that that a correctly specified statistical is used exists. That is, the distribution $\mathbb{P}^*(Y)$ that generated the ...
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1answer
140 views

When can't frequentist sampling distribution be interpreted as Bayesian posterior in regression settings?

My actual questions are in the last two paragraphs, but to motivate them: If I am attempting to estimate the mean of a random variable that follows a Normal distribution with a known variance, I've ...
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1answer
71 views

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 ...
6
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1answer
98 views

Bayesian vs. Frequentist calculation steps

This article contains an example of Bayesian vs. Frequentist philosophies. An old drug successfully treats 70% of patients. To test a new drug, researchers give it to 100 patients, 83 of whom ...
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1answer
55 views

Bayesian vs. frequentist view [duplicate]

I have tried to figure out the difference between the two views of looking at the world: Bayesian and frequentist. Can someone please let me know if I have it right? (Please do not refer me to some ...
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2answers
254 views

Why is maximum likelihood estimation considered to be a frequentist technique

Frequentist statistics for me is synonymous for trying to make decision that are good for all possible samples. I.e., a frequentist decision rule $\delta$ should always try to minimize the frequentist ...
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0answers
51 views

Confidence-interval / p-value duality vs. frequentist interpretation of CIs

Many sources suggest that there is a duality between confidence intervals and hypothesis testing.(*) But I'm having trouble making sense of this philosophically. The frequentist interpretation of a ...
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0answers
10 views

distribution of the probabliity of multivariate Bernoulli

A p-dimension vector $\mathbf{X}$ has multi-variate Bernoulli distribution and all dimensions are mutually independent. $\mathbf{X}$ has distribution ...
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1answer
36 views

Determining the consistency of two measurements

Suppose there are two independent measurements, $x_1 \pm \sigma_1$ and $x_2 \pm \sigma_2$, both of which purport to measure the same underlying quantity $X$ (which is apriori unknown). For simplicity, ...
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1answer
40 views

Why need frequentist considered “a distribution of possible data sets D” in likelihood function p(D|w)?

There some words in PRML: In a frequentist setting, w is considered to be a fixed parameter, whose value is determined by some form of ‘estimator’, and error bars on this estimate are obtained by ...
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2answers
96 views

Statistical significance with insufficient data

There is an article in Wikipedia which talks about p-values. In the example section it gives this example: One roll of a pair of dice Suppose a researcher rolls a pair of dice once and ...
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1answer
57 views

When to use bayesian methods and when to use frequentist methods

So, I'm diving into learning statistics. I'm finally starting to intuitively grasp the difference between bayesianism and frequentism. I understand that both are neither wrong nor right. To further ...
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1answer
62 views

Am I understanding differences between Bayesian and frequentist inference correctly?

Given a sequence of independent experiments, each having as its outcome either success or failure, the probability of success being some number p between 0 and 1: A Bayesian would consider the ...
2
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2answers
142 views

How exactly do Bayesians define (or interpret?) probability?

Part of a series of trying to understand Bayesian vs frequentist: 1 2 3 4 5 6 7 I think I get the difference of how Bayesians and frequentists approach choosing between hypotheses, but I'm not quite ...
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44 views

Role of the Objective Prior in the Unification of Bayesian and Frequentists

On a recent post asking about self-identified Bayesians (most comprehensive list: ISBA) there were great answers, yet little was mentioned about the drive towards unification. Except from Andrew ...
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40 views

What are frequentist approaches to logistic regression besides MLE?

Related to these two questions: Bayesian logit model - intuitive explanation?, How can Bayesian inference improve upon logistic regression in incorporating psychometric data? From what I know and ...
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3answers
628 views

Is OLS the frequentist approach to linear regression?

In this Wikipedia article, there is this sentence: This is a frequentist approach Is 'this' referring to OLS? Is it really 'a' rather than 'the'? What are some other frequentist approaches? As ...
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0answers
33 views

Frequentist statistics

Frequentist inference is the only form of statistics taught in my department, and I feel like it has a strong hold over many students here. But when I read data science blogs, I get the feeling that ...
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12answers
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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 ...
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1answer
53 views

Is this posterior probability integral right?

From Wiki: where , k is binomially distributed, and I'm not sure about u. I'm thinking that the second line should be: I mean, if we let X represent the toss of a die, then $P(X = 1, 2, ...
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1answer
117 views

How do frequentists guess a distribution?

With competing hypotheses such as testing if a coin is fair, frequentists and Bayesians have their own approaches. What about for coming up with a distribution? In An Essay towards solving a Problem ...
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0answers
33 views

Percentile vs Percentile rank

I have the read the definitions many times and I still don't quite understand the difference. This article says: A statement such as: "A score of 600 has a percentile rank of 80" has a ...
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0answers
67 views

How would frequentists reason about the sunrise problem if forced to abandon the 'many worlds' assumption?

I think the 'many worlds' assumption is much more than a technicality yet it has no solid theoretical foundations. The sunrise problem asks for the probability that the sun will rise tomorrow given ...
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0answers
51 views

How do you solve Bayes' Billiards game with frequentist statistics?

The problem goes like this: Alice and Bob are playing a game that they cannot directly observe. The game starts with a referee rolling a ball on a billiard table and marking the location where it ...
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67 views

Can anyone give a simple example of when Bayesian and frequentist methods give exactly the same answer? [closed]

Is this even possible given the differences in the philosophies of the two methods?
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1answer
93 views

Interpretation of Bayesian vs Frequentist statement

Although I am completely new to Bayesian Analysis I struggle sometimes when trying to investigate some intersections between Bayesian and Frequentist analysis. I would like to discuss the different ...
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1answer
82 views

What are some examples of statistics problems where Bayesian and frequentist approaches give different answers? [duplicate]

I've heard of the one found here: http://www.behind-the-enemy-lines.com/2008/01/are-you-bayesian-or-frequentist-or.html about flipping a coin fourteen times, having it come up heads ten times, and ...
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2answers
305 views

Question about the true nature of errors

In frequentist statistics, in regression analysis, errors, like random variables, have a distribution. Errors, like parameters, can be estimated and the residuals of the model are their estimates. So ...
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2answers
110 views

When Bayesian and frequentist statistics give different answers, is there a way to empirically test which one corresponds more closely to reality?

For example for this problem: You have a coin that when flipped ends up head with probability p and ends up tail with probability 1−p. (The value of p is unknown.) Trying to estimate p, you ...
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0answers
44 views

What is Frequentist Inference?

Frequentist Inference is defined as (according to the tag wiki) : In the frequentist approach to inference , statistical procedures are assessed by their performance over a hypothetical long run ...
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0answers
71 views

Correcting for p-value for “frequentist” sampling methodology

I have a regression of the form: $$ Y = \alpha + \beta_{1}*X_{1} + \beta_{2}*X_{2} + \epsilon $$ There are a few subtleties, however, that cause me to suspect the p-values are artificially low. ...
6
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1answer
87 views

Estimating bias in surveys

Say a company runs a survey across random N cities independently in some country estimating the fraction of males and females on each city. E.g.: Males = $X_1$% ...
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22 views

Confidence interval syntax in frequentist probability [duplicate]

Let $\theta$ be an unknown population characteristic (say average height). A confidence interval written as $P(\hat \theta - \delta < \theta < \hat \theta + \delta) = 1 - \alpha$ makes perfect ...
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0answers
7 views

Analytic determination of exact confidence intervals (without making approximations)

I would like to determine 95% confidence intervals for the mean of a negative binomial distribution. I have read a number of papers that use Gamma, Normal and Chi-squared approximations in order to ...
7
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2answers
657 views

What frequentist statistics topics should I know before learning Bayesian statistics?

I was wondering if there is a subset of topics of frequentist statistics that one should know before starting to learn Bayesian statistics. Once I read that it seems that the two trends are ...
10
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2answers
596 views

Does a confidence interval actually provide a measure of the uncertainty of a parameter estimate?

I was reading a blog post by the statistician William Briggs, and the following claim interested me to say the least. What do you make of it? What is a confidence interval? It is an equation, of ...
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1answer
70 views

Intuitive interpretation of Bayes risk $R(\delta, \lambda) = \int_{\Omega}R(\theta, \delta) \lambda(\theta) d\theta$

Consider the risk function R of an estimator (statistic) $\delta(X)$ trying to estimate parameter $\theta$: $$R(\theta, \delta) = E_{X \sim P_{\theta}}[Loss(\theta,\delta(X)]$$ Which can be ...
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1answer
87 views

How is data generated in the Bayesian framework and what is the nature on the parameter that generates the data?

I was trying to re-learn Bayesian statistics (every time I thought I finally got it, something else pops out that I didn't consider earlier....) but it wasn't clear (to me) what the data generation ...
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1answer
79 views

Why can we assume that samples $X_i$'s are independent if the parameter is fixed (though unknown)?

To put it in context, I was trying to learn Bayesian parameter estimation (by an example of learning the probability of heads of a coin) and was trying to understand the independence of the samples ...
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What is the frequentist take on the voltmeter story?

What is the frequentist take on the voltmeter story and its variations? The idea behind it is that a statistical analysis that appeals to hypothetical events would have to be revised if it was later ...
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0answers
54 views

How can you judge the statistical confidence and validity of output from a multi arm bandit algorithm like UCB1

To say something about the validity of outcomes in frequentist statistics we have concepts like significance levels and statistical power and in Bayesian analytics we have credible intervals. In a ...