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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How would a bayesian and a frequentist answer this question? [on hold]

I have a site which which in which there are lets say 1000 visitors every month and out of 1000, 10 people actually sign up on my site which leads to a 1% conversion rate. Now I invest in the ...
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68 views

How to correctly calculate the type I error in a two-step clinical trial when stopping after the first step?

I just finished reading the following article by Berger & Berry (1988) in which they explain how subjectivity enters statistical analyses. One of their examples concerns a clinical trial with ...
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54 views

How to understand difference between Frequentist Statistics and Bayesian Statistics [on hold]

I have already searched about following . Couldn't find any which suffice a layman on topic like me to build up the concept. How do the frequentist and bayesian approaches compare each other (e.g., ...
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DIfferent zero-inflated poisson model outputs of Frequentist and Bayesian

I modeled zero-inflated poisson regression using crime data. There are 10034 obs and let assume spatial autocorrelation is not significant. For the Frequentist approach, R was used and code is ...
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1answer
147 views

Did frequentist statistics try to squash Bayesian ones?

From http://www.bayesianphilosophy.com/dont-ban-p-values/: When Frequentists dominated statistics from about 1930 to 1990 or so, they engaged in every kind of draconian, career destroying, and ...
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133 views

Should I have “Confidence” in Credibility Intervals?

Preliminaries First, I know that the Bayesian/Frequentist debate is rather long in tooth at this point, but I hope my question is sufficiently different from the others I reviewed on this site before ...
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5answers
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What do confidence intervals say about precision (if anything)?

Morey et al (2015) argue that confidence intervals are misleading and there are multiple bias related to understanding of them. Among others, they describe the precision fallacy as following: The ...
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48 views

Bayesian vs Frequentist: Linear Regression [closed]

I was reading up the Bayesian and Frequentist approach in determining the estimator for building the linear regression model. From what I understood, in case of a frequentist approach, one needs to ...
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26 views

How to determine lift (percentage of improvement) in Frequentist Statistics

In Bayesian statistics, I can easily compute the lift of an experiment by computing the relative increase distribution of both posterior distributions. How would I compute the lift of an experiment ...
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7answers
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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 ...
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1answer
59 views

Why does frequentist statistics have a reputation for not giving uncertainty?

We can compute confidence intervals in frequentist statistics. That gives us an indicator on how uncertain our estimate is. I've read numerous times that Bayesian statistics is way better because we ...
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58 views

Is Statistical Significance only a concept in Frequentist statistics - not Bayesian statisticians?

Statistical significance is denoted to occur when: ...
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1answer
55 views

Frequentist vs Bayesian Linear Gaussian Models

Consider the following linear Gaussian system: where $p(x)$ is our prior. The Bayesian inference problem can be expressed in closed-form as1: Where can I find an equivalent "frequentist" ...
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11answers
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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
22 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
313 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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22 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
35 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 ($u(X)$, $v(X)...
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48 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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39 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
84 views

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

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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45 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
170 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
97 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 ...
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1answer
103 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
83 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
280 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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102 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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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 $p(X)=\Pi_{i=1}^pp_i^{X_i}(1-p_i)^{1-X_i},\;X_i\in\...
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41 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
127 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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62 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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73 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 ...
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2answers
173 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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54 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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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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685 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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44 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
8k 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 ...
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1answer
57 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, 3,...
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1answer
132 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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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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81 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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82 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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72 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
102 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
91 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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314 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 ...