Questions tagged [frequentist]

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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justification for 'population prediction intervals'?

Suppose we are living in a frequentist world and want to compute confidence intervals on some quantity that is a complicated function of the parameters $q_1 = f(\Theta)$ (i.e., there's no closed-form ...
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Frequentist method for random samples from unknown urn

Say you have two urns with a large number of red and blue marbles each and you know the proportion of red and blue marbles in each urn. Now we choose one urn at random (but don't know which) and ...
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Can we say the frequentist interpretation of probability is more appropriate in the dice rolling problem?

Suppose we role a dice and see what we get, the sample space is $\{1,2,3,4,5,6\}$ and each outcome occurs with probability 1/6. For example, if we look at the probability that 6 appears, it seems ...
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Frequentist vs bayesian statistics [duplicate]

Is the probability theory used in frequentist and bayesian statistics the same? I know that the interpretation of the concept of probability is different under both approaches, but is it the case too ...
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Bayesian or Frequentist goodnes of fit: depends on the data?

I'm working with the data of the real masses of exoplanets published in the catalogues (NASA, exoplanet.eu). Those catalogues update almost everyday by adding new exoplanet data or correcting some of ...
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Why are there n interpretations of probability, yet only two of those interpretations led to philosophies in statistical inference?

Why are the subjectivist (bayesians) and frequentist (objectivist) statisticians but no propensity statisticians? It seems that every interpretation of probability should yield its own branch of ...
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Are there any (exponential) families without a minimal sufficient statistic?

Bahadur's theorem says that if a minimal sufficient statistic exists, then a complete sufficient statistic is also minimal sufficient. Are there any (homogenous, identifiable) families with a complete ...
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Are CI and hypothesis tests purely frequentist tools?

I've been learning statistics for a long time but I still struggle to understand the "philosophical" differences between frequentist and bayesian statistics. One of my questions is the ...
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bayesian vs frequentist statistics conceptual question [duplicate]

I've been learning statistics for a long time but I still struggle to understand the "philosophical" differences between frequentist and bayesian statistics. AFAIK, frequentist and bayesian ...
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Comparison of frequentist methods (say, averaged over Monte Carlo simulations) and Bayesian method

I have read a lot of questions with answers like this one, How do Bayesians verify their methods using Monte Carlo simulation methods?, which stated that Monte Carlo methods are not suitable for ...
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Frequentist interpretation of probability for different/multiple experiments

Suppose I have a population of interest, let's say P1, I obtain data through a sample, D1 and obtain a 95% confidence interval on a parameter value of interest, CI1. The interpretation of the ...
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Comparison of bayesian and frequentist methods example

I am trying to understand the intuition behind Bayesian and frequentist hypothesis testing and came up with the following example to understand the differences. Do you agree that the following ...
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Frequentist inference with Dirac delta as prior

Would likelihood-based frequentist inference amount to the same as Bayesian inference, but where the "frequentist prior" $\pi^F(\theta) = \delta_{\theta^*}(\theta)$ with $\delta_{\theta^*}$ ...
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Welford vs Bayes?

To incrementally estimate the mean and standard deviation of some data one can use an algorithm such as Welford’s algorithm or Bayesian updating by using the likelihood, a conjugate prior and ...
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Within the frequentist "school of thought" how are beliefs updated?

Background Edit: I realize my use of the word "hypothesis" is confusing, I do not mean specifically a null hypothesis. I mean a proposition that something is true. From my limited ...
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Combining frequentist and bayesian model

It has been said that combining frequentist model with a bayesian model is mathematically incorrect. Is this true? Can there be genuine cases where these two types of equations or algorithms can be ...
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Is it incorrect to say that $\text{Power} = P(\text{reject } H_0)$?

Is it incorrect to say that $\text{Power} = P(\text{reject} H_0)$? I've seen in my textbook as well as other sources power is always defined as the conditional probability $P(\text{reject } H_0 : H_a ...
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Binomial test p-value matches Bayesian posterior probability

I recently observed, for the binomial distribution, an equivalence between the frequentist significance level and the Bayesian posterior probability, as I describe below. I would like to know if this ...
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Can Bayesian statistical models reproduce the results of frequentist ones by choosing parameters a certain way?

I am just starting to learn about Bayesian statistics, so forgive me if this is a basic question. For Bayesian counterparts of classical frequentist methods (such as linear regression, ANOVA, t-tests, ...
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Do we really know what does probability mean? [closed]

When I read debates or listen to videos about probabilities and bayesians versus frequentists, it reminds me like a lot the question of "do we know what infinite means?" (related to the ...
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Can there be such things like supervised learning in bayesian approach?

Whenever I encounter articles on supervised learning examples are things like regression, classification, object detection, which are obviously ones following frequentist approach. I've recently ...
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Estimating the error in 3D phase fraction calculations

I am trying to estimate the error of a 3D volume fraction measurement (from X-Ray Microtomography experiments). Kind of like a CT-scan of a small inorganic material with embedded particles. ...
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Bootstrapped regression model for quasi-posterior distributions?

I'm very much of the Bayesian mind and do enjoy the ability to literally integrate my prior beliefs about a system into my parameter estimation. However, the aspect I enjoy most about Bayesian ...
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What's wrong with this interpretation of a 95% confidence interval?

Note: I asked a version of this as part of another question, but I'm re-asking it as a stand-alone question with more detail. I've been trying to come up with more intuitive/less confusing ways to ...
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Is the t-test to test the difference from 0?

I have a variable x with a mean 1 and sd of 3. So most of the mass is above zero. Let's say I have n=100 observations. A t-test will tell me whether the mean of x E(x) is different from 0 or above 0. ...
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Non-self-referential interpretation of confidence intervals?

Interpreting what a (say) 95% confidence interval actually means is obviously tricky, especially when you are trying to teach it to students just beginning to learn stats. One of the biggest ...
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Basic Sampling - Provide confidence of estimate

I tried searching the site but nothing came up. I have a simple situation for a business problem - We have a population of 50 million files. We want to review a sample and see whether a file contains ...
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Mathematically finding a threshold for deciding on rare word

I am implementing spell-correction facility as a preprocessing step of for a text classification project. For this reason I have to make a knowledge-base where I shall be putting all the words along ...
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Why do we trust credibility intervals to contain the true parameter?

I understand confidence intervals and to what extent they can be trusted (and why). However, I’m not so sure how to motivate why I should trust credibility intervals except insofar as they can also ...
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What would be the proper distribution to model the number of particles in a state in canonical ensemble

Suppose my system has $N$ particles, and I want to find a distribution for $n_i$, the number of particles in the $\epsilon_i$ energy state. What I do know is the boltzmann probability, which tells me ...
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How to understand the results of Bayesian analysis from a large scale of observations?

With the sequential equilibrium, the weight of prior is getting weaker and weaker,MAP becomes MLE,Bayesian results become frequentist results. It looks like that, whether using Bayesian or ...
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Multiple comparisons correction methods

I come from a primarily Bayesian background; in my new role at a social networking company, we exclusively use Frequentist statistics and by in large it's in an A/B testing capacity. Often, we'll look ...
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Why can't be hypothesis testing done in opposite way?

When doing hypothesis testing, we calculate the distribution of test statistic (for example z) under null hypothesis and then compare the actual ...
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A Frequentist approach to modeling uncertainty around decision optimization

I'm curious about how a Frequentist would approach an optimization problem, where said problem is constructed using inferred parameters. As an example, I'll use price optimization given a demand curve....
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What is the frequentist interpretation of uncertainty vs. variability?

I have been reading Begg, Welsh, and Bratvold (2014), which is an excellent and lucid discussion of the distinction between uncertainty and variability (from a petro/geostatistics perspective). The ...
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Certainty that probability of survival is greater than threshold - using confidence interval from Cox model

I want to assess the usefulness of a certain risk score. The risk score creates categories, and several studies report cumulative incidences for each risk category. I would like to assess how certain ...
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Statistics question: Why is the standard error, which is calculated from 1 sample, a good approximation for the spread of many hypothetical means?

I'm re-learning statistics and got confused by the idea of taking the standard error from 1 sample's worth of data (standard deviation of sample divided by the square root of sample size, i.e. $\frac{...
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Frequentist Justification for using Student's t-Distribution to Construct Confidence Intervals

In my most recent statistics class, the general1 frequentist approach to constructing confidence intervals2 for an estimator (of any kind) was described as follows: Specify the estimator and the data ...
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Standard Notion of Limit for relative frequency to define probability

I am self studying probability theory and am reading the book: Understanding Probability: Chance Rules in Everyday Life by Henk Tijms. In second chapter he explains about what challenges relative ...
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Bayesian analysis used merely as a computational tool?

I have sometimes seen some statisticians used bayesian analysis and related techniques such as MCMC simply as a tool when a frequentist approach is not satisfying, typically for example when the ...
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What can a p-value (& sign) tell me about the marginal posterior distribution of a model parameter, and when?

EDIT: The tl;dr here would broadly be: given that both frequentist standard errors and a quadratic approximation of a Bayesian joint posterior can be obtained from the square root of the diagonal ...
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Frequentist perspective of regression coefficients and significance (coming from Bayesian background)?

I come from a primarily Bayesian background when using performing statistical analysis. In the context of linear regression, I would look at the posterior distributions for each regression coefficient....
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What is the point of using a Bayesian prior?

I do struggle with the most basic starting point of Bayesian statistics: why is using a prior useful? It seems to me that if anything they hurt much more than help. Moreover, Bayesians always say ...
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Do likelihood-based confidence intervals avoid general criticisms of confidence intervals?

In the literature, I see post-sample criticisms of frequentist confidence intervals — but the usual targets are intervals that use somewhat weak methods such as assumed normality or other long-run/...
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How do Bayesians interpret $P(X=x|\theta=c)$, and does this pose a challenge when interpreting the posterior?

I have seen the post Bayesian vs frequentist interpretations of probability and others like it but this does not address the question I am posing. These other posts provide interpretations related to ...
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Two categorical variables with many levels, dependent samples

I have data from many participants, who each answered the same question about each of several stimuli, assigning each stimulus to a category (with replacement). This would be an example of said data ...
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Central Limit Theorem: Is the likelihood of obtaining some sample mean exact when n is not infinity?

The central limit theorem states: $$ \lim _{n\to \infty}{\sqrt{n}}{\left({\frac {{\bar {X}}_{n}-\mu }{\sigma }}\right)} \sim \mathcal{N}(0,1) $$ Which means if I ran an infinite number of experiments, ...
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Two step regression - should we account for 'consumed' degrees of freedom?

One approach to determine whether the relationship between an exposure (x) and outcome (y) is linear is to use a flexible model with smoothing spline terms, such as a generalized additive model (GAM). ...
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Converting a confidence interval into a credible interval

The problem of correctly interpreting confidence intervals has been discussed at length here. I have a related question which I believe may be a useful contribution: Frequentist probabilities by ...
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Isn't frequentism flawed, at least in the case of small samples?

In his talk on Frequentism and Bayesianism, Jake VanderPlas discusses Bayes' billiard game (10:57). Jake sketches how frequentists arrive at an odds 0.053 of winning for Bob after three more moves ...

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