# 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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### 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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### Logit-link logistic regression: Calculating effect size between a continuous predictor's max and min value

Let's assume I have a logistic regression logit-link model as follows. binary_y ~ year I mostly work with bayesian regression models. Calculating the effect size ...
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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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### How do I estimate a Bayesian linear regression without assuming normal likelihood?

Frequentist linear regression makes no assumptions about the joint distribution beyond finite second moments. How can I perform similar agnostic Bayesian linear regression, without imposing additional ...
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### Probability distribution of new data given old data

Say we observe data $D$, which comes from a probability distribution $P[D|\theta]$, where $\theta$ are the unknown model parameters. Given this information, what is the probability distribution of the ...
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### 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 ...
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### How to answer critiques about the inapplicability of the framework of frequentist statistics to the real world?

I often hear the argument that frequentist stats is useless or contorted because no event is precisely repeatable, let alone repeatable infinitely many times, and because there are no iid sequences in ...
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### Should Likelihood add to 1 in frequentist case? [duplicate]

I know maximum likelihood and Bayes formula works for both frequentist and Bayesian approach. We know there are two approaches to statistics, and likelihood is a term that is used in both frequentest ...
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### Why isn't the probability of an event happening in $L$ days given the probability $p$ it happens on any day $\frac{(2^L - 1)}{p^{-L}}$?

I feel like this is probably a dumb question, but there is something I am fundamentally misunderstanding here. The problem is essentially the same as the one mentioned in this question. I understand ...
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### Upper Limits in High-Energy Physics

I am not sure where to write my question. This is a Particle Physics question, but it has more to do with Statistics than with Physics, I think. Please tell me if this is not the right site. So: In ...
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### Why do we assign probability to theta even though we consider it constant in frequentist statistics? [duplicate]

i am trying to understand the differences between bayesian and frequentist statistics. I read that in frequentist statistics the unknown population parameter theta is considered a constant but in ...
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### Population distributions/data generating functions in Bayesian Statistics

In many frequentist stats courses, random variables come from some distribution at the population level and as such we could say that $y=X \beta + \epsilon$ is the true function for something like ...
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### Regression methods for indicator function as covariate

I am looking for a regression method to fit the following model: $$Y=\beta_0 + \beta_1X+\beta_2 I(X>\beta_3)X + \varepsilon,$$ where $\varepsilon \sim N(0, \sigma^2)$, and $I$ is the indicator ...
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### Adjusting probabilities when testing lots of subgroups

If you fit the same regression lots of times to noise, you get a coefficient significant at 5%, 5% of the time. If you have lots of subgroups, and you fit the same regression to each of the subgroups,...
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### Interpretation of GAMM with Factor level Predictors

I'm running the following model in R using the package mgcv: ...
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### Frequentist Regression Analysis & Pearson's $r$

I find that a polynomial trend line gives a better $r^2$ value. Is Pearson's Correlation Coefficient $r$ still a good indicator in this scenarios between the strength of correlation between my two ...
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### frequentist vs Bayesian approaches to Gaussian Processes?

I've been reading this blog post, which has been tremendously helpful in understanding Gaussian Processes (GP.) The author has used the terms "prior", "posterior", and "95% ...
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### Need Concrete Example of Where a Frequentist Clustering Technique Outperforms the Existing Bayesian Clustering Techniques

I'm looking for a concrete example of frequentist clustering outperforming Bayesian clustering (using the best Bayesian algorithm for the problem, using the testing criteria below). There are many ...
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### What about the "p-value" of the non-null hypothesis?

So my understanding is that the p-value is the likelihood of observing an effect at least as extreme as that shown in the sample data, if the null hypothesis is true. But how is this a useful value? ...
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### Does the Bernstein–von Mises theorem imply convergence in distribution between a Bayesian estimator and the MLE analogue?

Does the Bernstein–von Mises theorem imply convergence in distribution between a Bayesian estimator and its MLE analogue? Say I have \begin{equation*} \begin{aligned} & \mu \sim N(m, s^2) \\ & ...
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### Probabilistic predictions from a frequentist point of view [duplicate]

I'm trying to understand how a frequentist would approach statements like "having observed X, the probability of Y happening is Z". For concreteness, let's say we conducted $n_1$ identical, ...
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### How to calculate the winning probability for Tottenham vs LiverPool? [closed]

I wonder how frequentist and bayesian calculate the winning probability for Tottenham versus Arsnel, Saturday. For frequentists, the following is how I understand: Imagine a population made of all ...
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### How would Bayesian Statistics overcome a problem that Frequents would encounter?

For example, I want to calculate the probability that measures the winning chance of England against Italy in the World Cup. For this problem, I wonder how frequentists with what specific assumptions ...
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### Is there an R package that runs frequentist zero-one inflated beta models? [closed]

I have a set of proportion data (below) with a many 1s. I would like to run a one inflated beta model in R, and want to use frequentest statistics. However the only zero-one inflated beta package I ...
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### True parameter in relation to credible interval

I know that in the frequentist approach, the confidence interval contains the true parameter $\theta$ with some minimum probability (e.g. 95%); while in the bayesian approach, the credible interval ...
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### How to find variance within and between batches

I have some data for 5 different batches of bacteria counts with 5 observations each - Batch 1: 3.890, 4.675, 7.345, 2.950, 5.675 Batch 2: 4.345, 5.875, 3.665, 2.935, 5.455 Batch 3: 7.145, 5.550, 6....
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### Lost in multiple comparisons: is there a princepled way out?

Suppose I am planning to run some well-powered factorial experiment based on a random sample with several treatments and several levels. I am interested in the effects of all of all levels vs. some ...
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### 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 ...
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### How can I use Bayesian statistics to test this particular hypothesis?

There is a set $R=\{r_1, r_2, ..., r_K\}$ of $N$ ranks (where $N>> K$). I test the hypothesis that the ranks in $R$ are not homogeneously distributed in $\{1, 2, ..., N\}$. As I am interested in ...
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### Bayesian vs. Frequentist results question [closed]

A researcher computes both a frequentist confidence interval, and a Bayesian credible interval. After the computation, the researcher realizes that the credible interval is much more narrow than the ...
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### Frequentist vs Bayesian and deterministic vs stochastic [closed]

So this is sort of a general/basic, likely dumb question. I'm hoping to get a general idea, to better guide what I search/read. How do these terms relate to each other. I know with Bayesian theory, ...
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### What does "Parameters are fixed and data vary" in frequentists' term and "Parameters vary and data are fixed" in Bayesians' term exactly mean?

I hear the sentence in my question a lot, I kind of understand what it means but never have a clear picture of it. Hope to get the clear picture of what the sentence exactly mean.
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### Reporting: using bayesian and frequentist statistics interchangeably in a study

What would you expect to read in a work's "data analysis" or "statistics" section if this used Bayesian and frequentist methods interchangeably? I used Bayesian regression, since ...
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### Is Bayesian estimation useful for causal analyses?

Is Bayesian estimation useful for causal analyses? For analyses like randomized experiments or even observational studies of natural experiments, we want unbiased estimators of the causal effect (...
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### Is Frequentist Inference Objective?

Bayesian statistics is criticized for being subjective, as it requires a prior distribution encapsulating the subjective befiefs of the observer. Frequentist statistics is commonly advertised as being ...
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### Crossing Frequentism and Bayesian Analysis

Has anyone considered giving the posteriors of an analysis a sampling distribution and seeing where, methodologically, things could go from there? For details, check out: https://sdba-stats.weebly.com
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### "It was the correct play even though I lost"

*sorry if this isn't the right SE community, maybe it's more philosophical* You often hear this refrain in games like Poker or Hearthstone. The idea is that making play A this game resulted in a loss, ...
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### Coin flipping: Relationship between Bayesian and Frequentist's point estimates

I have a (biased) coin that has an unknown Head probability $p\in(0,1)$. To point estimate $p$, say that I'm going to use two approaches. Approach 1. I can use the Bayesian inference technique. ...
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### Can Random Forest be considered as a Frequentist method?

I am very new to machine learning so I apologize if this is a silly or even a repetitive question. I am running a Random forest model in R and was just wondering whether this is a frequentist method ...
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### Bayesian vs Frequentist Prediction Methods and Frequencey Garantees

After reading Larry Wassermans blog on the difference between Bayesian and Frequentist inference I started to appreciate that frequency guarantees can be desirable regardless of the inference method ...