# 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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33 views

### Understanding the Intersection Between Causal and Statistical Inference

Assume a simple example motivating a causal research design. Say that I collect a data set on rural counties in Texas and I wish to understand if rainfall causes a change in crop sales. Working with ...
76 views

### Bayesian and frequentist connections regarding the central limit theorem

I have been wondering how the central limit theorem may be useful in Bayesian statistics with potentially misspecified model distribution. Suppose $x$ is a random variable that follows an unknown (and ...
678 views

### Probability of winning a game: frequentist vs Bayesian approach

Alice and Bob play the game - the rules of the game are not important, and after 8 rounds Alice has 5 points and Bob has 3 points. Every round one of 2 players gets 1 point and the winner of the game ...
1 vote
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### Understanding the significance level of a confidence interval

I generated 1000 confidence intervals with 95% significance level and I am testing H0: μ = 0 vs H1: μ != 0. What means if 97.5% of my confidence intervals have the 0 included? It should be exactly 95% ...
21 views

### Practical use of a confidence interval [duplicate]

I wrapped up my undergraduate statistics degree recently and am about to start a stats heavy role as my first job. I've been brushing up on my frequentist knowledge and I'm currently trying to find a ...
105 views

### What misunderstanding does this refer to?

The confidence interval entry in Wikipedia lists a number of common misunderstandings about confidence intervals. One of these is described as follows: A confidence interval is not a definitive range ...
16 views

### What is the advantage of running generalized mixed effect linear regression model with bayesian with non-informative prior vs frequentist approach?

I am curious as to whether the bayesian approach with non-informative prior (flat prior) is more suitable for generalized mixed effects linear model than frequentist approach and what the reasons may ...
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### For mixed effects model with multiple random intercepts, are bayesian approaches (with MCMC) more robust than frequentist?

I stumbled upon this particular webpage from UCLA containing the following text: [...] Inference from GLMMs is complicated. Except for cases where there are many observations at each level (...
141 views

### Simple example where Bayesian > Frequentist (Unambiguously)? [duplicate]

I'm trying to understand the main appeal of Bayesian methods & whether they are indeed capable of offering more than regular frequentist methods. The thing is my impression is that by default the ...
140 views

### Simple unbiased mean estimator for censored data

Suppose I have an i.i.d. random sample of size $n$ s.t. $X_i \sim \mathcal{N}(\mu, \sigma^2)$ for all $i$. But suppose my observed sample is left censored, such that any $x_i$ observation is replaced ...
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### Where is the number "0.963" in the paper "Why Isn't Everyone a Bayesian?" by Bradley Efron coming from? [duplicate]

This paper by Bradley Efron (also available here) concerning Bayesian vs. frequentist interpretation of probability contains an example I don't quite understand. It's on page two in the right column ...
177 views

### iid data (Bayesian) vs iid random variables (Frequentist)?

I've been pondering the differences in notation / language used in some of the resources I've read for statistics / machine learning. Warning: this might be embarrassingly obvious to any decent ...
1 vote
33 views

### Why do tau2 and I2 estimations differ between frequentists and Bayesian models

I was conducting a network metanalysis of treatments and found out that I2 and tau2 esitmates are widely different between the models (as an example, for the same outcome, I have a tau2= 0.0078 and I2=...
603 views

### Does the Frequentist approach to forecasting ignore uncertainty in the parameter's value?

I am reviewing textbooks for our new undergraduate course in Bayesian Statistical Methods. In chapter 7 of Ben Lambert's book, A Student's Guide to Bayesian Statistics, he states Because of the two ...
158 views

### When and how was the Bernoulli distribution with real binomial proportion introduced?

I certainly should read Jakob Bernoulli's Ars Conjectandi again but let me share my concerns. I'm just wondering when and how the Bernoulli distribution $Be(p)$ (and related distributions like the ...
62 views

### Lindley's (1993) analysis of a version of Fisher's tea tasting lady example, using a mix of discrete and continuous priors

I am interested in explaining the version of Fisher's tea tasting lady example that is discussed in Lindley's (1993) 'The Analysis of Experimental Data: The Appreciation of Tea and Wine'. A similar ...
268 views

### Why are Bayesian mixed-effects models (e.g., brms) more able to estimate complex models than Frequentist mixed models (e.g., lme4)?

It is commonly suggested that if you are having trouble getting your lme4, Frequentist mixed-effects model to converge, you can either (a) simplify and drop random effects in the model, or (b) pivot ...
205 views

### Combining Bayesian and Frequentist Estimation into a Single Model?

We are usually told the following: In the Frequentist Probability Approach, we are told that: the data is random but the parameters being estimated are fixed In Bayesian Probability Approach, we are ...
1 vote
20 views

### Who first described a statistical estimate as an approximation of a population parameter?

At some point in the history of statistics, there surely was a transition from thinking of statistical measures strictly as imperfect approximations of real quantities, to thinking of them as ...
27 views

### Top 2 box (T2B) margin of error calculation. Where's the mistake?

I have a survey asking customers to rate their satisfaction on 1-5 scale. I'm interested in learning the margin of error for a derived quantity, namely the "top2box%", i.e. the percentage of ...
22 views

### Model marginal and joint distributions from a sample of unkown number of categories

To illustrate the problems imagine I'm drawing labelled spheres from a box. I may or may not know the number of spheres in the box (does it make a difference?) If I draw 10 spheres from the box and ...
31 views

### Any meaningful interpretation t-distribution, when rescaled using the sample SD?

To visualize p-values or confidence intervals, the t-distribution is sometimes rescaled using the sample standard deviation and then centered at a certain value. To be more specific, consider drawing ...
20 views

### How to apply Bayesian statistics to this (general) Quality Control problem

This more an academic question than practical. I like that ;) I have been thoroughly trained in frequentist statistics. Zealously, actually - to the point that no one even told me it’s called “...
72 views

### Random effect exactness in Bayesian vs Frequentist paradigms

In this post, Frank Harrell advocates for Bayesian methods when random effects are used. Now, he is a known Bayesian, so this is not surprising, but his expansion in the comments suggests a stronger ...
74 views

### Are bias and variance used as metrics to evaluate estimators in Bayesian inference?

Consider the parameter $\theta$, which is a deterministic unknown in the frequentist paradigm. Given a random variable $X \sim p_X(x ; \theta)$, consider the estimator $\Theta(X)$ of $\theta$, and the ...
151 views

1 vote
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### How is Bayes Stats supposedly more "intuitive" when it requires us to think probabilistically which IS NOT intuitive for most folks? [closed]

People don’t naturally think in probabilistic ways, they often form priors through point estimates because it’s less cognitively taxing to reduce everything down to single numbers. So if the ...
47 views

### Design of proportions comparison experiment (Frequentist and Bayesian)

I need to design an animal experiment where I test the survival proportion following administration of a vaccine and inoculation of the disease. I have 3 vaccines in the trial, the control (C), the ...
190 views

### Why still use Frequentist Methods? [closed]

It is possible to do hypothesis testing, regression, classification, ect, all using Bayesian methods. Furthermore, these Bayesian methods are more flexible and easily interpret-able than Frequentist ...
38 views

### Is data random in Bayesian inference?

I am trying to understand the Bayesian method. From Wasserman, my understanding is that the process for parametric inference is roughly: Choose a statistical model $\mathcal{F} = \{F_\Theta\}$. ...
3k views

### Why are standard frequentist hypotheses so uninteresting?

In almost any textbook introducing the topic of frequentist statistics, null hypotheses of the form $H_0: \mu=\mu_0$ or similar are presented (the coin is unbiased, two measurement devices have ...
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### Sample size needed to show difference of means is smaller than $y\%$

The unpaired $t$-test is commonly used to reject the null hypothesis that two sample means are equal. However, suppose one wants to prove that the sample means are no different than some given maximal ...
634 views

### Is likelihood a conditional probability?

If we have a set of observations $\mathcal{D} = \{x_i\}_{i=1}^n$ then the likelihood $\mathcal{L}$ is: $$\mathcal{L}(\theta \mid \mathcal{D}) = P_\theta(\mathcal{D})$$ and if the observations are ...
168 views

### 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 ...
28 views

### 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 ...
134 views

### 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 ...
1 vote
25 views

### 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 ...
39 views

### 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 ...
244 views

### What is the probability of a fair coin flip that has already occurred?

My friend flipped (past tense) a fair coin and does not tell me the result. From a frequentist perspective, what is the probability of heads for the flip? The strict frequentist says, "The flip ...
1 vote
78 views

### 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 ...