# 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's the difference between Bayesian and frequentist curve fitting?

I was reading Bishop's Pattern Recognition and Machine Learning (PRML) and I am not completely sure I understand Bayesian (polynomial) curve-fitting. This might be an elementary question, but I ...
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### Do they use some Bayesian-frequentist amalgamate in astrophysics?

Below is a figure (highlighting is mine) from Madhusudhan et al. (2023). It caught my attention in a recent video by Becky Smethurst, where she explains some more context (but that's not necessary for ...
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### Is the Sufficiency Principle an axiom?

Sufficiency Principle as defined in Casella: Where Sufficient Statistic is defined as: Question: Is the Sufficiency Principle an axiom? My thoughts and research so far: I'm uncertain if the ...
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### Highest-density vs equal-tailed confidence interval

When a sampling distribution is symmetric (and I'm okay assuming unimodal too, if necessary), it's natural to center confidence intervals around the point estimate. But for a skewed distribution (e.g. ...
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### Is it incorrect terminology to say "confidence interval of a random variable"?

I have seen claims that "population paramter is not a random variable" when discussing confidence intervals. eg here Be sure to note that the population parameter is not a random variable. ...
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### When a credible interval coincides with a confidence interval, can one interpret confidence interval as credible interval and vice versa?

Let's say I have a frequentist model with $n$ data points to derive a confidence interval for a parameter. I also have a Bayesian model with $n$ data points to derive posterior for the parameter. In ...
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### Having a second bite of the data-apple without p-hacking

My hypothesis concerns intervention versus control in a randomised controlled trial (between-subjects, n=500 per group, online survey experiment). I pre-registered that my primary test would be a ...
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1 vote
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### References on when to choose Bayesian vs. frequentist analysis

I'm looking for references discussing and comparing the advantages and drawbacks of Bayesian vs. frequentist analysis in various contexts. If it makes sense, I'd be particularly interested in learning ...
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### Thought and doubt about Student's t-distribution and confidence interval

Let's say I have $N$ observations $X_1,X_2,\ldots,X_N$, where $X_i\sim\mathcal\mu,\sigma^2$, $\forall\,i\in\mathbb{N}$, where $\mu$ and $\sigma^2$ are unknown. I want to predict $X_{N+1}$ and ...
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### When is it important for a practitioner to understand CIs?

I have a physician friend who asks me questions about stats. He gets confused about stuff, e.g., the definition of a confidence interval (CI) and its intricacies. For example, he finds the following ...
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### Is comparing the AIC of a Bayesian and a frequentist model right?

I’m trying to fit a general linear model where the dependant variable is a probability. It is zero-inflated and continuous, then following the advice here blog of Ben Bolker, I separated my data pool ...
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### Are “Data are fixed” in Bayesian viewpoint and “Data are random” in frequentist viewpoint talking about the same thing mathematically?

In my opinion, in BOTH Bayesian and Frequentist inferences, observational data $x$ are modelled as the observed value of a random variable $X$ which follows a certain probability distribution. ...
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### Finding a specific reference on the construction of a confidence interval where by inspection we can see it does contain the parameter

I realise this is a long shot but I am trying to find a reference to a specific example of a construction of a confidence interval which I came across in the past. My memory on this is hazy and I may ...
1 vote
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### What are the Bayesian "system sellers"?

Many frequentist methods have direct Bayesian analogues, and vice versa. But there are some instances where the frequentist version is extremely cumbersome if not outright impossible. Those methods, ...
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### R packages for multivariate (two response variables) generalized linear mixed effects models

Are there any R packages with multivariate (multiple response variable) generalized linear mixed effects model capabilities? Specifically, are there any using a frequentist framework (I am aware of ...
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### Can I convert a frequentist p-value into a Bayesian Posterior Probability

I am drafting a teaching session for fellow clinicians to try and provide a somewhat intuitive understanding on how Bayesian statistics differs from the frequentist methods we are taught at medical ...
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1 vote
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### An alternative to BSTS method with non bayesian method

If I have to select an alternative way for causally finding the impact of a treatment using frequentist methods for a time series data, Bayesian Structural Time Series is one of them but is there a ...
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### Why do we use hypothesis tests instead of just letting people do Bayesian updates?

Why do we need discretize our judgements using hypothesis tests? Why can't we just have people report the data every time a study is done, and the p-values and effect size, and then report how the ...
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### Repeated Sampling and Confidence Interval Theory

I thought I'd ask a fairly fundamental question regarding confidence intervals at the risk of potentially furious backlash from the stats.stackexchange community. However, I've never quite yet found a ...
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### Interpretation of Statistical Tests and the Importance of Statistical Power [duplicate]

I was planning on running a statistical test for hypothesis testing, but was confused if statistical power is important once a test is run. Looking at this confusion matrix, one would ideally set ...
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### Statistical Integration of Bayesian and Frequentist Approaches: Weighing Methodology

I'm uncertain about where to post this question. I'm currently working with geotechnical data (soil parameters) and aiming to obtain realistic and safer parameter values. To achieve this goal, I've ...
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1 vote
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### Estimating different random effects based on a between-subject factor in a mixed model?

Background I have a between-subject factor of GROUP with 2 levels (Control and Active) and a within-subject factor of TIME with 3 levels (Time1, Time2, and Time3). Code below to generate some dummy ...
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### Long-term frequentist decision strategy. How to "unreject" H0 when false positive occurs?

TLDR: How to quantify the H0/H1 plausibility, when there are multiple statistics available on the matter? What is a good source to learn more about frequentist decision making strategy? Once in a ...
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### One-sided test for the difference of medians in two independent samples

I have two independent samples 1 and 2, and want to test a null hypothesis that the median of sample 2 is lower or equal to the median of sample 1. Is there a non-parametric test for that?
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### Bayesian equivalent of the frequentist test of equal or given proportions

I am interested in comparing the prevalence of common mental disorders (CMDs) such as posttraumatic stress disorder (PTSD), anxiety, and depression. I would like to know whether the prevalence I ...
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### 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 ...
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### 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 ...
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### 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% ...
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### 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 ...
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### 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 ...
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### 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 (...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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=...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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
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### 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 ...
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### 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 ...
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