# 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.

415 questions
Filter by
Sorted by
Tagged with
20 views

### 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 ...
• 69
48 views

### 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 ...
• 331
213 views

### 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 $\delta_{\theta^*}$ ...
• 39
36 views

### 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 ...
• 151
1k views

### 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 ...
23 views

### 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 ...
• 73
70 views

• 691
54 views

### 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 ...
1 vote
52 views

### 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 ...
• 75
1k views

### 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 ...
• 387
71 views

### 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 ...
611 views

### 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....
• 1,700
354 views

### 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 ...
• 781
18 views

### 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/...
• 326
1k views

### 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 ...
• 2,470
7 views

### 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 ...
• 1,533
47 views

### 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 ...
35 views

### 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, ...
• 252
1 vote
15 views

### 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). ...
• 446
256 views

### 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 ...
168 views

### 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 ...
69 views

### 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 ...
33 views

### 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 ...
• 1,509
5k views

### 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 ...
• 403
168 views

### 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 ...
• 15.9k
1 vote
71 views

### 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 ...
67 views

### 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 ...
• 43
1 vote
14 views

### 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 ...
• 789
### 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 ...