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.

Filter by
Sorted by
Tagged with
0 votes
0 answers
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 ...
user avatar
  • 69
3 votes
2 answers
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 ...
user avatar
  • 331
3 votes
2 answers
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 $\delta_{\theta^*}$ ...
user avatar
  • 39
0 votes
1 answer
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 ...
user avatar
19 votes
3 answers
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 ...
user avatar
0 votes
0 answers
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 ...
user avatar
0 votes
2 answers
70 views

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 ...
user avatar
0 votes
0 answers
46 views

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 ...
user avatar
0 votes
0 answers
35 views

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, ...
user avatar
1 vote
0 answers
22 views

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 ...
user avatar
0 votes
2 answers
36 views

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 ...
user avatar
  • 111
0 votes
0 answers
21 views

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. ...
user avatar
1 vote
0 answers
19 views

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 ...
user avatar
  • 1,700
1 vote
2 answers
129 views

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 ...
user avatar
1 vote
1 answer
74 views

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. ...
user avatar
3 votes
1 answer
123 views

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 ...
user avatar
4 votes
5 answers
372 views

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 ...
user avatar
1 vote
1 answer
50 views

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 ...
user avatar
  • 185
1 vote
0 answers
36 views

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 ...
user avatar
  • 326
0 votes
1 answer
40 views

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 ...
user avatar
  • 101
0 votes
0 answers
16 views

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 ...
user avatar
  • 31
0 votes
0 answers
22 views

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 ...
user avatar
  • 1,700
1 vote
2 answers
107 views

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 ...
user avatar
0 votes
1 answer
56 views

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....
user avatar
  • 1,700
6 votes
2 answers
186 views

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 ...
user avatar
  • 5,013
0 votes
0 answers
30 views

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 ...
user avatar
  • 131
5 votes
3 answers
429 views

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{...
user avatar
  • 691
0 votes
1 answer
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 ...
user avatar
  • 1
1 vote
0 answers
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 ...
user avatar
11 votes
4 answers
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 ...
user avatar
  • 387
3 votes
0 answers
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 ...
user avatar
3 votes
3 answers
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....
user avatar
  • 1,700
5 votes
6 answers
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 ...
user avatar
  • 781
0 votes
0 answers
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/...
user avatar
  • 326
8 votes
11 answers
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 ...
user avatar
0 votes
0 answers
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 ...
user avatar
  • 1,533
0 votes
0 answers
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 ...
user avatar
0 votes
0 answers
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, ...
user avatar
  • 252
1 vote
0 answers
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). ...
user avatar
  • 446
6 votes
2 answers
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 ...
user avatar
0 votes
4 answers
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 ...
user avatar
0 votes
1 answer
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 ...
user avatar
0 votes
0 answers
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 ...
user avatar
45 votes
6 answers
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 ...
user avatar
  • 403
6 votes
3 answers
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 ...
user avatar
  • 15.9k
1 vote
1 answer
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 ...
user avatar
2 votes
1 answer
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 ...
user avatar
  • 43
1 vote
0 answers
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 ...
user avatar
  • 789
0 votes
1 answer
65 views

Interpretation of GAMM with Factor level Predictors

I'm running the following model in R using the package mgcv: ...
user avatar
0 votes
1 answer
37 views

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 ...
user avatar

1
2 3 4 5
9