# 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.

423 questions
Filter by
Sorted by
Tagged with
1 vote
23 views
+50

### 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 ...
• 36.2k
23 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 ...
78 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 ...
• 1,898
1 vote
20 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 ...
• 111
29 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 ...
• 11
1 vote
50 views

### Why are there n interpretations of probability, yet only two of those interpretations led to philosophies in statistical inference?

Why are the subjectivist (bayesians) and frequentist (objectivist) statisticians but no propensity statisticians? It seems that every interpretation of probability should yield its own branch of ...
1 vote
57 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 ...
24 views

### Are CI and hypothesis tests purely frequentist tools?

I've been learning statistics for a long time but I still struggle to understand the "philosophical" differences between frequentist and bayesian statistics. One of my questions is the ...
• 111
22 views

### bayesian vs frequentist statistics conceptual question [duplicate]

I've been learning statistics for a long time but I still struggle to understand the "philosophical" differences between frequentist and bayesian statistics. AFAIK, frequentist and bayesian ...
• 111
1 vote
42 views

### Comparison of frequentist methods (say, averaged over Monte Carlo simulations) and Bayesian method

I have read a lot of questions with answers like this one, How do Bayesians verify their methods using Monte Carlo simulation methods?, which stated that Monte Carlo methods are not suitable for ...
• 11
24 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 ...
• 134
75 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 ...
• 361
232 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 $\delta_{\theta^*}$ ...
• 49
39 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
2k 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 ...
29 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 ...
• 83
72 views

• 777
59 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
73 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 ...
658 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....
• 1,728
385 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 ...
• 773
19 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
58 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 ...
36 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, ...
• 262
1 vote
18 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). ...
• 531