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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Bayesian Hypothesis Testing after Frequentist Parameter Estimation

Is it sound to use a Bayesian hypothesis testing framework after a frequentist parameter estimation (via the implied distribution by the estimated parameters)?
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Bayesian A/B Testing vs Frequentist A/B Testing?

I was reading the book Probabilistic Programming for Hackers and came across Bayesian A/B Testing. So basically, I get a Posterior Distribution for $P(A), P(B)$ and the $\Delta$ between $P(A)$ and $P(...
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How is uncertainty handled in Frequentist inference?

In Bayesian Inference, uncertainty is seen as prior on the parameters and learning is achieved by computing a posterior on the parameters using the data available. This makes quite a lot of sense. I ...
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Random variables with known ratios

I have $n$ samples with $m$ random variables in each: $\{x_{i\alpha}|i=1..n, \alpha=1..m\}$. The variables are expected to obey known ratios (they are fractions of an unknown quantity), e.g. $x_{\...
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Derivation of score vector

Can anyone explain the process of this derivation, step by step? This derivation is from Joint Models for Longitudinal and Time-to Event Data by Dimitris Rizopoulos. \begin{equation} \begin{aligned} ...
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BCA bootstrap intuition

The papers below claims that BCa bootstrap improves bootstrap estimate accuracy over standard quantile bootstrapping, I think by adjusting for the underlying distribution's skew and bias. I am looking ...
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Two-way ANOVA vs. simple differencing scheme [closed]

I am just learning about the ANOVA and have a question about an alternative approach that I thought was reasonable, but I am doubting now. Suppose my data is in the form of a matrix $\mathbf{Y}$ of ...
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34 views

When does the MLE have a p-value equal to 1?

Suppose we have data $X_1,\ldots,X_n$ that is independently and identically distributed from a distribution $\mathbb{P}_\theta$, with unknown parameter $\theta \in \Theta$. Consider the hypothesis $...
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1answer
82 views

Interpreting frequency statistics to find fair dice

I was just in a lecture where my (bayesian evangelist) professor claimed that for questions like 'Is this a fair die?', frequency statistics gives an answer of {0, 1}, meaning that the probability is ...
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1answer
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Comparing Means of different Subscales

a friend recently asked me if she could compare the means in different subscales of one Questionnaire (measuring more or less distinct construct) in one sample. In concrete she has a sample of 100 ...
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Expressing one-sided p values of directional hypothesis tests as Bayes factors

Assume we want to test the directional hypothesis that $µ<0$. From a frequentist angle we use a one-tailed $t$-test and imagine we obtain a 1-sided $p$ value of say 0.07, which then would imply ...
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60 views

Why do Uncertainty Quantification using a Bayesian Perspective?

Besides the reasons stated in this article, Stuart(2010) (chapter 2) - related to equivalence between using a certain prior on the observation error and defining which norms to use when doing a ...
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Posterior variance vs variance of the posterior mean

This question is about the frequentist properties of Bayesian methods. Suppose we have data ${\bf y}$ generated from a distribution with a single parameter $\theta$, equipped with a prior $\pi(\...
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Why is rejection of null hypothesis not a case of prosecutor's fallacy?

Here is what my understanding is: p-value - probability of finding the observed, or more extreme, results when the null hypothesis (H0) of a study question is true which is to say p-value$=P(...
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Differences between a frequentist and a Bayesian density prediction

What are some essential differences between a frequentist density forecast/prediction and a Bayesian posterior for an outcome of a random variable? Of course, there will be differences in how they ...
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35 views

confidence contours for linear model with multiple dependent variables

A book I have on regression analysis describes a technique for determining confidence contours of the parameters of a linear model $$ Y^{\textrm{model}} = f(\boldsymbol{x}, \boldsymbol{\theta}) = \...
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How does an observation condition the next one, if the numbers are exp. distributued with uknown average?

We have a process that generates exponentially distributed random numbers, i.e., $P(X=x) = \lambda e^{-\lambda x}$. However, we don't know the value of $\lambda$. We observe the first realization with ...
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Non-frequentist Consistency of Bayesian Estimates

this question seems weird. But I am just wondering if there exists any sorts of theories about 'non-frequentist consistency' of Bayesian methods? So far all the results I found are about the ...
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For GARCH model Bayesian estimation is better than ML estimation [closed]

In the work of [Ardia] - Financial Risk Management with Bayesian Estimation of GARCH Models_ Theory and Applications in which the Bayesian estimation method with uninformative prior ...
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Using bootstrap to calculate a confidence interval for the distance between two matrices

I'm a little bit stuck with different methods of bootstrapping for estimating confidence intervals for distances. All methods (like BCa, studentized bootstrapping) except the percentile one use ...
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20 views

Expected frequency of three-way combination given all two-way combination frequencies

Given an alphabet {A, B, C}, and observed frequencies of each element, a, b, and c respectively; I can calculate the expected frequency of the combination AB as a*b. I want to know how to do the same ...
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Why do non-informative a priori distributions be chosen to compare the Bayesian and frequentist estimation method?

For example for GARCH models $$\sigma_t^2=\alpha_0 +\alpha_1 y_{t-1}^2 + \beta_1 \sigma^2_{t-1}$$ it is usual to use as distributions for the parameters of truncated normal distributions with very ...
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Why do the non-informative a priori distributions give better results than the frequentist estimate?

For example, in the specific case of Markov-Switching GARCH models why is a non-informative prior distribution chosen for GARCH models with Bayesian estimation and why is this approach better than the ...
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Likelihood, posterior, prior interpretation and credibility/confidence_level with bayesian/frequentist approaches

This question was originally posted on physics exchange but one advised me to transfer it here. I try to understand the following article : testing general relativity from curvature and energy ...
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Did Jaynes ever comment on Lindley’s paradox?

I wondered whether ET Jaynes ever wrote or expressed an opinion about Lindley’s famous statistical paradox? I would be curious about his take on it, and imagine he must have done since he wrote ...
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When does a confidence interval “make sense” but the corresponding credible interval does not?

It is often the case that a confidence interval with 95% coverage is very similar to a credible interval that contains 95% of the posterior density. This happens when the prior is uniform or near ...
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3answers
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Combining p-values when the trials are independent but their number is data-dependent and random

Consider the following scenario (it's just a motivating example, not something I am doing for real): I run a trial, drawing an i.i.d. sample $S_1$ from population $P$, to test a hypothesis $\mathcal{H}...
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1answer
38 views

Statistically significant definition of power

After a not-quick literature research I noticed that there are two types od definition for what power is: One is: it's the probability of not making type II error' (A) The other is: it is the ...
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1answer
63 views

Is a Bayesian posterior kind of like the marginal distribution of a frequentist estimator?

I've been thinking a lot about the relationships between various concepts like hypothesis testing, posterior distributions, and estimators. If I understand correctly, a frequentist estimator $\hat\...
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38 views

Is pseudorandom number generator testing atypical?

Particular pseudo-random number generators are tested for their their ability to produce sequences of numbers that behave like values of independent variables that are each uniformly distributed on [0,...
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1answer
128 views

Interpretation of confidence interval in Bayesian terms

Motivation: I was standing in front of a class to introduce into the concept of confidence interval using the example of differences in means (purely frequentist setting) and I was torturing the ...
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Ridge logistic regression and posterior distribution

We know that glm regression with gaussian prior can be assimilated to Bayesian regression. Let say I fit the model with frequentist approach and I have the optimal ridge parameter. If I want the ...
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178 views

How do Bayesians verify their methods using Monte Carlo simulation methods?

Background: I have a PhD in social psychology, where theoretical statistics and math were barely covered in my quantitative coursework. Through undergrad and grad school, I was taught (much like many ...
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Can I use Poisson regression to model prevalence ratios if I only have information on events?

I often used Poisson regression models to estimate prevalence ratios. However, in these cases my data contained information on the whole population, including events (1) and non events (0). ...
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How does the frequentist approach to probability estimation work when the number of outcomes is greater than 2?

I've read Checking_whether_a_coin_is_fair and I'm trying to find a resource which generalizes the frequentist approach to the case where there are $k$ distinct outcomes and $n$ trials. Can someone ...
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Bayes vs trial factor (particle physics)

In the statistical inference for particle physics is the trial factor analogous to Bayes factor but for the frequentist analysis?
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Modeling and testing for trends in hospital-surveillance (count, event) data

Intro Hi all, I'm working with hospital-based surveillance data. My peers and I are trained (loosely speaking) as frequentists. I'm mindful of the aphorism: Statistics: A subject which most ...
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What does it mean when Risk function turns out to be a number?

I have a statistical decision making theory problem.I have to calculate the Risk Function for each of 4 decision rules.However,it turns out that the fourth Risk function is not a function of θ and it ...
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Understanding Bayesian HDIs for paired samples vs independent samples

According to Kruschke (http://www.users.csbsju.edu/~mgass/robert.pdf), if I have two different groups and collect their response times to a certain task, to determine if the two groups are ...
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Bayesian vs Frequentist inference in the presence of noisy data

I'm wondering how Bayesian inference and Classical/Frequentist inference fair towards noisy data. I can't seem to find too much literature addressing this issue and it seems the conclusion is usually ...
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What are some introductions to classical statistics that emphasize unifying principles? [duplicate]

I'd like to know an introduction to classical statistics, that: Emphasizes connections and unifying principles (I checked this question and the links posted therein, but didn't find an introduction ...
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Why is Bayesian Statistics becoming a more and more popular research topic? [closed]

Browsing through the research area of the top 100 US News statistics program, almost all of them are heavy in Bayesian statistics. However, if I go to lower tier school, most of them are still doing ...
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How to reconcile the frequentist method with assessing the fairness of a coin?

Imagine I have a factory for assessing the fairness of coins. I have no assumptions on the coins; i.e, a given coin has an equal probability of exhibiting any form of "bias". For example. the ...
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1answer
66 views

Effect sizes independent of sample size

So I have a small sample size (N=24) but found an extremely large effect size for an effect. A common phrase appearing is 'effect size is independent of sample size,' which I had taken to suggest ...
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Bootstrap to calculate confidence intervals

I’ve seen two ways to use bootstrapping to estimate confidence intervals of parameters estimated via maximum likelihood The first method fits the data with the assumed distribution. Then in a loop ...
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1answer
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How is 'updating priors' in Bayesian stats different from adding more measurements to the distribution in frequentist stats?

I'm an experimental physicist so please pardon me if my thinking about this is too concrete. Let's say I am taking a measurement over and over and trying to determine the "real" value of something, ...
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285 views

Interpreting prediction intervals, and prediction intervals for a specific parameter?

Can someone correct my thinking if I'm off course here? Confidence intervals provide an estimate of precision$^1$ for a specific parameter, but they can also be used for a regression equation (i.e., ...
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Are confidence intervals useful?

In frequentist statistics, a 95% confidence interval is an interval-producing procedure that, if repeated an infinite number of times, would contain the true parameter 95% of the time. Why is this ...
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Coherence and calibration

I am trying to find good definitions and examples for both these concepts regarding frequentist vs Bayesian statistics. Can anyone please shed light on them and explain them? Furthermore, why are ...
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In AB test do the sample size calculations represent the minimum or maximum size required for measuring difference between the test and control

A quick question on the frequentest approach of sample size calculation. I recently came across this below note: The sample size required should be strictly enforced; if the power analysis shows ...