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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6
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2answers
428 views

Does there exist a Frequentist or Non-Bayesian solution to Gull's Lighthouse Problem?

Does there exist a Frequentist or ODE or Non-Bayesian solution to Gull's Lighthouse Problem which is correctly modeled with cauchy distribution? See The Lighthouse Problem and Dave Harris' answer to ...
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3answers
90 views

Would you say this is a trade off between frequentist and Bayesian stats?

I'm trying to review frequentist and Bayesian in parallel. Let's say we are doing the typical scenario of estimating the population mean. In frequentist stats, if sample size is large enough, we ...
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4answers
392 views

Does Bayesian statistics bypass the need for the sampling distribution?

Let's take the classic case where the population follows a normal distribution, observations are iid, and we want to estimate the mean of the population. In Frequentist stats, we calculate the ...
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2answers
191 views

What is the Frequentist definition of fixed effects?

Bolker (2015) writes on p. 313 that Frequentists and Bayesians define random effects somewhat differently, which affects the way they use them. Frequentists define random effects as categorical ...
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0answers
30 views

What is two tailed test actually testing?

I know the two-tailed test procedure, that's not the issue. I am wondering about the philosophy about it. The null hypothesis $ \mu = X $ makes sense to me, we assume a certain value for the ...
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2answers
34 views

How to interpet this equation? [closed]

Can I get some help on interpreting this equation? Is it saying which ever section separated by the commma is bigger would be the answer? How do you intepret Sigma pi= 1? Thanks!
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1answer
25 views

Is sequential probability ratio test bayesian or frequentist or both?

Is sequential probability ratio test bayesian or frequentist or both? Is there a way to implement a bayes decision rule with "sprt"?
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21 views

Is the interpretation of a “Compatibility Interval” (Greenland, 2019) valid in general?

I was reading this short paper by Gelman and Greenland, where Greenland proposes to use the term "compatibility interval" instead of "confidence interval" with the following interpretation: [...] ...
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1answer
45 views

Understanding an example of using Bayesian and Frequentist inference

I have problems to understanding the following discussion. The questions are: 1)In "Some computation shows that this rule had probability 0.083,..." how $0.083$ calculated?(In a different version ...
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0answers
15 views

Estimate parameter estimates of hierarchical model

I have the following hierarchical model, where t stands for time and y_t, x_1t, x_2t, ..., z_1t, z_2t,... are known. I want to estimate the parameters of the model using a frequentist approach, not a ...
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16 views

AB/Hypothesis testing in multiple groups

Let's say I have two variants of my website and I would like to know which variant generates more revenue. This website operates in multiple countries and I will choose a variant for all countries at ...
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0answers
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How to evaluating inconsistency and heterogeneity in a frequentist Network meta-analysis based exclusively on multi-armed studies?

I have been trying to perform a network meta-analysis on a set of 5 multi-armed trials, each having 3 arms (placebo, treatment 1, and treatment 2). I am using the network and network graphs packages ...
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Multiple test adjustments of p values: Data Mining vs Single tests

This discussion was triggered between me and a student after a significant p-value in a highly interesting correlation between two variables dissappeared after the p values were adjusted for multiple ...
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1answer
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Typo in Deepleariningbook.org or am I misunderstanding Bayesian stats?

This is on page 133 of the book: https://www.deeplearningbook.org/contents/ml.html#pf10 In the above, it says that the data set is directly observed and so is not random If that data we observe ...
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1answer
96 views

Are two coin flips conditionally independent if we know that the coin is biased towards heads?

Suppose Alice (A) and Bob (B) each flip the same, potentially-biased coin. Then, P(A=H) < P(A=H | B=H), because Bob's flip increases our suspicion that the coin is biased towards heads. Now ...
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Could we move directly from frequentist interpretation $P(data|hypothesis)$ to Bayes interpretation $P(hypothesis|data)$ by using Bayes theorem?

Could we move directly from frequentist interpretation $P(data|hypothesis)$ result to Bayes interpretation $P(hypothesis|data)$ result by using Bayes theorem, or is it not legitimate ?
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Why would a Bayesian want to maximize expectation? [closed]

A Frequentist interprets probability as an estimate of how frequent an event is giving that we can repeat the experiment many times. It is natural for them to try to maximize the expected utility ...
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1answer
29 views

How to interpret a sampling distribution from a Frequentist and Bayesian perspective

I've read multiple of the threads about Bayesian vs Frequentist interpretations of probability, but I'm having trouble trying to reconcile them with the idea of the sampling distribution when ...
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4answers
2k views

Flaws in Frequentist Inference

I have problem to understanding the following example. (1) After the next day that the glitch discovered what can tell about the observation? $X_i\nsim N(\mu,1)$ or just $X_i\sim N(\mu_2,1)$. Some ...
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1answer
26 views

Is it possible to test if a parameter is positive?

Say I'm doing 1D linear regression. How can I test the hypothesis that the slope is positive? I have mostly been doing Bayesian analysis where this could be done easily by computing the proportion of ...
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1answer
21 views

Compare Event frequency in two different data set

Assume we have two groups of categorical data: Group A: 10000 categorical events, such as Event1, Event2, Event3, ..., Event10 Group B: 100 categorical events, same events of group A, but recorded at ...
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2answers
327 views

Why is considering a maximum likelihood as a random variable a frequentist approach?

In the notes through which I'm working, the following is said: in order to compute the variance of a maximum likelihood estimator for $\mu$, $\hat{\mu}_{ML}$, we adopt a frequentist approach and ...
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45 views

Optimal decisions based on frequentist estimators

Consider a decision problem aimed at minimizing the expected loss1 where the argument is a parameter estimate. In a Bayesian setting, given a posterior distribution of the parameter and the loss ...
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1answer
39 views

Do frequentists rely less on entropy-based methods than Bayesian or Machine Learners? [closed]

From what I heard many times, Bayesian and Machine Learning people use entropy based methods. Do frequentists use entropy less?
6
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1answer
89 views

A reliance on repeated sampling ideas can lead to logical paradoxes that appear in common rather than esoteric procedures?

I am currently studying the textbook In All Likelihood -- Statistical Modelling and Inference Using Likelihood by Yudi Pawitan. Section Repeated sampling principle: the frequentists of chapter 1 says ...
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2answers
131 views

Why would considering $\theta$ to be a random variable not be 'Bayesian'?

I am currently studying the textbook In All Likelihood -- Statistical Modelling and Inference Using Likelihood by Yudi Pawitan. Section Inverse probability: the Bayesians of chapter 1 says the ...
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2answers
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Why are frequentists uncomfortable with bayesian statistics when “optimization” algorithms used in frequentist statistics is bayesian?

In Step 1, we have a prior. Using bayes rule we construct the posterior. In step 2 of some iterated bayesian procedure, the prior becomes the posterior from step one and use bayes rule to calculate ...
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47 views

Linear regression $Y=X\beta+e$ with random coefficients $\beta$

Consider a linear regression model $Y=X\beta_0+\epsilon$. Here $Y$ is the response random vector of length $n$, $X$ is an $n\times p$ matrix, $\beta_0$ is a constant vector of length $p$, and $\...
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0answers
10 views

Do confidence interval frequency properties hold across parametric forms?

Say I run 100 entirely different estimation procedures on 100 different datasets and estimate 95% confidence intervals for each (e.g. logistic regression, linear regression, etc.). Purely based on the ...
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26 views

Randomness in parameters per se captures the incomplete knowledge on the phenomenon: analysis in Bayesian models

I have been studying some books on uncertainty quantification for stochastic systems: Numerical Methods for Stochastic Computations: A Spectral Method Approach and Spectral Methods for Uncertainty ...
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1answer
53 views

Is it ok to refer to frequentist statistics as traditional or classical statistics? [closed]

I don't know of any statisticians or work in the data science industry so I'm not really in the know about all the lingo. I am trying to explain stats to others and was wondering if I could use the ...
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1answer
43 views

Does frequentist statistics support the use of priors?

My understanding of the main difference between Frequentist vs Bayesian stats is that the former treats parameters as variables with fixed but unknown values whereas the latter treats them as random ...
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0answers
25 views

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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1answer
41 views

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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29 views

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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0answers
13 views

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_{\...
3
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1answer
55 views

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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72 views

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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0answers
41 views

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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0answers
37 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
87 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
59 views

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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0answers
92 views

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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1answer
75 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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0answers
260 views

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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1answer
237 views

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(...
3
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2answers
106 views

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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0answers
59 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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2answers
85 views

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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0answers
27 views

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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