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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29 views

A simulation risk formulation where Bayesianism and frequentism is combined

For my mathematics bachelor-thesis at the Statistics Netherlands, i became acquainted with frequentist and Bayesian statistics. I had set up a simulation-study, and I am not sure if the risk I ...
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172 views

Frequentest and Bayesian analyses contradicting each other

I have the following set of data which I'm trying to analyse: ...
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65 views

Bayesian interpretation of non-Bayesian estimates

Problem from Bayesian Data Analysis (Bayesian interpretation of non-Bayesian estimates): Consider the following estimation procedure, which is based on classical hypothesis testing. A matched pairs ...
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Maximum likelihood is not re-parametrization invariant. So how can one justify using it?

There is something that is confusing me about max-likelihood estimators. Suppose my I have some data and the likelihood under a parameter $\mu$ is $$ L(D|\mu) = e^{-(.7-\mu)^2} $$ which is ...
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Is it a problem that limiting frequencies (can) violate countable additivity?

I`ve stumbled upon the following paper by Alán Hajek https://www.jstor.org/stable/40267419, in which the author states that the Frequentist interpretation of probabilities as limiting frequencies ...
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241 views

What is an example of an event for which frequentist probability doesn't apply?

I'm on the hunt for an example to illustrate the difference between frequentist and subjective Bayesian probability. In particular, I'd like a type of event for which frequentist probability doesn't ...
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How do Frequentist vs. Bayesian views of probability lead to their different treatments of data/hypotheses? [closed]

I have read that a key difference between Bayesians and Frequentists is their treatment of probability. Frequentists treat probability as the frequency with which something will happen over the long ...
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Can we think of a probability in both the classical and subjective sense simultaneously?

I'm a statistics student. I am trying to understand the classical and objective definitions of probability and how they are related to frequentist and Bayesian inference. It's not obvious to me why ...
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299 views

Confidence Interval vs Credible Interval for the Variance

I understand the conceptual difference between confidence and credible intervals. But I have difficulties applying these concepts to my application. I would like to know the concrete difference ...
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Return on investment for a vaccine

I have been tasked with finding the return on investment of a vaccine. The vaccine is used by farmers for their cows and the number of cows kept varies drastically between farmers (from $1$ to $1,000'...
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506 views

Forecasting with no prior knowledge - Bayesian vs Frequentist

I have a basic question about Bayesian statistics. Lets say that I want to make forecasts of a certain response variable, based on explanatory variables and lagged responses variables, while I have ...
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4answers
100 views

Probability and randomness

Assume that we toss a coin n times and the result looks like this HTHTHTHTHTHTHTHT... . Would a (Probability-) Frequentist conclude that that the probability for the coin to land heads is 0.5? It ...
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477 views

What is the difference between classical frequentist methods and likelihood methods?

You may assume that I'm familiar with the material in Casella and Berger. This question is identical to What is the difference between Fisherian vs frequentist statistics?; however, the question was ...
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Frequency properties of posterior predictive checked bayesian models

Does a bayesian model passing a posterior predictive check imply any frequency properties outside the tested data?
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137 views

Under what circumstance does $P(X|H) = P(H|X)$?

I came across a Machine Learning exam question regarding the difference between the Frequentist and Bayesian approach to classification; it specifically asked what condition must be met for the two to ...
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481 views

Frequentist Predictive Distribution for a Cauchy variable

I have not been able to find this in the literature, but that probably means I am looking in the wrong spot. I am looking to find the Frequentist predictive distribution, assuming it exists, for a ...
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691 views

Bayesian updating with discrete priors + possibly unknown classes

I'm following along with some lecture notes on Bayesian updating with discrete priors. They give an example problem to illustrate some of these concepts, which I briefly restate here: Someone tells ...
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Are Bayesian models just frequentist models with one more layer?

We all know the formula for Bayesian inference: $$P(\theta|\mathbf{x}) = \frac{P(\theta|\gamma)P(\mathbf{x}|\theta)}{P(\mathbf{x})}$$ In this approach, we replace a fixed $\theta$ with a latent, ...
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Does Central Limit Theorem Apply to Bayesian inference?

In reading a Paper on Bayesian estimation, I came across a sentence that had me think: "Bayesian statistics is not based on large samples (i.e., the central limit theorem) and hence may produce ...
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533 views

What is the difference between Fisherian vs frequentist statistics? [closed]

I just read a research paper that said implicitly that there was a difference between the two. I thought that Fisherian statistics was another word for frequentist statistics.
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Is the invariance property of the ML estimator nonsensical from a Bayesian perspective?

Casella and Berger state the invariance property of the ML estimator as follows: However, it seems to me that they define the "likelihood" of $\eta$ in a completely ad hoc and nonsensical way: ...
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824 views

Introduction to frequentist statistics for Bayesians [closed]

I'm a simple minded Bayesian who feels comfortable in the cosy world of Bayes. However, due to malevolent forces outside my control, I now have to do introductory graduate courses about the exotic ...
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1answer
88 views

3-level hierarchical model and ferquentist approach

Could I use maximum likelihood method or any other frequenist method to estimate parameters for 3-level hierarchical model? Is there any references help me in this case? Thank you
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Is the mean (Bayesian) posterior estimate of $\theta$ a (Frequentist) unbiased estimator of $\theta$?

I am wondering about the different ways that Bayesian and Frequentist statistic connect with each other. I recalled that the Maximum Likelihood estimate of a parameter $\theta$ is not necessarily an ...
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91 views

Correct model specification and pre-specification: Is this problem solved in Bayesian statistics?

In frequentist statistics, the validity of the inference depends on the assumption that the model is correctly specified as well as pre-specified. Violations of these assumptions (i.e. we only specify ...
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741 views

Forecasting A Noisy Time Series

I have daily time series data of the number of views that a YouTube channel has, alongside daily data on the views that the videos in that channel receive. I would like to predict three months of ...
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Same results from bayesian and frequentist hypothesis testing? References needed

Are there any articles or books on the sameness the Bayesian and frequentist inference? I'm looking for more than just a statement that 'in large samples and for uninformative priors the results are ...
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608 views

How to estimate a probability of an event to occur based on its count?

I have a generator of random symbols (single act of generation produces exactly one symbol). I know all the symbols that could be generated and for each symbols I would like to estimate the ...
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225 views

Statistic analysis x = categorical, y = boolean in R

I have a data frame: ...
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98 views

Is a frequentist approach to inference appropriate when working with non-repeatable data?

Jackman (2009) writes on p.xxxi-xxxii: Consider researchers analyzing cross-national data in economics, political science, or sociology, say, using national accounts data from the OECD. [...] ...
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115 views

Bayesian Statistics - Understanding When to Use

I have basic understanding of Stats and till now have worked with Linear & Logistic Regression, Random Forests etc. Introduction to Statistical Learning was my go to book.I never worked with or ...
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1answer
89 views

Comparing Binomial samples (probability)

I'll try to make this as to the point as possible. Consider 2 people playing a few games against a computer. Player 1 gets 6/10 wins Player 2 gets 56/100 wins What's the chance that player 1 is ...
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The Bayesians critique of intention dependency

In Kruschke's book, in chapter 11, he gives an example of testing whether a coin is biased. He shows how, if one conditions on $N$ (the number of flips), $z$ (the number of heads), or on the duration (...
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277 views

Utility of the Bayesian Cramer-Rao Bound (van Trees inequality)

In frequentist statistics, one can hardly take a sip of coffee without someone mentioning Fisher information and the Cramer-Rao lower bound. On the other hand, from my limited experience in the field ...
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Probabilities of medical risks

Recently, I read a UK Supreme Court judgment Montgomery (2015), a judicial decision advocating patient's dignity and safety. The Court held that no matter how small the percentage of a certain risk ...
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342 views

Bayesian vs Frequentist example

As far as I studied, the Bayesian approach is the most correct in Machine Learning. Thought, I solved an exercise where it was required to find out the decision boundary in predicting two different ...
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53 views

How to interpret a meta-analytic Confidence Interval through the lens of Frequentism [duplicate]

In a single study, a researcher can obtain a relevant summary statistic, and construct an $x$% confidence interval for that summary statistic. Under the frequentist framework, this obtained confidence ...
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124 views

When Bayesian and frequentist hypothesis testing leads to same results?

Under what conditions do the Bayesian and frequentist hypothesis testing lead to the same conclusion (rejection or acceptance of a hypothesis)? For example, if the test concerns statistical ...
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Is bias a frequentist concept or a Bayesian concept?

I know that bias is the difference between this estimator's expected value and the true value of the parameter being estimated. In classical approach the parameter has one particular true value, ...
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577 views

How to calculate confidence intervals for linear mixed effects models when default methods with default settings fail?

I have a simple linear model describing a set of straight lines and would like to estimate confidence intervals for the parameters and the covariance matrix describing the hidden parameters. First ...
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101 views

Is a standard error equal to a maximum likelihood sampling distribution?

Let's say we want to estimate $\mu$ in a normal model. I'm interested in the estimation error. Using R code as an example; ...
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Is a Bayesian framework more in keeping with neurobiologic processes? [closed]

Human thinking appears based on intercommunicating neurons and plastic synapses. In keeping with these neurobiologic premises and the evident assumption that every human thought, hypothesis and ...
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728 views

Is the frequentist framework more appropriate than the Bayesian one, according to Popper's theory?

According to Karl Popper, only falsifiable hypotheses are truly scientific (quoting Wikipedia): no number of positive outcomes at the level of experimental testing can confirm a scientific ...
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Using p-value to compute the probability of hypothesis being true; what else is needed?

Question: One common misunderstanding of p-values is that they represent the probability of the null hypothesis being true. I know that's not correct and I know that p-values only represent the ...
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153 views

How important are interpretations of probability to the practice of statistics?

I know that the frequentist interpretation of probability is associated with classical statistics and maximum likelihood estimation, and that a subjective interpretation of probability is considered ...
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104 views

Bayesian Methods with high number of regressors (high dimensional)

I'm comparing Bayesian (generalized) linear methods vs Frequentist ones in the case when $p>n$ ($p,n$ being respectively number of regressors, number of samples). In the frequentist context when $...
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109 views

Compare FDR adjustment in frequentist and Bayesian settings

Say I would like to compare two large-scale regression analyses, one in a frequentist framework (producing t-statistics or p-values) and the other in a Bayesian framework (producing marginal posterior ...
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568 views

Logistic Regression - Newton Raphson or MCMC?

From The Elements of Statistical Learning I know that logistic regression parameters can be fit using the Newton Raphson (NR) method on the likelihood function. So then why would you ever want to use ...
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285 views

Flat prior in Bayesian? Confidence intervals in classical statistics turn into credible interval?

We know confidence interval can't be used for probability statement, this is something reserved for credible interval. However, ...
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105 views

If Bayesian and Frequentist approaches give different answer, why can't we settle the matter by experiment once and for all?

As we have seen, Bayesian and Frequentist approaches sometimes give different answers to real world problem. So why can't we perform experiments and determine (with a very high likelyhood) who is ...

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