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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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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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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103 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
92 views

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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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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29 views

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 ...
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50 views

Specifying frequency parameter in the absence of occurrences

Let's say I have a process where the occurrences are independent, proportional to time. I made $n$ observations for which I only observed no occurrences. My goal is to define a frequency parameter and ...
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Is the sampling distribution of a complete sufficient statistic free from relevant subsets?

Let $T_{\theta}(\mathbf{x})$ be a complete, sufficient statistic $T_{\theta}: \Omega \mapsto \mathbb{R}$, where $T_{\theta}$ is indexed by the parameter $\theta \in \mathbb{R}^n$. Is it true that the ...
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471 views

Frequentist vs. Bayesian bias-variance decomposition

Iv'e read the answer to this related question and still have some issues. Suppose that given some data $X$, we want an estimator $\hat{\theta}$ for some parameter $\theta$. A common approach is to ...
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Discussing regression results in a frequentist framework

There have been excellent debates about how to discuss treatment effects in a frequentist framework, for example: Language for communicating frequentist results about treatment effects What about ...
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2answers
90 views

Likelihood of rejecting a fair coin (repeated significance testing)

Suppose I have a fair coin and I flip it numerous times, testing after every time using Pearson's $\chi^2$ test of fit to fairness. What is the likelihood that I will, at some point, reject that the ...
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102 views

Can the Bayesian but not the frequentist “just add more observations”?

Since the frequentist's p-values are uniformly distributed under the null hypothesis, it is a highly problematic practice to add more and more data to your sample until you find a significant result. ...
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51 views

when an exact binomial confidence interval should be used?

Is exact binomial confidence interval only appropriate for extremely rare events or extremely frequent events? If so, what are the rule of thumb for the definitions of extremely rare (<0.01?) And ...
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Contemporary Frequentists?

My background is Bayesian. I know who to turn to for foundational discussion on this school of thought. To writers like MacKay, Gelman and Jaynes. Who do I turn to for a recent exposition of ...
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301 views

Hypothesis testing with beta binomial. Dealing with overdispersion

To make the question more understandable I will use a reproducible example. I have count data, how many connections different groups share with a unique group. In my case I have an upper bound of <...
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32 views

Sample size determination for analysis with several multiple regressions

In a proposed analysis that involves several multiple regressions, how can we determine the required sample size? If, for example, we can tolerate a type I error rate of 5% ($\alpha$ = 0.05) and a ...
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1answer
190 views

Should you be concerned with statistical power if you reject the null hypothesis?

My understanding of statistical power is that it is the likelihood of correctly rejecting the null hypothesis, with low power meaning you are very likely to make a beta error (failing to reject the ...
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555 views

A question on Bayesian credible interval vs frequentist confidence interval

The difference of Bayesian credible interval (BCI) and the frequentist confidence interval (FCI) is well explained with a nice example in this answer. Here is my own summary of the situation in the ...
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Frequentist definition of probability and prediction?

The frequentist definition of probability states that: The probability of an event is the ratio of the number of cases favorable to it, to the number of all cases possible when nothing leads us to ...
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161 views

Questions on issues with using Frequentist and Bayesian approach for the same test

One quick stats question, if I use Binomial Cumulative Distribution Function to get a sample size n for desired confidence level and tolerable error. Then we pick a sample of sample size n and find k ...
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82 views

How do Bayesians gamble?

Try to earn the most at this game: there are two discrete random processes x(t) and y(t) with two unknown continuous distributions, both are IID processes at iteration (t-1) you pick either "x" or "...
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124 views

Aren't these statements about confidence intervals equivalent? [duplicate]

I just read the following sentence from Wikipedia: A 95% confidence interval does not mean that for a given realized interval there is a 95% probability that the population parameter lies within ...
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2answers
857 views

Probability conditional on a parameter?

This is a definition of the sufficient statistic from Wikipedia. A statistic $t = T(X)$ is sufficient for underlying parameter $θ$ precisely if the conditional probability distribution of the data $...
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Estimate of population mean that minimises squared error

When reading Susan Athey's lecture slides here, I was confused by her claim that the population mean estimate for a given sample that minimises squared prediction error was not the sample mean, but ...
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1answer
57 views

How much similarity between observations and an event is needed in order to count them for calculating the probability of event happening?

Say my goal is to predict whether event $X$ will happen, and all I have is observation $O$. Is obervation $O$ applicable to calculate $\Pr(X)$? E.g. how similar observations in $O$ need to be to the ...
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1answer
707 views

Monte Carlo maximum likelihood vs Bayesian inference

I recently heard about MCMLE (Monte Carlo maximum likelihood estimation) for finding $$ \hat\theta = \underset{\theta}{\text{argmax}} \frac{\exp\left(\theta^TT(y)\right)}{c(\theta)} $$ when the ...
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352 views

If Bayesian is better than frequentist(and it's tractable) then how can it be as practical?

In a textbook Probability Theory: The Logic of Science written by E. T. Jaynes and others, on page 13 it reads that: For many years, there has been controversy over ‘frequentist’ versus ‘Bayesian’ ...
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359 views

Is there a difference between Bayesian and Classical sufficiency?

The title pretty much says it all. I wonder whether there is any difference in the way Bayesians understand sufficiency vs. the way orthodox statistics understands sufficiency, or are they equivalent? ...
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1answer
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Why, *intuitively*, in regular parametric problems, does uncertainty go down at a $\sqrt{ n }$ rate on the SE/posterior SD scale?

consider the simplest regular statistical inference problem: $( y_1, \dots, y_n | F ) \sim$ $\text{IID}$ from a cumulative distribution function $F$ on $\mathbb{ R }$ with mean $\mu$ and finite ...
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622 views

How do frequentists address this paradox of hypothesis testing?

Suppose we sample a person from the population. They are a member of US Congress. We define the null hypothesis $H_0$ as "the person is American". We calculate the $p$-value: $P[member\ of\ Congress | ...
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1answer
57 views

What are the consequences when large-sample asymptotics does not hold?

Lots of (frequentist) statistical inference is based on large-sample asymptotics. What are the specific consequences when a sample size is not big enough for the sampling distribution of an ...
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4answers
119 views

How does a bayesian interpret a null association?

After reading about the bayesian approach, I'm wondering how they would interpret a null finding from a regression coefficient. I ask because in a frequentist approach, if the p<.05 you'd say that ...
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2answers
118 views

Formulating a statement about an estimated confidence interval

Consider a data generating process with a parameter of interest $\theta$. I would like to estimate $\theta$ as precisely as possible and also quantify the estimation imprecision / uncertainty. I ...
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178 views

Deterministic or stochastic universe in frequentist statistics

Does frequentist statistics take a stand on whether the universe / world (or at least the processes that are being modeled) is deterministic or stochastic? If so, where in the methodology does that ...
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1answer
174 views

$X_i \sim \text{Uniform}(0, \theta)$ iid; $Y = \max{(X_1,..,X_n)}$. Why is $\theta$ necessarily larger than $y$?

I'm going through Statistical Inference by Casella & Berger, and on page 419, in the intro section of interval estimation there is the following example (note: most of the text was left out as it'...
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1answer
452 views

Is the Poisson-Gamma Model Bayesian?

I was earlier learning about the Poisson-Gamma Model: $$Y|Z \sim Poisson(Z)$$ $$Z \sim Gamma(a,b) $$ This was introduced without any Frequentist flavoring, but since Z, a parameter is now treated as ...
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Frequentist Methods for Bayesians [duplicate]

Over time I've learned that many (most?) methods used in classical statistics can be interpreted as evaluating a Bayesian model in some plausible way while I find the standard explanations much less ...
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1answer
2k views

Why the names Type 1, 2 error?

What is the motivation of introducing an additional level of indirection from the descriptive 'false positive' to the integer '1'? Is 'false positive' really too long?
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101 views

Classical Probability Approach

The definition of classical probability is Classical Probability: If a random experiment can result in $n$ mutually exclusive and equally likely outcomes and if $n_A$ of these outcomes have an ...
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884 views

Calculating minimum detectable effect from sample size and conversion rate

I have a function for calculating the required sample size based on four inputs: baseline conversion rate, minimum detectable effect, confidence and statistical power: ...
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2answers
346 views

Statistics without hypothesis testing

In his blog posts, Andrew Gelman says he is not a fan of Bayesian hypothesis testing (see here: http://andrewgelman.com/2009/02/26/why_i_dont_like/), and if I'm not misremembering, I think he also ...
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Is there any difference between Frequentist and Bayesian on the definition of Likelihood?

Some sources say likelihood function is not conditional probability, some say it is. This is very confusing to me. According to most sources I have seen, the likelihood of a distribution with ...
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1answer
106 views

Does maximum likelihood estimation analysis treat model parameters as variables which is contrary to frequentist view?

As far as I understand (strict) Frequentists treat hypothesis (model parameters) as fixed and don't allow to assign probabilities to a range of model parameters. That is the reason why they compute ...
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68 views

How would a frequentist solve this?

I think i understand what bayesian viewpoint is and what frequentist viewpoint is. But i always feel like i am missing something. I think there is a blind spot. so as an attempt :- Can somebody ...
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158 views

MCMC with flat prior vs. glmer

Is MCMC-based mixed model with flat prior basically just a robust variant of a classical mixed model? I mean – frequentist analyses work with a flat prior anyway so the only difference should be in ...

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