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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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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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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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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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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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54 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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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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28 views

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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53 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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Maximum likelihood deviance = lowest Bayesian deviance?

I've just run a logistic regression using the standard frequentist maximum likelihood approach and then again using Bayesian MCMC (weak priors, all ~ $n(0, 100)$). I calculated the deviance for each ...
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71 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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79 views

If Bayesian approaches are better than frequentist 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 ‘...
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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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49 views

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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7answers
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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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4answers
70 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
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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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2answers
58 views

Deterministic or stochastic universe in frequentist statistics

Does frequentist statistics take a stand on whether the universe (or at least the processes that are being modeled) is deterministic or stochastic? If so, where in the methodology does that matter?
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$X_i \sim \text{Uniform}(0, \theta)$ 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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267 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

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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887 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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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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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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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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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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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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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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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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68 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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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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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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156 views

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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158 views

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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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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Can I decide whether the real regression coefficient is positive without going Bayesian?

I would like to decide whether a particular coefficient of a hidden linear model is positive, from which I only know the regression on a sample of points. Let's say I assume the underlying model is ...
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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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Need of experiment duration in an A/B test

The Law of Large Numbers states that as a sample size increases, the sample mean will get closer to the population mean. But when we run a fixed sample A/B test, why don't we consider it running for a ...
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4answers
58 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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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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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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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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1answer
163 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 ...