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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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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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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
69 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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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
49 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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62 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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234 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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25 views

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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869 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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46 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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0answers
106 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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221 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
47 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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0answers
45 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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63 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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21 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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60 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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847 views

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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1answer
102 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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1answer
101 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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1answer
149 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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177 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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1answer
57 views

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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127 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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19 views

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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187 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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31 views

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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121 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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3answers
238 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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1answer
109 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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60 views

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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259 views

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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0answers
167 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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634 views

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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683 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
56 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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1answer
399 views

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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1answer
56 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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1answer
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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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86 views

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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177 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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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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What is the difference between frequentism and bayesian in the case of uninformative priors as well as uniform distribution? (with example)

What is the difference between frequentist and bayesianism in the case of uninformative priors as well as uniform distribution? (with example)
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93 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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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 ...