Stack Exchange Network

Stack Exchange network consists of 175 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.

Visit Stack Exchange

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.

8
votes
0answers
35 views

How do Bayesians verify their methods using Monte Carlo simulation methods?

Background: I have a PhD in social psychology, where theoretical statistics and math were barely covered in my quantitative coursework. Through undergrad and grad school, I was taught (much like many ...
0
votes
0answers
14 views

Can I use Poisson regression to model prevalence ratios if I only have information on events?

I often used Poisson regression models to estimate prevalence ratios. However, in these cases my data contained information on the whole population, including events (1) and non events (0). ...
1
vote
0answers
27 views

How does the frequentist approach to probability estimation work when the number of outcomes is greater than 2?

I've read Checking_whether_a_coin_is_fair and I'm trying to find a resource which generalizes the frequentist approach to the case where there are $k$ distinct outcomes and $n$ trials. Can someone ...
0
votes
0answers
6 views

Bayes vs trial factor (particle physics)

In the statistical inference for particle physics is the trial factor analogous to Bayes factor but for the frequentist analysis?
1
vote
0answers
8 views

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 ...
1
vote
0answers
15 views

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 ...
0
votes
0answers
15 views

Understanding Bayesian HDIs for paired samples vs independent samples

According to Kruschke (http://www.users.csbsju.edu/~mgass/robert.pdf), if I have two different groups and collect their response times to a certain task, to determine if the two groups are ...
0
votes
0answers
17 views

Bayesian vs Frequentist inference in the presence of noisy data

I'm wondering how Bayesian inference and Classical/Frequentist inference fair towards noisy data. I can't seem to find too much literature addressing this issue and it seems the conclusion is usually ...
0
votes
0answers
63 views

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 ...
9
votes
1answer
168 views

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 ...
0
votes
1answer
52 views

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 ...
0
votes
1answer
28 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 ...
1
vote
0answers
25 views

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 ...
1
vote
1answer
58 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, ...
0
votes
0answers
32 views

Interpreting prediction intervals, and prediction intervals for a specific parameter?

Can someone correct my thinking if I'm off course here? Confidence intervals provide an estimate of precision$^1$ for a specific parameter, but they can also be used for a regression equation (i.e., ...
11
votes
5answers
674 views

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 ...
1
vote
1answer
36 views

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 ...
0
votes
1answer
21 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 ...
1
vote
1answer
42 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 ...
4
votes
1answer
52 views

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 ...
2
votes
1answer
98 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 ...
0
votes
0answers
23 views

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 ...
4
votes
2answers
75 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 ...
4
votes
1answer
74 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. ...
0
votes
0answers
23 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 ...
4
votes
0answers
48 views

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 ...
1
vote
0answers
62 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 <...
0
votes
0answers
26 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 ...
3
votes
1answer
50 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 ...
3
votes
1answer
123 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 ...
0
votes
1answer
36 views

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 ...
2
votes
1answer
47 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 ...
2
votes
1answer
78 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 "...
1
vote
1answer
112 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 ...
1
vote
2answers
104 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 $...
1
vote
0answers
31 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 ...
0
votes
1answer
54 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 ...
2
votes
1answer
319 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 ...
1
vote
1answer
115 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 ‘...
6
votes
2answers
254 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? ...
0
votes
1answer
53 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 ...
2
votes
7answers
526 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 | ...
2
votes
4answers
85 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 ...
2
votes
2answers
84 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 ...
3
votes
2answers
72 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?
2
votes
1answer
86 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'...
1
vote
1answer
354 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 ...
1
vote
0answers
26 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 ...
21
votes
1answer
966 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?
1
vote
2answers
52 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 ...