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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Estimating bias in surveys

I run into the following problem on a job interview, and am still wondering what is a principled way to solve it. I think the problem is general enough that will hopefully have enough educational ...
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20 views

Confidence interval syntax in frequentist probability [duplicate]

Let $\theta$ be an unknown population characteristic (say average height). A confidence interval written as $P(\hat \theta - \delta < \theta < \hat \theta + \delta) = 1 - \alpha$ makes perfect ...
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5 views

Analytic determination of exact confidence intervals (without making approximations)

I would like to determine 95% confidence intervals for the mean of a negative binomial distribution. I have read a number of papers that use Gamma, Normal and Chi-squared approximations in order to ...
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557 views

What frequentist statistics topics should I know before learning Bayesian statistics?

I was wondering if there is a subset of topics of frequentist statistics that one should know before starting to learn Bayesian statistics. Once I read that it seems that the two trends are ...
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510 views

Does a confidence interval actually provide a measure of the uncertainty of a parameter estimate?

I was reading a blog post by the statistician William Briggs, and the following claim interested me to say the least. What do you make of it? What is a confidence interval? It is an equation, of ...
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48 views

Intuitive interpretation of Bayes risk $R(\delta, \lambda) = \int_{\Omega}R(\theta, \delta) \lambda(\theta) d\theta$

Consider the risk function R of an estimator (statistic) $\delta(X)$ trying to estimate parameter $\theta$: $$R(\theta, \delta) = E_{X \sim P_{\theta}}[Loss(\theta,\delta(X)]$$ Which can be ...
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40 views

How is data generated in the Bayesian framework and what is the nature on the parameter that generates the data?

I was trying to re-learn Bayesian statistics (every time I thought I finally got it, something else pops out that I didn't consider earlier....) but it wasn't clear (to me) what the data generation ...
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66 views

Why can we assume that samples $X_i$'s are independent if the parameter is fixed (though unknown)?

To put it in context, I was trying to learn Bayesian parameter estimation (by an example of learning the probability of heads of a coin) and was trying to understand the independence of the samples ...
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55 views

What is the frequentist take on the voltmeter story?

What is the frequentist take on the voltmeter story and its variations? The idea behind it is that a statistical analysis that appeals to hypothetical events would have to be revised if it was later ...
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32 views

How can you judge the statistical confidence and validity of output from a multi arm bandit algorithm like UCB1

To say something about the validity of outcomes in frequentist statistics we have concepts like significance levels and statistical power and in Bayesian analytics we have credible intervals. In a ...
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49 views

Using simulation to estimate type-I error in Bayesian Tests

When doing a bayesian test, it is possible to estimate a "type-I error" of the test procedure by generating data from the null-hypothesis and running the bayesian test procedure several times. While ...
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261 views

Is MLE with regularization a bayesian method?

It is usually said that priors on bayesian statistics can be regarded as regularization factors since they penalize solutions where the prior places low density of probability. Then, given this ...
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561 views

2-Gaussian mixture model inference with MCMC and PyMC

The problem I want fit the model parameters of a simple 2-Gaussian mixture population. Given all the hype around Bayesian methods I want to understand if for this problem Bayesian inference is a ...
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2answers
100 views

Should corrections for multiple comparisons be used when evaluating independent experiments?

I understand why corrections for multiple comparisons (e.g., the Bonferroni correction) are used in some cases. For example, if I run a a single experiment and check significance of many factors, the ...
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1answer
100 views

Bayesian inference of a clinical trial for clinicians

I am a clinician who is more adept than average at interpreting clinical trials in a frequentist manner. At this point, interpreting a trial as a frequentist has kind of become a procedure: check ...
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1answer
56 views

Question about the Bayesian Inference of a parameter

In order to understand the difference between the Frequentist and Bayesian inference, I was reading the presentation at: http://www.stat.ufl.edu/archived/casella/Talks/BayesRefresher.pdf . In order to ...
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18 views

Set hypothesis instead of point hypothesis [duplicate]

Statisticians are often interested on testing point null hypotesis, such as: $$H_0: \mu =0 \,\,\, vs. \,\,\, H_1:\mu\neq0.$$ As Jeffreys himself said, this actually corresponds to some presumption ...
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1answer
1k views

Why does frequentist hypothesis testing become biased towards rejecting the null hypothesis with sufficiently large samples?

I was just reading this article on the Bayes factor for a completely unrelated problem when I stumbled upon this passage Hypothesis testing with Bayes factors is more robust than frequentist ...
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431 views

Subjectivity in Frequentist Statistics

I often hear the claim that Bayesian statistics can be highly subjective. The main argument being that inference depends on the choice of a prior (even though one could use the principle of ...
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49 views

Confidence interval definitions

Wikipedia provides the following definition for a confidence interval for a parameter $\theta$: A confidence interval for the parameter θ, with confidence level or confidence coefficient γ, is ...
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386 views

When are Bayesian methods preferable to Frequentist?

I really want to learn about Bayesian techniques, so I have been trying to teach myself a bit. However, I am having a hard time seeing when using Bayesian techniques ever confer an advantage over ...
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1answer
51 views

Designing Frequentist A/B Experiments

What parameters should one pre-specify before designing/running an experiment? (e.g. a two-sample, one-side, t-test) My understanding is that on establishes: Null hypothesis Maximum Significance ...
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105 views

How many different approaches (or schools, or methods) is in statistics?

I am beginning to learn statistics and made some searches in Internet about statistics. Most of the articles I found says that there are two different approaches (or schools, or methods) in statistics ...
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229 views

Is multilevel modelling simpler, more practical, or more convenient using Bayesian methods or frequentist methods?

In this community wiki page a twice-upvoted comment asserted by @probabilityislogic asserted that "Multi-level modelling is definitely easier for bayesian, especially conceptually." Is that true, and ...
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38 views

Pitfalls of posterior simulation when analysis didn't begin as Bayesian

I've got a situation where I'd like to evaluate a function of a fitted model, and account for the uncertainty in the fitted model. For example, say I want to calculate the minimum of the function ...
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1answer
90 views

The Bayesian approach to computing estimator bias and variance

From what I understand, jackknife and bootstrapping are frequentist methods for computing statistics (bias, variance, etc.) of an estimator. Given a sample of my data and an estimator, and assuming ...
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69 views

Hierarchical model: question on frequentist estimation

I am interested in understanding the differences between Bayesian and Frequentist estimation in the context of hierarchical models. Consider $n$ subjects, where for subject $i$ there are $k_i$ ...
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Why is a Bayesian not allowed to look at the residuals?

In the article "Discussion: Should Ecologists Become Bayesians?" Brian Dennis gives a surprisingly balanced and positive view of Bayesian statistics when his aim seems to be to warn people about it. ...
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282 views

Are sampling distributions legitimate for inference?

Some Bayesians attack frequentist inference stating that "there is no unique sampling distribution" because it depends on the intentions of the researcher (Kruschke, Aguinis, & Joo, 2012, p. 733). ...
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249 views

Prediction interval for number of biased coin tosses to get 2 consecutive heads

Suppose I am given a possibly biased coin, which turns up heads an unknown fraction $p$ of the time. Initially I flip the coin 10 times (e.g. generating data = TTHTTHHTHH). Next, I have to flip ...
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37 views

A random variable that is invariant under null & alternative hypotheses

Suppose a random variable $X$ has probability density function $f_0$ and $f_1$ under null and alternative hypothesis, respectively. Is it possible to find another random variable, $g(X)$, which has ...
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1answer
42 views

A Question from textbook “Learning with Kernels”

I am reading the book "Learning with Kernels: Support Vector Machines, Regularization, Optimization, and Beyond (Adaptive Computation and Machine Learning)". I finished the first chapter and didn't ...
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95 views

Distribution of logically constrained parameters in Monte Carlo simulation

Papers like Briggs et al. 2002 say that logical constraints on inputs such as probability parameters exclude the the Normal distribution from consideration due to its unboundedness. In this example, ...
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659 views

Q: what book on Bayesian statistics, preferably with R? [duplicate]

I am frequentist by training and practice, but I'd like to learn more about Bayesian statistics. I know the basics, but I would be at a loss if I had to, for example, replace my normal ANOVA ...
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93 views

Do Bayesians interpret the likelihood distribution as subjective as well?

One of the main differences between Bayesians and frequentists is that they have a subjective interpretation to probability. However, do Bayesians actually interpret subjectively the probabilities ...
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216 views

Bayesian and frequentist interpretations vs approaches

I have been reading about the frequentist vs bayesian issue (this article has helped a lot, specially with the example; also this one), and I haven't come to terms with it. At the moment it seems like ...
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4k views

What does the inverse of covariance matrix says about data? (Intuitively)

I'm curious about the nature of $\Sigma^{-1}$. Can anybody tell something intuitive about "What does $\Sigma^{-1}$ say about data?" Edit: Thanks for replies After taking some fantastic courses, I'd ...
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218 views

Why are Bayesian methods widely considered particularly “convenient”?

Several times I have come across (in lectures, papers, etc.) informal/tangential remarks that have the following basic form: Philosophical issues aside, Bayesian methods are extremely convenient. ...
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374 views

Given a frequency distribution, calculate probability of A given B

My test recorded the number of times a variable reached a threshold value when a predetermined event occurred. Then, the test recorded the number of times the variable surpassed the threshold value by ...
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134 views

Probability is not frequency

I was just told in comments that probability p=1/n does not mean that I have 1 occurrence in n experiments in average, for large number of experiments because observed frequency has nothing to do with ...
5
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1answer
214 views

A Bayesian perspective on omitted-variable bias (and other covariate-selection bias problems)

As I know OVB, from a frequentist education, when you leave a variable $(z)$ out of your control set $(X)$ that is correlated with both your independent variable of interest (treatment $T$) and your ...
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217 views

Does talking about a probability of future events make you a Bayesian?

Okay, so I sent a confession of love to a girl detailing several reasons and coming up with a 90% probability that I will be with her together for my whole life. But I then thought that I was ...
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1answer
136 views

Confusion related to a post related to statistics in xkcd [duplicate]

I came across this post http://xkcd.com/1132/ and this image I didn't get why the Bayesian statistician is saying no. Any suggestion
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83 views

Statistical error in Bayesian framework

Residuals and errors are related but not exchangeable. In Wikipedia I read: In statistics and optimization, statistical errors and residuals are two closely related and easily confused measures of ...
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165 views

Outline of benefits/costs of using Bayesian rather than Frequentist OLS and time-series?

I'm reading up on Bayesian techniques for Linear models and time series. While the texts are great at teaching the theory I would like to get a better handle on the pro's/con's of Bayesian analysis vs ...
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201 views

Under what conditions do Bayesian and frequentist point estimators coincide?

With a flat prior, the ML (frequentist -- maximum likelihood) and the MAP (Bayesian -- maximum a posteriori) estimators coincide. More generally, however, I'm talking about point estimators derived ...
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88 views

What if the MVUE depends on the parameter?

The minimum variance, unbiased estimator $\hat \theta$ of $\theta$ is defined by $$\hat \theta = \text{argmin}_{\hat \theta} \; \mathbb{E} \left( (\hat \theta - \theta)^2 \, | \, \theta\right), \quad ...
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Bayesian uninformative priors vs. frequentist null hypotheses: what's the relationship?

I came across this image in a blog post here. I was disappointed that reading the statement did not elicit the same facial expression for me as it did for this guy. So, what is meant by the ...
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Confusion related to Kulldorff's scan statistics

I was reading this paper related to Bayesian spatial scan statistics where I came across the Kulldorff's scan statistics. I have attached the screenshot of the paper. My objective is to find a ...
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120 views

Priors for parameters of normal distribution leading to same results as frequentist formula

Given a sample vector $x$ of size $N$ from a normally distributed population. With frequentist methods the population mean is estimated as $\hat{\mu}=\frac{\Sigma{}x_i}{N}$, population sigma is ...