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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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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536 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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2answers
350 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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1answer
36 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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4answers
258 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
34 views

Designing Frequentist A/B Experiments

What parameters should one pre-specify before running an experiment? (e.g. a two-sample, one-side, t-test) My understanding is that on establishes: Null hypothesis Maximum Significance level ...
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92 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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2answers
126 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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27 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
65 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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0answers
50 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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2answers
1k views

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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26 views

Weakly or strongly identified parameters?

I was reading this paper. Authors talk about "weakly identified parameters" or "strongly identified parameters" continuously. Rigorously, what does it mean when one say a parameter is strongly or ...
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247 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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1answer
137 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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1answer
33 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
37 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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1answer
73 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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2answers
342 views

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

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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1answer
85 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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2answers
185 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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2answers
1k 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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3answers
195 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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1answer
71 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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1answer
129 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 ...
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1answer
145 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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3answers
192 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
124 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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76 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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1answer
125 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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1answer
139 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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60 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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4answers
799 views

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 illicit the same facial expression for me as it did for this guy. So, what is meant by the ...
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28 views

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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1answer
109 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 ...
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177 views

Which is the null hypothesis for testing whether I've broken my simulation?

The situation: I'm writing agent-based computer simulations in which there are random effects which can be biased by various parameters. I run the simulation with the same parameters many times in ...
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1answer
220 views

On FDA guidance about Bayesian practice

US FDA authorizes the use of Bayesian statistics with informative priors (in certain contexts): ...
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50 views

Anomaly prediction confidence for frequentist vs bayesian parameter inference

I am comparing the behavior of some implementations of Bayesian and frequentist approaches to parametric anomaly detection and currently trying to figure out the differences when the sample set is ...
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1answer
254 views

Bayesian and frequentist approaches: What are some success stories for the former? [duplicate]

Possible Duplicate: Examples of Bayesian and frequentist approach giving different answers What are some practical examples where a Bayesian approach has an edge over frequentist ...
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2answers
215 views

Results Difference: Frequentist vs. Bayesian

I fit a lognormal model on some data points using both frequentist and Bayesian (using a non-informative prior) approaches. However, I got different results. Here are my codes and outputs: ...
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68 views

Defining Empirical Risk Minimization

I am reading Machine Learning - A probabilistic Perspective by Kevin Murphy and in chapter 6.5 the author discusses Empirical Risk Minimization, and provides the following definition: ...
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2answers
660 views

Questions on paramatric and non-parametric bootstrap

I am reading the chapter on Frequent Statistics from Kevin Murphy's book "Machine Learning - A Probabilistic Perspective". The section on bootstrap reads: The bootstrap is a simple Monte Carlo ...
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1answer
73 views

how do I interpret the following hypothesis test?

Let's say I have two hypotheses for a coin with probability $p$ for heads: $H_0$ - the null hypothesis - the coin is fair $p = 0.5$. $H_1$ - coin is unfair $p \neq 0.5$. Say the test is $|X-n/2| ...
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1answer
145 views

how would you approach giving an introductory class about Bayesian statistics?

I need to give a lecture about Bayesian statistics, introducing it to people who have already basic knowledge of classic statistics (but not too much of it in general). I want to start with some ...
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1answer
233 views

How to estimate right-skewed distribution with very small sample size?

Suppose we have a data set consists of, say, 5 or 10 observations. The only thing we know about this set is that it came from a positive right skewed distribution. How can we fit a probability ...
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2answers
146 views

Frequentist confidence intervals = constant trapping probability?

In the case of estimating an unknown mean of a normal distribution with known variance, if I'm not mistaken, the confidence interval contains $\theta$ with probability $1 - \alpha$, regardless of the ...
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5answers
3k views

Examples of Bayesian and frequentist approach giving different answers

Note: I am aware of philosophical differences between Bayesian and frequentist statistics. For example "what is the probability that the coin on the table is heads" doesn't make sense in frequentist ...
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11answers
9k views

What's wrong with XKCD's Frequentists vs. Bayesians comic?

This xkcd comic (Frequentists vs. Bayesians) makes fun of a frequentist statistician who derives an obviously wrong result. However it seems to me that his reasoning is actually correct in the ...
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6answers
1k views

List of situations where a Bayesian approach is simpler, more practical, or more convenient

There have been many debates within statistics between Bayesians and frequentists. I generally find these rather off-putting (although I think it has died down). On the other hand, I've met several ...
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142 views

frequentist coverage, and besides?

One day I gave a $95\%$-confidence interval to a requester who know nothing about statistics. He asked me what does it mean. Roughly, I answered "The population parameter is inside the interval $95\%$ ...