# Questions tagged [empirical-bayes]

Procedures for statistical inference in which the prior distribution is estimated from the data.

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### How is empirical Bayes valid?

So I just finished reading a great book Introduction to Empirical Bayes. I thought that the book was great, but building priors from the data felt wrong. I was trained that you come up with an ...
2answers
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### Cross-validation vs empirical Bayes for estimating hyperparameters

Given a hierarchical model $p(x|\phi,\theta)$, I want a two stage process to fit the model. First, fix a handful of hyperparameters $\theta$, and then do Bayesian inference on the rest of the ...
1answer
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### hierarchical Bayesian models vs. empirical Bayes

Would you consider the HBM vs EB to be two alternatives in which the hyperparameters are "in the game" of being sampled/estimated/etc.? There is clearly a connection between these two. Would you ...
1answer
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### Is there a connection between empirical Bayes and random effects?

I recently happened to read about empirical Bayes (Casella, 1985, An introduction to empirical Bayes data analysis) and it looked a lot like random effects model; in that both have estimates shrunken ...
0answers
188 views

### Empirical Bayes (In)Admissibility

Sticking to a pure Bayesian approach to statistics with proper priors most of the time leads to admissible estimators. Nevertheless there is good reason to use Empirical Bayes in many cases, and the ...
1answer
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### Empirical Bayes vs “non-informative” priors

I am familiar with the mechanics with both methods, but don't know what factors I should consider when choosing between these two approaches for adjusting a prior. I would imagine that, on a case by ...
1answer
305 views

### Empirical Bayes/MCMC references

I'm interested in references for running empirical Bayes (EB) in conjunction with MCMC. The closest thing I've found to what I'm looking at is a surprisingly recent and somewhat obscure paper ...
1answer
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### How do Bayesian hierarchical models adaptively learn the prior?

It seems the main difference between a hierarchical and a non hierarchical model is that the hierarchical model learns the prior. That is it adaptively comes up with a regularizing prior to be applied ...
1answer
160 views

### Learning prior distribution from data

Suppose I have a dataset. How can I learn the prior distributions of the parameters of a model from this data? I want to learn the prior from this data in order to use them in a Bayesian model. Sorry ...
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### Empirical Bayes Estimation

Suppose $X_i$ conditioned on $\mu$ is iid $N(\mu, \sigma^2)$ and $\mu$ is distributed as $N(\mu_0, \tau^2)$. Is there a way to estimate $\tau^2$?
1answer
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### What is the empirical Bayes estimator for a gamma-Poisson with more than 1 observation for each Poisson parameter?

I am looking at the Wikipedia entry for empirical Bayes, but it's a bit confusing - it seems to me the solution must apply only to the case in which there's only $n=1$ sample $y$ for each $\theta$ and ...
1answer
636 views

### How to pick starting parameters for MASS:fitdist() with the beta distribution?

I have data set of ~700k yes/no events that I want to first aggregate on various features (e.g. group by average), always resulting in a 34 length vector. From there, I want to fit a beta ...
1answer
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### Robbins estimate Empirical Bayes

From the compound sampling model where: $Y_i | \theta_i \sim Poi(\theta_i)$ The marginal distribution of $\theta_i$ is $G$, non-parametric. We get that the Bayes estimate of $\theta_i$ under ...
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### Is expectation maximization an example of empirical Bayes?

I don't think I truly understand what methods are classified as "empirical Bayes". Is expectation maximization considered an example of this?
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### Why the local Bayes fdr is greater than the Bayes FDR?

My question is related to empirical Bayes and large-scale inference. It is explained that the local Bayes false discovery rate (fdr) is greater than the Bayes false discovery rate (FDR). It is argued ...
0answers
321 views

### How to calculate the inverse cdf for a sample with unknown distribution?

I'm stuck with an exercise that I'll just write down first: Based on a sample $x_1,...,x_{47}$, that can be considered coming from an unknown distribution, we study a qq-plot where the empirical ...
1answer
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### Empirial Bayes for means

I have data for US ~3100 counties where the variable is a mean score based on a sample. However, for many small counties, the sample size is quite small (like 5), and so these mean values fluctuate a ...
0answers
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### Modeling the Probability of Falling Asleep

Problem The goal of this exercise is to estimate $p = \text{Pr}(\text{fall asleep})$, the probability of falling asleep imminently, as a mental exercise for those nights when sleep doesn't seem to be ...
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### Get posterior distribution of categorical variable given empirical continuous-categorical priors?

Suppose I have categorical variable $Z \in D$ defined for some finite domain $D$. I also have a continuous variable $X \in \mathbb{R}$ which is observed. From historical data samples I have the ...
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### question about empirical Bayes（EB）

In David Robinson's blog：Understanding empirical Bayes estimation (using baseball statistics) he used the hit ratio to fit the beta distribution as a prior distribution，Where hit rate = hits/total. ...
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137 views

### Why does Empirical Bayes work in my simple case?

I have a problem where I am trying to classify data into two groups using a single parameter. The distribution of this parameter is Gaussian for two groups, so what I'm dealing with is two overlapping ...