# Questions tagged [empirical-bayes]

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

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13 views

### Empirical Bayes for normal likelihood and normal prior

Here's my simulated data: ...
1 vote
28 views

### How to calculate the log marginal distribution in Tweedie's formula?

2018 Bayes, oracle Bayes, and empirical Bayes 2021 Empirical Bayes: Concepts and methods Two modeling strategies for empirical Bayes estimation 2013 Empirical Bayes modeling, computation, and ...
116 views

### Doing empirical Bayes with improper prior - marginals that do not exist?

I am considering a Bayesian linear model for which the prior is not proper. The model is as usual $y = X \theta + w$ where $w \sim N(0, \sigma^2)$, and $\theta, \sigma^2$ are unknown. The distribution ...
28 views

### Is there a proper way to combine two beta prior distributions?

I'm working on a research project which involves the assessment of NHL goalie performance (save percentage) using empirical Bayes. I found that the goalie distribution for career games played was ...
203 views

### Is Bayesian model selection with empirical parameter priors sound?

Overview I want to perform a Bayesian model selection on many datasets and use these datasets to determine the required parameter priors. Example Scenario: Coins Suppose I have a collection of ...
75 views

### Possibility priors in Bayesian analysis?

A couple of trains of thought have come together for a model I am designing. Let's start with the first part: Bayesian inference doesn't update strongly enough. One of the parameters $\theta$ is an ...
108 views

### Trying to understand if a model is an empirical Bayes or not

I am trying to understand if the model published in section 4.1.1 here is or is not an Empirical Bayes model (which the author claims it is). Or, maybe, if it is a valid one or not. The model looks as ...
378 views

### Is it wrong to use sufficent statistc estimated from the data as a prior in Bayesian data analysis?

First I want to state that I got unexpected feedback from a reviewer in regard to my question and I am simply interested in others' views in this regard (I have already sent in my rebuttal). Suppose ...
1 vote
44 views

### Why are fisher-scoring estimates of the fixed-effects not used to calculate empirical bayes estimates of random-effects? Are they in-admissible?

Why is it not practiced using estimates of fixed-effects from fisher scoring used to calculate GEE coefficients to estimate random-effects via empirical bayes? We have another estimate of $\theta$ in ... 1 vote
138 views

### In Bayesian hierarchical models, what is the difference between an Empirical Bayesian approach to parametrising priors vs using flat hyperpriors

Say I have a simple hierarchical model, where: $y_{g,i} = \beta_g x_{g,i} + e_{g,i}$ where $g$ represents the group, $i$ represents the individual within the group, and $e$ is the error. So the ...
100 views

### How to combine priors for empirical bayes

I am trying to estimate $Z_{i} = P(Y=1 | A=a_{i}, B = b_{i}, C =c_{i})$ using something like empirical Bayes as in http://varianceexplained.org/r/empirical_bayes_baseball/ aggregating a massive amount ...
1 vote
83 views

### Which marginal likelihood is maximized in empirical Bayes?

I am reading up on empirical Bayes, and I am finding it really hard to understand what exactly is going on. As far as I understand, it is based on maximizing the marginal likelihood of the data (so ...
59 views

### Why Are Empirical Bayes Methods Not Considered "Controversial"? [duplicate]

I was reading about Empirical Bayesian Methods and came across the following: My Question: As this text explains, I have often heard that the priors used in Bayesian Methods should be decided prior ...
1 vote
75 views

### Empirical bayes estimation of variograms for multiple variables

I am looking to estimate variograms, or spatial correlation matrices on all columns of a data matrix $\mathbf{X}_{n\times p}$ with $p>n$. The matrix of spatial coordinates $\mathbf{Y}_{n\times 2}$ ...
1 vote
88 views

### Empirical Bayes prediction

I've been working with a GLMM in SAS. Using the proc GLIMMIX procedure, I've extracted the EB estimates of the random-effects. I was looking into empirical Bayes estimates and their predictive power. ...
47 views

### How to manually adjust predicted probabilities from lm based on prior lognormal distribution parameters?

@drob showed a great example of adjusting batting averages using a beta-based prior distribution. He used a prior calculated Beta distribution to adjust batting averages individually, and it’s as ...
148 views

### Is empirical Bayes estimation still possible without common parameters?

In An Introduction to Empirical Bayes Data Analysis by George Casella (1985), it is given that \begin{align} X|\theta &\sim N(\theta,\sigma^2) \\ \theta &\sim N(\mu,\tau^2) \\ \theta|X &\...
From the Wikipedia article on the empirical Bayes method (emphasis mine): In, for example, a two-stage hierarchical Bayes model, observed data $y=\{y_{1},y_{2},\dots ,y_{n}\}$ are assumed to be ...