Meaning of non-parametric empirical Bayes

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In summary, the conversation discusses the definition of non-parametric in the context of Bayesian modeling and empirical Bayes methods. The speaker is confused because while non-parametric in Bayesian modeling usually means an infinite number of parameters, they cannot find this in the description of non-parametric empirical Bayes methods. They suggest providing a link to clarify the meaning, specifically mentioning the "Robbins method" as an example of a non-parametric empirical Bayes method.
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mersecske
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As far as I know non-parametric in non-parametric Bayesian modelling means infinite number of parameters. Therefore I expected the same meaning in non-parametric empirical Bayes methods, however I am a little bit confused, because I cannot find infinite number of parameters in the description of non-parametrics empirical Bayes methods. Is it possible that in this case non-parametric means only no parameter?
 
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  • #3
Yes, Robbins method.
 

FAQ: Meaning of non-parametric empirical Bayes

What is the meaning of non-parametric empirical Bayes?

Non-parametric empirical Bayes is a statistical approach used to estimate parameters in a Bayesian framework without making assumptions about the underlying distribution of the data. It involves using data-driven methods to estimate the prior distribution, rather than specifying it beforehand.

How does non-parametric empirical Bayes differ from traditional Bayesian methods?

In traditional Bayesian methods, the prior distribution is specified based on prior knowledge or assumptions about the data. Non-parametric empirical Bayes, on the other hand, estimates the prior distribution from the data itself.

What are the advantages of using non-parametric empirical Bayes?

One advantage is that it allows for more flexibility in modeling complex data that may not fit into a specific parametric distribution. It also reduces the subjectivity of choosing a prior distribution, as it is estimated from the data.

In what types of situations is non-parametric empirical Bayes useful?

Non-parametric empirical Bayes is useful when there is limited prior knowledge about the data or when the data is complex and does not follow a specific distribution. It is also beneficial when dealing with high-dimensional data, as it can handle a larger number of parameters compared to traditional Bayesian methods.

What are some common techniques used in non-parametric empirical Bayes?

Some common techniques include the empirical Bayes method, which estimates the prior distribution based on the observed data, and the hierarchical Bayes method, which uses multiple levels of prior distributions to estimate the parameters. Other techniques include non-parametric density estimation and machine learning algorithms such as Gaussian processes.

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