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Is Meta Analysis the Future of Bayesian Statistics?

To summarize these two concepts:

  • Bayesian Statistics involve using historical information about the distribution of model parameters to supplement directly observed information. This historical information is referred to as "Bayesian Priors".

  • Meta Analysis is a form of "statistical analysis that combines the results of multiple scientific studies, with each individual study reporting measurements that are expected to have some degree of error. The aim then is to use approaches from statistics to derive a pooled estimate closest to the unknown common truth based on how this error is perceived."

All in all, these two concepts (Bayesian Statistics and Meta Analysis) seem to naturally complement each other. They both aim at using "prior" available information for the purpose of augmenting statistical models in order to derive more "truth" within the environment.

However, for some reason this does not seem to be directly addressed within Meta Analysis.

My Question: In the future, is it reasonable to expect that Bayesian Statistics and Meta Analysis will become more closely related and be almost synonymous with one another?

Thanks!

References:

stats_noob
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1 Answers1

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No.

They are not synonymous but they are closely related.

You are correct, a prior could be created from previous research on a topic. Likewise, that previous research could be used to create a meta-analysis.

The differences do matter.

First, a meta-analysis works over the sample space. It averages over it. Done well, it should have good Frequentist properties. It is also performed ex-post. It is not used as a regularity condition for the next study. It should soundly inform the creators of the next study, but should not alter the next study's conclusions.

A meta-analysis is a conclusion.

A prior works over the parameter space. In addition to prior studies, it can bring in other information believed to be true but which has not been studied already. An informative prior will generally not create good Frequentist properties. It is also performed ex-ante to another research study or to create a prior predictive distribution. The prior will alter any study's conclusions.

A prior is preparatory work for the next study.

For certain types of studies, the difference between working in the parameter or the sample space produce no differences, but there can be differences. For certain simple problems, the two methods can end up mapping to the same estimators, but that is not always so. When a generalized Bayes rule is not being used by the person using a Bayesian method, then they will likely diverge from each other.

Probably the best post on here regarding the differences is the article on the differences between confidence and credible intervals.

If you read the article, you will see vastly different reported intervals with the same data. Doing a second study in the cookie story linked above, while it will produce a better estimator when combined with a first study, won't make the two methods produce similar intervals in the general case.

Dave Harris
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