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Bayesian Methods and Bias Analysis
(without Bayes Theorem or MCMC)
Sander Greenland
Professor of Epidemiology, UCLA School of Public Health
Professor of Statistics, UCLA College of Letters and Science
Part I:
Bayesian methods continue to grow more popular in advanced statistical modeling, but have as
yet had little impact on basic teaching and analysis. This lag may be due to the common
misconception that Bayesian methods are computationally difficult and require special software.
Nonetheless, perfectly adequate Bayesian analyses can be carried out with ordinary software for
standard (frequentist) analysis, with no special programming required. Under a wide range of
priors, the accuracy of these approximations is just as good as the frequentist accuracy of the
software, and more than adequate for observational studies in health and social sciences. An easy
way to do Bayesian analyses is via inverse-variance (information) weighted averaging of the
prior with the frequentist estimate. A more general method expresses the prior distributions in
the form of prior data or “data equivalents,” which are then entered in the analysis as a new data
stratum. That form reveals the strength of the prior judgments being introduced, and leads to
methods for modeling biases, which will be discussed in Part II.
Part II:
This session describes extensions of the basic Bayesian methods in part I to analyses involving
non-normal priors and regression analysis, including hierarchical (multilevel) modeling. These
methods provide an alternative to the parsimony-oriented approaches of standard regression
analysis. In particular, they replace arbitrary variable-selection criteria by prior distributions; by
doing so they facilitate realistic use of vague but important prior information. They also allow
Bayesian analyses to be conducted with standard regression packages, without any special
programming; one need only be able to add variables and records to the data set. The methods
thus facilitate the use of Bayesian solutions to problems of sparse data, multiple comparisons,
and study bias.
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