Slamming the sham: A Bayesian model for adaptive adjustment with noisy control data
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It is not always clear how to adjust for control data in causal inference, balancing the goals of reducing bias and variance. In a setting with repeated experiments, Bayesian hierarchical modeling yields an adaptive procedure that uses the data to determine how much adjustment to perform. We demonstrate this procedure on the example that motivated this work, a much-cited series of experiments on the effects of low-frequency magnetic fields on chick brains, as well as on a series of simulated data sets. We also discuss the relevance of this work to causal inference and statistical design and analysis more generally.
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