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Is Bayesian estimation useful for causal analyses?

For analyses like randomized experiments or even observational studies of natural experiments, we want unbiased estimators of the causal effect (unbiased ATE or ATT). This lends itself really well to frequentist methods where estimators are unbiased (like OLS). However, unbiasedness doesn't seem to be to goal for Bayesian analyses.

So is there a good reason to use Bayesian estimation when the treatment is randomized so causality can be identified?

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While you say we want unbiased estimators of the causal effect, generally we are interested in obtaining an accurate/precise estimate of a quantity of interest. When offered a range of estimators to choose from, a sensible selection criterion is to choose one that minimizes the expected loss, where loss is due to the estimation error. A convenient special case is square (quadratic) loss. Due to the bias-variance trade-off, a biased estimator may have lower expected squared error (lower expected loss) and thus higher precision/accuracy than an unbiased one. Bayesian methods take advantage of that as they introduce bias into their estimators but simultaneously achieve a reduction in variance. If the trade-off is favorable as compared to an unbiased estimator, i.e. the reduction in variance outweighs the squared bias, this looks like a good-enough reason for opting for Bayesian estimation. This applies not only to estimators of causal effects but also more generally.

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  • $\begingroup$ Great explanation! can you add a bit more details on how Bayesian methods can introduce the bias into their estimators? $\endgroup$ – yoav_aaa Sep 24 '20 at 8:16
  • $\begingroup$ @yoav_aaa, thanks! I could add that but I am afraid this is common knowledge, so no need to get into it here. For your own interest, you could take a look at this thread; I am sure there also are more threads containing a similar message. $\endgroup$ – Richard Hardy Sep 24 '20 at 8:31
  • $\begingroup$ Yup - was just looking for a good reference for this - thanks. $\endgroup$ – yoav_aaa Sep 24 '20 at 15:05
  • $\begingroup$ That makes lots of sense! I've heard this explanation (bias-variance trade-off) in reference to predictive models but you show that it's just as applicable for estimating causal effects. $\endgroup$ – Michael Webb Sep 29 '20 at 15:24
  • $\begingroup$ @Great38, I am glad you have found it useful! $\endgroup$ – Richard Hardy Sep 29 '20 at 16:07

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