  Substantial advances in Bayesian methods for causal inference have been
developed in recent years. We provide an introduction to Bayesian inference for
causal effects for practicing statisticians who have some familiarity with
Bayesian models and would like an overview of what it can add to causal
estimation in practical settings. In the paper, we demonstrate how priors can
induce shrinkage and sparsity on parametric models and be used to perform
probabilistic sensitivity analyses around causal assumptions. We provide an
overview of nonparametric Bayesian estimation and survey their applications in
the causal inference literature. Inference in the point-treatment and
time-varying treatment settings are considered. For the latter, we explore both
static and dynamic treatment regimes. Throughout, we illustrate implementation
using off-the-shelf open source software. We hope the reader will walk away
with implementation-level knowledge of Bayesian causal inference using both
parametric and nonparametric models. All synthetic examples and code used in
the paper are publicly available on a companion GitHub repository.
