"The validity of a causal inference hinges on a research design with both strong internal validity and strong external validity (Shadish et al. 2002). Unfortunately, such research is rare so that causality is typically inferred through a small-scale randomized experiment or a large-scale observational study (Schneider et al. 2007). In light of this gap, the robustness indices of causal inferences have been proposed by Frank et al. (2013) to measure the robustness of causal inference by quantifying the proportion of the observed sample that needs to be replaced with unfavorable unobserved cases. Drawing on the Bayesian discussion in Frank & Min (2007), this dissertation purposes developing the Bayesian framework of the robustness indices of causal inferences for causal research with either limited internal validity or limited external validity. This dissertation has two chapters: The first chapter lays the foundation of the Bayesian paradigm of robustness indices by formally defining prior as distribution built on an unobserved sample. For a particular family of prior and likelihood distributions, the posterior can be interpreted as distribution built on an ideal sample. The Bayesian paradigm of robustness indices of causal inferences focuses on the relationship between the posterior probability of invalidating an inference and the unobserved sample statistics and the central task is to locate the threshold of an unobserved sample statistics with regard to a given value of the posterior probability of invalidating an inference. Considering the first chapter targets the simple group-mean-difference estimator only, the second chapter extends the Bayesian paradigm of robustness indices to regression models. This dissertation promotes the scientific discourse of causality and critical thinking by linking the probability of invalidating an inference to detailed thought experiments characterized by the thresholds of sufficient statistics pertaining to an unobserved sample."--Pages ii-iii.
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