  Synthetic data is a promising approach to privacy protection in many
contexts. A Bayesian synthesis model, also known as a synthesizer, simulates
synthetic values of sensitive variables from their posterior predictive
distributions. The resulting synthetic data can then be released in place of
the confidential data. An important evaluation prior to synthetic data release
is its level of privacy protection, which is often in the form of disclosure
risks evaluation. Attribute disclosure, referring to an intruder correctly
inferring the confidential values of synthetic records, is one type of
disclosure that is challenging to be computationally evaluated. In this paper,
we review and discuss in detail some Bayesian estimation approaches to
attribute disclosure risks evaluation, with examples of commonly-used Bayesian
synthesizers. We create the $\texttt{AttributeRiskCalculation}$ R package to
facilitate its implementation, and demonstrate its functionality with examples
of evaluating attribute disclosure risks in synthetic samples of the Consumer
Expenditure Surveys.
