Traffic simulation software is used by transportation researchers and engineers to design and evaluate changes to roadways. These simulators are driven by models of microscopic driver behavior from which macroscopic measures like flow and congestion can be derived. Many models are designed for a subset of possible traffic scenarios and roadway configurations, while others have no explicit constraints on their application. Work zones (WZs) are one scenario for which no model to date has reproduced realistic driving behavior. This makes it difficult to optimize for safety and other metrics when designing a WZ. The Federal Highway Administration commissioned the USDOT Volpe Center to develop a car-following (CF) model for use in microscopic simulators that can capture and reproduce driver behavior accurately within and outside of WZs. Volpe also performed a naturalistic driving study to collect telematics data from vehicles driven on roads with WZs for use in model calibration. During model development, Volpe researchers observed difficulties in calibrating their model, leaving them to question whether there existed flaws in their model, in the data, or in the procedure used to calibrate the model using the data. In this thesis, I use Bayesian methods for data analysis and parameter estimation to explore and, where possible, address these questions. First, I use Bayesian inference to measure the sufficiency of the size of the data set. Second, I compare the procedure and results of the genetic algorithm based calibration performed by the Volpe researchers with those of Bayesian calibration. Third, I explore the benefits of modeling CF hierarchically. Finally, I apply what was learned in the first three phases using an established CF model, Wiedemann 99, to the probabilistic modeling of the Volpe model. Validation is performed using information criteria as an estimate of predictive accuracy.