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Visual inspection is a common approach for collecting data over time on transportation infrastructure. However, the evaluation method in visual inspections mainly depends on a subjective metric, as well as the experience of the individual performing the task. State-space models (SSMs) enable quantifying the uncertainty associated with the inspectors when modeling the degradation of bridges based on visual inspection data. The main limitation in the existing SSM is the assumption that each inspector is unbiased, due to the high number of inspectors, which makes the problem computationally demanding for optimization approaches and prohibitive for sampling-based Bayesian estimation methods. The contributions of this paper are to enable the estimation of the inspector bias and formulate a new analytical framework that allows the estimation of the inspectors' biases and variances using Bayesian updating. The performance of the analytical framework is verified using synthetic data where the true values are known, and validated using data from the network of bridges in Quebec province, Canada. The analyses have shown that the analytical framework has enabled reducing the computational time required for estimating the inspectors' uncertainty and is adequate for the estimation of the inspectors' uncertainty while maintaining a comparable performance to the gradient-based framework. [ABSTRACT FROM AUTHOR]