We study the algorithmic process of human statistical inference using a rational process model based on Markov chain Monte Carlo. In the computationally rational limit of a limited number of samples, this model successfully replicates several biases found in human probabilistic judgments that involve statistical inference over a large space of possibilities. The successful modeling of these biases can then be leveraged by intentionally biasing some estimates and gauging their effects on other estimates as a proxy for studying reuse of computation or amortization. Future research includes probing the interaction between these sampling or simulation based approximations, and rule or heuristic based strategies in how humans make inferences.