Biomarker measurements such as blood lead concentrations and hair mercury concentrations are often used to make inferences about previous rates of toxicant intake. Exposure rates are typically estimated from these measurements using a "steady state" assumption. However, toxicant exposures are typically episodic and vary in magnitude over time, violating the steady state model. Treating each biomarker measurement as linear combination of previous daily exposure magnitudes is a simple but reasonable toxicokinetic model for many situations. When exposure patterns are intermittent each day's exposure magnitude is described by a mixture distribution with a probability mass at zero and some continuous density over a range of positive values, and each biomarker measurement can be represented as a convolution of differentially weighted mixture distributions across the entire exposure history. Likelihood functions are difficult to obtain in this setting, but generalized estimating equations can be applied successfully. Bayesian solutions are also available using Markov Chain Monte Carlo methods. I will present probability models for this setting, describe the frequentist and Bayesian approaches, and demonstrate the methods using blood mercury measurements.