One of the principal challenges in epidemiological modeling is to parameterize models with realistic estimates for transmission rates in order to analyze strategies for control and to predict disease outcomes. Using a combination of replicated experiments, Bayesian statistical inference, and stochastic modeling, we introduce and illustrate a strategy to estimate transmission parameters for the spread of infection through a two-phase mosaic, comprising favorable and unfavorable hosts. We focus on epidemics with local dispersal and formulate a spatially explicit, stochastic set of transition probabilities using a percolation paradigm for a susceptibleinfected (S-I) epidemiological model. The S-I percolation model is further generalized to allow for multiple sources of infection including external inoculum and host-to-host infection. We fit the model using Bayesian inference and Markov chain Monte Carlo simulation to successive snapshots of damping-off disease spreading through replicated plant populations that differ in relative proportions of favorable and unfavorable hosts and with timevarying rates of transmission. Epidemiologically plausible parametric forms for these transmission rates are compared by using the deviance information criterion. Our results show that there are four transmission rates for a two-phase system, corresponding to each combination of infected donor and susceptible recipient. Knowing the number and magnitudes of the transmission rates allows the dominant pathways for transmission in a heterogeneous population to be identified. Finally, we show how failure to allow for multiple transmission rates can overestimate or underestimate the rate of spread of epidemics in heterogeneous environments, which could lead to marked failure or inefficiency of control strategies.Bayesian inference ͉ crop mixture ͉ susceptible-infected (S-I) epidemic ͉ spatially structured host populations ͉ Markov chain Monte Carlo O ne of the principal challenges in epidemiological modeling is to parameterize models with realistic estimates for transmission rates in order to analyze strategies for control and to predict disease outcomes. Although the durations of infectious and latent periods often can be estimated from observation of individuals challenged with inoculum, the probabilities and the associated rates for transmission of infection between infected and susceptible individuals are notoriously difficult to measure or estimate (1, 2). The problem is especially acute in spatially structured, heterogeneous host populations, in which hosts differ in susceptibility and infectivity. The magnitudes of the transmission rates typically change over space, according to the nature of the infected donor and the susceptible recipient, and also may change over time (2). In human diseases, infectivity and susceptibility may be affected by genetic, physiological, or social differences (3-5) as well as by immune and vaccination history. Examples also occur in animal epidemiology, with transmission of infection of a common path...