In this article, we develop statistical models to predict the number and geographic distribution of fires caused by earthquake ground motion and tsunami inundation in Japan. Using new, uniquely large, and consistent data sets from the 2011 Tōhoku earthquake and tsunami, we fitted three types of models—generalized linear models (GLMs), generalized additive models (GAMs), and boosted regression trees (BRTs). This is the first time the latter two have been used in this application. A simple conceptual framework guided identification of candidate covariates. Models were then compared based on their out-of-sample predictive power, goodness of fit to the data, ease of implementation, and relative importance of the framework concepts. For the ground motion data set, we recommend a Poisson GAM; for the tsunami data set, a negative binomial (NB) GLM or NB GAM. The best models generate out-of-sample predictions of the total number of ignitions in the region within one or two. Prefecture-level prediction errors average approximately three. All models demonstrate predictive power far superior to four from the literature that were also tested. A nonlinear relationship is apparent between ignitions and ground motion, so for GLMs, which assume a linear response-covariate relationship, instrumental intensity was the preferred ground motion covariate because it captures part of that nonlinearity. Measures of commercial exposure were preferred over measures of residential exposure for both ground motion and tsunami ignition models. This may vary in other regions, but nevertheless highlights the value of testing alternative measures for each concept. Models with the best predictive power included two or three covariates.