The statistical benefits of joint multivariate analyses compared with univariate analyses are well documented, and increasingly widely appreciated. But we believe this potential nonetheless remains under-exploited. With mash we aim to provide a set of flexible and general tools to facilitate such analyses. In particular, mash is generic and adaptive. It is generic in that it can take as input any matrix of Z scores (or, preferably, a matrix of effect estimates and a matrix of corresponding standard errors) that test many effects in many conditions. These scores could come from many sources; e.g., from linear regression, generalized linear models or linear mixed models13. And mash is adaptive in that it learns correlations among effects from the data, allowing it to maximize power and precision for each setting. Consequently, mash should be widely applicable to many settings involving estimation of multivariate effects.
