The space‐time decision theory of acoustic fields is developed from an examination of the conditions necessary for uniform and nonuniform spatial sampling. Basic transformation relations between spatial sampling and direction sampling are given. From this sampling theory, the monochromatic space likelihood ratio, the broadband space likelihood ratio, and the general space‐time likelihood ratio are developed. Examples of the general theory include the point, blurred point, and ring signal fields and several (spatially) statistical noise fields. Superdirectivity and the spatial matched filter are related to the space‐time likelihood ratio, and the paper concludes with a brief discussion of necessary and complete information inherent in an acoustic field.