Many computational systems need to deal with various forms of imprecision and uncertainty in their data; it is also the case that many systems, especially mobile and distributed systems, must be able to trade off the precision of their data and operations against the cost of performing those operations. Unfortunately, for many applications, trying to make these tradeoffs severely complicates the program, because there does not yet exist a programming model that gives the programmer the ability to easily describe the relevant tradeoffs between precision and cost of operations or to express in an algorithm what tradeoffs are appropriate under what circumstances. This paper lays a solid foundation for exploring

There has been great interest in creating probabilistic programming languages to simplify the coding of statistical tasks; however, there still does not exist a formal language that simultaneously provides (1) continuous probability distributions, (2) the ability to naturally express custom probabilistic models, and (3) probability density functions (PDFs). This collection of features is necessary for mechanizing fundamental statistical techniques. We formalize the first probabilistic language that exhibits these features, and it serves as a foundational framework for extending the ideas to more general languages. Particularly novel are our type system for absolutely continuous (AC) distributions (those which permit PDFs) and our PDF calculation procedure, which calculates PDFs for a large class of AC distributions. Our formalization paves the way toward the rigorous encoding of powerful statistical reformulations.

Abstract not found