Stochastic lambda calculus and monads of probability distributions
POPL '02 Proceedings of the 29th ACM SIGPLAN-SIGACT symposium on Principles of programming languages
Evaluating Derivatives: Principles and Techniques of Algorithmic Differentiation
Evaluating Derivatives: Principles and Techniques of Algorithmic Differentiation
Embedded Probabilistic Programming
DSL '09 Proceedings of the IFIP TC 2 Working Conference on Domain-Specific Languages
Measure transformer semantics for Bayesian machine learning
ESOP'11/ETAPS'11 Proceedings of the 20th European conference on Programming languages and systems: part of the joint European conferences on theory and practice of software
A type theory for probability density functions
POPL '12 Proceedings of the 39th annual ACM SIGPLAN-SIGACT symposium on Principles of programming languages
A model-learner pattern for bayesian reasoning
POPL '13 Proceedings of the 40th annual ACM SIGPLAN-SIGACT symposium on Principles of programming languages
A model-learner pattern for bayesian reasoning
POPL '13 Proceedings of the 40th annual ACM SIGPLAN-SIGACT symposium on Principles of programming languages
Tabular: a schema-driven probabilistic programming language
Proceedings of the 41st ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages
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The probability density function of a probability distribution is a fundamental concept in probability theory and a key ingredient in various widely used machine learning methods. However, the necessary framework for compiling probabilistic functional programs to density functions has only recently been developed. In this work, we present a density compiler for a probabilistic language with discrete and continuous distributions, and discrete observations, and provide a proof of its soundness. The compiler greatly reduces the development effort of domain experts, which we demonstrate by solving inference problems from various scientific applications, such as modelling the global carbon cycle, using a standard Markov chain Monte Carlo framework.