@article{jacobs_formal_2017,
title = {A {Formal} {Semantics} of {Influence} in {Bayesian} {Reasoning}},
url = {http://drops.dagstuhl.de/opus/volltexte/2017/8089/},
doi = {10/ggdgbc},
abstract = {This paper proposes a formal deﬁnition of inﬂuence in Bayesian reasoning, based on the notions of state (as probability distribution), predicate, validity and conditioning. Our approach highlights how conditioning a joint entwined/entangled state with a predicate on one of its components has ‘crossover’ inﬂuence on the other components. We use the total variation metric on probability distributions to quantitatively measure such inﬂuence. These insights are applied to give a rigorous explanation of the fundamental concept of d-separation in Bayesian networks.},
language = {en},
urldate = {2019-11-24},
journal = {Schloss Dagstuhl - Leibniz-Zentrum fuer Informatik GmbH, Wadern/Saarbruecken, Germany},
author = {Jacobs, Bart and Zanasi, Fabio},
year = {2017},
note = {ZSCC: 0000012},
keywords = {Bayesianism, Categorical probability theory, Programming language theory, Semantics}
}
@article{jacobs_predicate/state_2016,
series = {The {Thirty}-second {Conference} on the {Mathematical} {Foundations} of {Programming} {Semantics} ({MFPS} {XXXII})},
title = {A {Predicate}/{State} {Transformer} {Semantics} for {Bayesian} {Learning}},
volume = {325},
issn = {1571-0661},
url = {http://www.sciencedirect.com/science/article/pii/S1571066116300883},
doi = {10/ggdgbb},
abstract = {This paper establishes a link between Bayesian inference (learning) and predicate and state transformer operations from programming semantics and logic. Specifically, a very general definition of backward inference is given via first applying a predicate transformer and then conditioning. Analogously, forward inference involves first conditioning and then applying a state transformer. These definitions are illustrated in many examples in discrete and continuous probability theory and also in quantum theory.},
language = {en},
urldate = {2019-11-24},
journal = {Electronic Notes in Theoretical Computer Science},
author = {Jacobs, Bart and Zanasi, Fabio},
month = oct,
year = {2016},
note = {ZSCC: 0000030},
keywords = {Bayesianism, Categorical ML, Categorical probability theory, Effectus theory, Programming language theory, Semantics},
pages = {185--200}
}
@article{varacca_distributing_2006,
title = {Distributing probability over non-determinism},
volume = {16},
issn = {0960-1295, 1469-8072},
url = {http://www.journals.cambridge.org/abstract_S0960129505005074},
doi = {10/czs9sx},
language = {en},
number = {01},
urldate = {2019-11-26},
journal = {Mathematical Structures in Computer Science},
author = {Varacca, Daniele and Winskel, Glynn},
month = feb,
year = {2006},
note = {ZSCC: 0000108},
keywords = {Categorical probability theory, Denotational semantics, Programming language theory},
pages = {87}
}