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We develop Markov categories as a framework for synthetic probability and statistics, following work of Golubtsov as well as Cho and Jacobs.
Algebras of the extended probabilistic powerdomain monad
Jean Goubault-Larrecq and Xiaodong Jia · 1903
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Kantorovich problems and conditional measures depending on a parameter
Vladimir I. Bogachev and Ilya I. Malofeev · 1904
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Probabilistic mappings and Bayesian nonparametrics
Jürgen Jost, Hông Vân Lê, Duc Hoang Luu, and Tat Dat Tran · 1905
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Supplying bells and whistles in symmetric monoidal categories
Brendan Fong and David Spivak · 1908
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Robert M. Wald · 1908
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Probability, valuations, hyperspaces: three monads on Top and the support as a morphism
Tobias Fritz, Paolo Perrone, and Sharwin Rezagholi · 1910
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The zero-one laws of Kolmogorov and Hewitt–Savage in categorical probability
Tobias Fritz and Eigil Fjeldgren Rischel · 1912
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Application of the Radon-Nikodym theorem to the theory of sufficient statistics
Paul R. Halmos and L. J. Savage · 1949
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Completeness, similar regions, and unbiased estimation. I
E. L. Lehmann and Henry Scheffé · 1950
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Stochastic processes
J. L. Doob · 1953
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On statistics independent of a complete sufficient statistic
Debabrata Basu · 1955
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Sur quelques points d’algèbre homologique
Alexander Grothendieck · 1957
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Borel structures for function spaces
Robert J. Aumann · 1961
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The category of probabilistic mappings, 1962
Bill Lawvere · 1962
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Caractérisation des catégories abéliennes avec générateurs et limites inductives exactes
Nicolae Popesco and Pierre Gabriel · 1964
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The categories of mathematical statistics
N. N. Čencov · 1965
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Every standard construction is induced by a pair of adjoint functors
H. Kleisli · 1965
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Statistical isomorphism
Norman Morse and Richard Sacksteder · 1966
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A note on statistical equivalence
Richard Sacksteder · 1967
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Bases mathématiques du calcul des probabilités
Jacques Neveu · 1970
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Catégories Tannakiennes
Neantro Saavedra Rivano · 1972
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Monadic functors and convexity
Tadeusz Świrszcz · 1974
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Measurable weak sections
G. A. Edgar · 1976
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Algebraic foundation of mathematical statistics
N. N. Čencov · 1978
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Conditional independence in statistical theory
A. Philip Dawid · 1979
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Conditional independence for statistical operations
A. Philip Dawid · 1980
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Tenseurs et machines
René Guitart · 1980
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Borel spaces
K. P. S. Bhaskara Rao and B. V. Rao · 1981
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Statistical decision rules and optimal inference
N. N. Čencov · 1982
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A categorical approach to probability theory
Michèle Giry · 1982
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A class of fuzzy theories
Ernest G. Manes · 1982
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Multivariate statistics
Morris L. Eaton · 1983
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The existence of regular conditional probabilities: necessary and sufficient conditions
Arnold M. Faden · 1985
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Graphoids: a graph-based logic for reasoning about relevance relations, 1985
Judea Pearl and Azaria Paz · 1985
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Ergodic theory of random transformations
Yuri Kifer · 1986
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Cartesian bicategories. I
A. Carboni and R. F. C. Walters · 1987
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Extremal families and systems of sufficient statistics
Steffen L. Lauritzen · 1988
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Multi-information and the problem of characterization of conditional independence relations
Milan Studený · 1989
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Matrices, relations, and group representations
Aurelio Carboni · 1991
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The geometry of tensor calculus. I
André Joyal and Ross Street · 1991
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Markov invariant geometry on state manifolds
E. A. Morozova and N. N. Čencov · 1991
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Informativity in the category of linear measurement systems
Peter V. Golubtsov · 1992
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Sheaves in geometry and logic
Saunders Mac Lane and Ieke Moerdijk · 1992
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Probabilistic theories with purification
Giulio Chiribella, Mauro D’Ariano, and Paolo Perinotti · 2010
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Classical and quantum structuralism
Bob Coecke, Éric Oliver Paquette, and Dusko Pavlovic · 2010
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Combining statistical models
M. Sofia Massa and Steffen L. Lauritzen · 2010
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Selected works of Debabrata Basu
Debabrata Basu · 2011
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A survey of graphical languages for monoidal categories
P. Selinger · 2011
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Picturing classical and quantum Bayesian inference
Bob Coecke and Robert W. Spekkens · 2012
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Marek J. Druzdzel and Herbert A. Simon · 1993
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Theory of fuzzy sets as a theory of uncertainty and decision-making problems in fuzzy experiments
Peter V. Golubtsov · 1994
Cited alongside, same era.
Semantics of weakening and contraction
Bart Jacobs · 1994
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Probability and measure
Patrick Billingsley · 1995
Cited alongside, same era.
Relative informativity and a priori information in the category of linear information transformers
P. V. Golubtsov · 1995
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Spaces of valuations
Reinhold Heckmann · 1996
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Causal theories: A categorical perspective on Bayesian networks
Brendan Fong · 2012
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Selected works of E. L. Lehmann
E. L. Lehmann · 2012
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Causal categories: relativistically interacting processes
Bob Coecke and Raymond Lal · 2013
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Gavin J. Seal · 2013
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Terminality implies non-signalling
Bob Coecke · 2014
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Probability theory
Achim Klenke · 2014
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From Kleisli categories to commutative C*-algebras: Probabilistic Gelfand duality
Robert Furber and Bart Jacobs · 2015
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Codensity and the Giry monad
Tom Avery · 2016
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Cecilia Flori and Tobias Fritz · 2016
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The Algebra of Open and Interconnected Systems
Brendan Fong · 2016
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Beyond Bell’s theorem II: scenarios with arbitrary causal structure
Tobias Fritz · 2016
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A predicate/state transformer semantics for Bayesian learning
Bart Jacobs and Fabio Zanasi · 2016
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Monoidal categories with projections, 2016
Tom Leinster · 2016
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Monoidal categories with projections, 2016
Tom Leinster · 2016
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Categorical Duality in Probability and Quantum Foundations
Robert Furber · 2017
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A convenient category for higher-order probability theory
Chris Heunen, Ohad Kammar, Sam Staton, and Hongseok Yang · 2017
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Functional distribution monads in functional-analytic contexts
Rory B. B. Lucyshyn-Wright · 2017
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Denotational validation of higher-order Bayesian inference
Adam Ścibior, Ohad Kammar, Matthijs Vákár, Sam Staton, Hongseok Yang, Yufei Cai, Klaus Ostermann, Sean K. Moss, Chris Heunen, and Zoubin Ghahramani · 2017
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Probability sheaves and the Giry monad, 2017
Alex Simpson · 2017
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An algebraic theory of Markov processes
Giorgio Bacci, Radu Mardare, Prakash Panangaden, and Gordon Plotkin · 2018
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Oscar Cunningham and Chris Heunen · 2018
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Borel kernels and their approximation, categorically
Fredrik Dahlqvist, Alexandra Silva, Vincent Danos, and Ilias Garnier · 2018
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Bimonoidal structure of probability monads
Tobias Fritz and Paolo Perrone · 2018
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Categorical Probability and Stochastic Dominance in Metric Spaces
Paolo Perrone · 2018
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Category-theoretic structure for independence and conditional independence
Alex Simpson · 2018
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The beta-Bernoulli process and algebraic effects
Sam Staton, Dario Stein, Hongseok Yang, Nathanael L. Ackerman, Cameron E. Freer, and Daniel M. Roy · 2018
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Disintegration and Bayesian inversion via string diagrams
Kenta Cho and Bart Jacobs · 2019
Closest in time.
Brendan Fong and David Spivak · 2019
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Structured probabilistic reasoning, 2019
Bart Jacobs · 2019
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Categories for Quantum Theory: An Introduction
Chris Heunen and Jamie Vicary · 2020
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