A synthetic approach to Markov kernels, conditional independence, and theorems on sufficient statistics

@article{Fritz2019ASA,
  title={A synthetic approach to Markov kernels, conditional independence, and theorems on sufficient statistics},
  author={T. Fritz},
  journal={ArXiv},
  year={2019},
  volume={abs/1908.07021}
}
  • T. Fritz
  • Published 2019
  • Mathematics, Computer Science
  • ArXiv
  • Abstract We develop Markov categories as a framework for synthetic probability and statistics, following work of Golubtsov as well as Cho and Jacobs. This means that we treat the following concepts in purely abstract categorical terms: conditioning and disintegration; various versions of conditional independence and its standard properties; conditional products; almost surely; sufficient statistics; versions of theorems on sufficient statistics due to Fisher–Neyman, Basu, and Bahadur. Besides… CONTINUE READING
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    References

    SHOWING 1-10 OF 158 REFERENCES
    Probabilistic Mappings and Bayesian Nonparametrics
    • 4
    • PDF
    On the Computability of Conditional Probability
    • 14
    • PDF
    Conditional products: An alternative approach to conditional independence
    • 21
    • Highly Influential
    • PDF
    Borel Kernels and their Approximation, Categorically
    • 3
    • PDF
    Probabilistic conditional independence structures
    • M. Studený
    • Mathematics, Computer Science
    • Information science and statistics
    • 2005
    • 196
    Probability theory - a comprehensive course
    • A. Klenke
    • Computer Science, Mathematics
    • Universitext
    • 2008
    • 495
    A Categorical Approach to Probability Theory
    • 284
    • Highly Influential
    An Algebraic Theory of Markov Processes
    • 7
    • Highly Influential
    • PDF