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 …

The notions of disintegration and Bayesian inversion are fundamental in conditional
probability theory. They produce channels, as conditional probabilities, from a joint state, or …

We show that a measure-based denotational semantics for probabilistic programming is
commutative. The idea underlying probabilistic programming languages (Anglican, Church …

Extracting causal relationships from observed correlations is a growing area in probabilistic
reasoning, originating with the seminal work of Pearl and others from the early 1990s. This …

Effectuses have recently been introduced as categorical models for quantum computation,
with probabilistic and Boolean (classical) computation as special cases. These …

The framework of causal models provides a principled approach to causal reasoning,
applied today across many scientific domains. Here we present this framework in the …

This chapter offers an accessible introduction to the channel-based approach to Bayesian
probability theory. This framework rests on algebraic and logical foundations, inspired by the …

Bayesian networks are graphical first-order probabilistic models that allow for a compact
representation of large probability distributions, and for efficient inference, both exact and …

We develop an algebraic framework for sequential data assimilation of partially observed
dynamical systems. In this framework, Bayesian data assimilation is embedded in a …

Extracting causal relationships from observed correlations is a growing area in probabilistic
reasoning, originating with the seminal work of Pearl and others from the early 1990s. This …