21 citations · 42 across the 11 of their papers we have counts for
12 papers
The algebras of the Giry monad
Kirk Sturtz
The algebras of the Giry monad on the category of measurable spaces are derived. These algebras, which we denote as , are measurable convex spaces satisfying t…
Giry algebras for standard measurable spaces
Kirk Sturtz
The notion of "super convex spaces" generalizes the idea of convex spaces by replacing finite affine sums with countable affine sums. Using this notion permits a very elegant appro…
The existence and utility of Giry algebras in probability theory
Kirk Sturtz
Giry algebras are barycenters maps, which are coequalizers of contractible coequalizer pairs (like any algebras), and their existence, in general, requires the measurable space be…
Characterizing Giry-algebras as coseparable super convex spaces
Kirk Sturtz
We investigate the Eilenberg-Moore algebras for the Giry monad defined on the category of measurable spaces using super convex spaces. The category of super convex spaces has a sub…
Erratum and Addendum: The factorization of the Giry monad
K. Sturtz
The category of super convex spaces, a proper subcategory of convex spaces, possesses the property that it has a codense subcategory. This codense subcategory allows for an element…
The factorization of the Giry monad
Kirk Sturtz
We construct a factorization of the Giry monad through the category of convex spaces, and show that, provided that no measurable cardinals exist, probability measures can be viewed…
The equivalence between the categories of Giry-algebras and convex spaces
Kirk Sturtz
A duality between the category of convex spaces and measurable spaces arises from the existence of the unit interval, which is an object in both these categories. The full subcateg…
Bayesian Inference using the Symmetric Monoidal Closed Category Structure
Kirk Sturtz
Using the symmetric monoidal closed category structure of the category of measurable spaces, in conjunction with the Giry monad which we show is a strong monad, we analyze Bayesian…
Categorical Probability Theory
Kirk Sturtz
We present a categorical viewpoint of probability measures by showing that a probability measure can be viewed as a weakly averaging affine measurable functional taking values in t…
Bayesian machine learning via category theory
Jared Culbertson, Kirk Sturtz
From the Bayesian perspective, the category of conditional probabilities (a variant of the Kleisli category of the Giry monad, whose objects are measurable spaces and arrows are Ma…
Quantifiers as Adjoint in Probability
Kirk Sturtz
Using the Kleisi category of the Giry monad the deterministic existential and universal quantifiers are generalized to incorporate nondeterminism. These probabilistic quantifiers a…
A categorical foundation for Bayesian probability
Jared Culbertson, Kirk Sturtz
Given two measurable spaces and with countably generated -algebras, a perfect prior probability measure on and a sampling distribution , th…