We compute explicit bounds in the Gaussian approximation of functionals of infinite Rademacher sequences. Our tools involve Stein’s method, as well as the use of appropriate discrete Malliavin operators. Although our approach does not require the classical use of exchangeable pairs, we employ a chaos expansion in order to construct an explicit exchangeable pair vector for any random variable wh...

This paper presents a categorical account of conditional probability, covering both the classical and the quantum case. Classical conditional probabilities are expressed as a certain “triangle-fill-in” condition, connecting marginal and joint probabilities, in the Kleisli category of the distribution monad. The conditional probabilities are induced by a map together with a predicate (the condit...

Experiments on generating compilers by specializing specializers with respect to interpreters have shown that the compilers thus obtained have a natural structure only if the specializer does variable splitting. Variable splitting can result in a residual program using several variables to represent the values of a single variable of the original program. In the case of functional programming v...

A current limitation for imaging of brain function is the potential confound of anatomical differences or registration error, which may manifest via apparent functional "activation" for between-subject analyses. With respect to functional activations, underlying tissue mismatches can be regarded as a nuisance variable. We propose adding the probability of gray matter at a given voxel as a covar...

Background: Different patterns of gender-based relationships between attitude toward smoking and self-esteem with smoking behavior have reported. However, such associations may be much more complex than a simply supposed linear relationship. We aimed to propose a method of providing hand details on the total and gender-based scenarios of the relationships between attitude toward smoking and sel...

The nu-calculus of Pitts and Stark was introduced as a paradigmatic functional language with a very basic local-state effect: references of unit type. These were called names, and the motto of the new language went as follows. “Names are created with local scope, can be tested for equality, and are passed around via function application, but that is all.” Because of this limited framework, the ...

We prove a uniformly computable version of de Finetti’s theorem on exchangeable sequences of real random variables. As a consequence, exchangeable stochastic processes in probabilistic functional programming languages can be automatically rewritten as procedures that do not modify non-local state. Along the way, we prove that a distribution on the unit interval is computable if and only if its ...