Related papers: The Geometry of Bayesian Programming

Optimal design facilitates intelligent data collection. In this paper, we introduce a fully Bayesian design approach for spatial processes with complex covariance structures, like those typically exhibited in natural ecosystems. Coordinate…

In the study of natural and artificial complex systems, responses that are not completely determined by the considered decision variables are commonly modelled probabilistically, resulting in response distributions varying across decision…

Bayesian learning is built on an assumption that the model space contains a true reflection of the data generating mechanism. This assumption is problematic, particularly in complex data environments. Here we present a Bayesian…

Realizing the full potential of interconnecting the large amounts of data created in physics experiments, phenomenological models and theory simulations requires robust tools for statistical inference. Here I review a particularly promising…

We introduce a graphical framework for Bayesian inference that is sufficiently general to accommodate not just the standard case but also recent proposals for a theory of quantum Bayesian inference wherein one considers density operators…

Bayesian learning using Gaussian processes provides a foundational framework for making decisions in a manner that balances what is known with what could be learned by gathering data. In this dissertation, we develop techniques for…

To support the understanding of declarative probabilistic programming languages, we introduce a lambda-calculus with a fair binary probabilistic choice that chooses between its arguments with equal probability. The reduction strategy of the…

In typical non-idempotent intersection type systems, proof normalization is not confluent. In this paper we introduce a confluent non-idempotent intersection type system for the lambda-calculus. Typing derivations are presented using proof…

Generalized metrics, arising from Lawvere's view of metric spaces as enriched categories, have been widely applied in denotational semantics as a way to measure to which extent two programs behave in a similar, although non equivalent, way.…

We apply a linear Bayesian model to seismic tomography, a high-dimensional inverse problem in geophysics. The objective is to estimate the three-dimensional structure of the earth's interior from data measured at its surface. Since this…

Bayesian quantum estimation provides a robust framework for quantum technologies, especially in scenarios with limited data and minimal prior information. Yet, its application to continuous-variable Gaussian systems has remained limited and…

We show that lambda calculus is a computation model which can step by step simulate any sequential deterministic algorithm for any computable function over integers or words or any datatype. More formally, given an algorithm above a family…

Decomposable models and Bayesian networks can be defined as sequences of oligo-dimensional probability measures connected with operators of composition. The preliminary results suggest that the probabilistic models allowing for effective…

The Bayesian approach to data analysis provides a powerful way to handle uncertainty in all observations, model parameters, and model structure using probability theory. Probabilistic programming languages make it easier to specify and fit…

With a view towards models of quantum computation and/or the interpretation of linear logic, we define a functional language where all functions are linear operators by construction. A small step operational semantic (and hence an…

A multivariate distribution can be described by a triangular transport map from the target distribution to a simple reference distribution. We propose Bayesian nonparametric inference on the transport map by modeling its components using…

Lambda calculus is the basis of functional programming and higher order proof assistants. However, little is known about combinatorial properties of lambda terms, in particular, about their asymptotic distribution and random generation.…

Mathematical models implemented on a computer have become the driving force behind the acceleration of the cycle of scientific processes. This is because computer models are typically much faster and economical to run than physical…

We consider discrete nonparametric priors which induce Gibbs-type exchangeable random partitions and investigate their posterior behavior in detail. In particular, we deduce conditional distributions and the corresponding Bayesian…

In robotics, simulation has the potential to reduce design time and costs, and lead to a more robust engineered solution and a safer development process. However, the use of simulators is predicated on the availability of good models. This…