ProbNum2026-Tutorial

Tutorial for the International Conference on Probabilistic Numerics 2026, built around message-passing Bayesian inference with RxInfer.

The series covers the five classic problem settings of probabilistic-numerics.org, each as a pair of notebooks — a Julia Pluto edition in julia/ and a Python Marimo edition in python/:

#	Topic	Julia (Pluto)	Python (Marimo)
1	Probabilistic linear algebra	julia/01-probabilistic-linear-algebra.jl	python/01-probabilistic-linear-algebra.py
2	Bayesian quadrature	julia/02-bayesian-quadrature.jl	python/02-bayesian-quadrature.py
3	Probabilistic optimization	julia/03-probabilistic-optimization.jl	python/03-probabilistic-optimization.py
4	Probabilistic ODE solvers	julia/04-probabilistic-ode-solvers.jl	python/04-probabilistic-ode-solvers.py
5	Probabilistic PDE solvers	julia/05-probabilistic-pde-solvers.jl	python/05-probabilistic-pde-solvers.py

Running the Pluto notebooks

julia> import Pkg; Pkg.add("Pluto")
julia> import Pluto; Pluto.run()

then open the notebook file from the Pluto welcome screen. Pluto's built-in package manager installs each notebook's dependencies (RxInfer, Plots, PlutoUI, SpecialFunctions) automatically on first open — the first run takes a few minutes.

Running the Marimo notebooks

Each python/ notebook declares its dependencies inline (PEP 723), so with uv installed a notebook is self-contained:

uvx marimo edit --sandbox python/01-probabilistic-linear-algebra.py

Or, in an environment with marimo, numpy, scipy and plotly:

marimo edit python/01-probabilistic-linear-algebra.py

The Julia editions use RxInfer for the message-passing section; since there is no Python equivalent, the Marimo editions reproduce that step with a small hand-rolled Gaussian belief-propagation routine (gaussian_bp) and check it digit-for-digit against the closed form, exactly as the Julia notebooks check against RxInfer.