Related papers: Bayesian nonparametric statistics, St-Flour lectur…
These are the lecture notes for a short course on geometric quantization given by the author at the XVIII Modave Summer School on Mathematical Physics, Sep 5 - Sep 9.
The usual nonparametric approach to spectral analysis is revisited within the regularization framework. Both usual and windowed periodograms are obtained as the squared modulus of the minimizer of regularized least squares criteria. Then,…
A substantial school in the philosophy of science identifies Bayesian inference with inductive inference and even rationality as such, and seems to be strengthened by the rise and practical success of Bayesian statistics. We argue that the…
We consider heteroscedastic nonparametric regression models, when both the mean function and variance function are unknown and to be estimated with nonparametric approaches. We derive convergence rates of posterior distributions for this…
The present overview and gentle introduction to Grassmannian calculus and some of its applications to probability collects the notes of a mini-course given by the authors at the Brazilian School of Probability, August 5-9, 2024, in…
Given an observed sample from a population of individuals belonging to species, "species-sampling" problems (SSPs) call for estimating some features of the unknown species composition of additional unobservable samples from the same…
This is a guide to the construction of nonlinear number fields, which includes new points not found in our earlier article ``Geometric Galois theory, nonlinear number fields and a Galois group interpretation of the idele class group''.
In this paper we consider the current status continuous mark model where, if the event takes place before an inspection time $T$ a "continuous mark" variable is observed as well. A Bayesian nonparametric method is introduced for estimating…
Subject of this paper is the simplification of Markov chain Monte Carlo sampling as used in Bayesian statistical inference by means of normalising flows, a machine learning method which is able to construct an invertible and differentiable…
These are the notes on two-dimensional conformal field theory, based on a lecture course for graduate math students, given by P.M. in fall 2022 at the University of Notre Dame. These notes are intended to be substantially reworked and…
Rare variants are hypothesized to be largely responsible for heritability and susceptibility to disease in humans. So rare variants association studies hold promise for understanding disease. Conversely though, the rareness of the variants…
It has historically been a challenge to perform Bayesian inference in a design-based survey context. The present paper develops a Bayesian model for sampling inference in the presence of inverse-probability weights. We use a hierarchical…
Due to their great flexibility, nonparametric Bayes methods have proven to be a valuable tool for discovering complicated patterns in data. The term "nonparametric Bayes" suggests that these methods inherit model-free operating…
This is a lecture notes for a mini-course in Department of Mathematics, Ghent University, 14 Mar.-25 Mar. 2023.
This paper, which is Part 1 of a two-part paper series, considers a simulation-based inference with learned summary statistics, in which such a learned summary statistic serves as an empirical-likelihood with ameliorative effects in the…
There have been extensive developments recently in modern nonparametric inference and modeling. Nonparametric and semi-parametric methods are especially useful with large amounts of data that are now routinely collected in many areas of…
The nonlinear Fourier transform discussed in these notes is the map from the potential of a one dimensional discrete Dirac operator to the transmission and reflection coefficients thereof. Emphasis is on this being a nonlinear variant of…
This survey paper, written in spanish, is an extended version of lecture notes for a mini-course taught at the 2022 Summer School in Geometric Group Theory, which took place in the Centro de Ciencias Matem\'aticas in Morelia, Mexico in July…
Lecture notes for 8 lectures on the `Physics of Lyman alpha Radiative Transfer', given at the 46th Saas-Fee winter school held in Les Diablerets, Switzerland on March 13-19 2016. These lectures aimed at offering basic insights into Lyman…
This paper comprises the written version of the lectures on string theory delivered at the 31st British Universities Summer School on Theoretical Elementary Particle Physics which was held in Manchester, England, August 28 - September 12…