Related papers: Bayesian nonparametric statistics, St-Flour lectur…
In this lecture notes we try to familiarize the audience with the theory of Bernoulli polynomials; we study their properties, and we give, with proofs and references, some of the most relevant results related to them. Several applications…
Bootstrapping and other resampling methods are increasingly appearing in the textbooks and curricula of courses that introduce undergraduate students to statistical methods. In order to teach the bootstrap well, students and instructors…
These notes gather recent results on robust statistical learning theory. The goal is to stress the main principles underlying the construction and theoretical analysis of these estimators rather than provide an exhaustive account on this…
This manuscript contains the lecture notes of the short courses given by one of us (F.Z.) at the summer school "Fundamental Problems in Statistical Physics XV", held in Brunico, Italy, in July 2021, and, just before that, at the summer…
This is the writeup of lectures delivered in Asian Pacific introductory school on superstring and the related topics in Beijing (2006) and the expanded version of these lectures in the 3rd summer school on strings, fields and holography in…
We should cease teaching frequentist statistics to undergraduates and switch to Bayes. Doing so will reduce the amount of confusion and over-certainty rife among users of statistics.
The regression discontinuity (RD) design is a popular approach to causal inference in non-randomized studies. This is because it can be used to identify and estimate causal effects under mild conditions. Specifically, for each subject, the…
Advances in statistical learning theory have resulted in a multitude of different designs of learning machines. But which ones are implemented by brains and other biological information processors? We analyze how various abstract Bayesian…
A large amount of observational data has been accumulated in various fields in recent times, and there is a growing need to estimate the generating processes of these data. A linear non-Gaussian acyclic model (LiNGAM) based on the…
For statistics courses at all levels, teaching and learning online poses challenges in different aspects. Particular online challenges include how to effectively and interactively conduct exploratory data analyses, how to incorporate…
These notes were originally prepared as additional material for the lessons I have given at the summer school Gamma-ray Astrophysics and Multifrequency: Data analysis and astroparticle problems, organized by the Department of Physics of the…
These lecture notes introduce some topics of classical statistical physics, particularly those that are relevant for neural networks and deep learning. Statistical physics is treated as a branch of probability theory or statistics, with the…
The paper addresses general aspects of experimental data analysis, dealing with the separation of ``signal vs. background''. It consists of two parts. Part I is a tutorial on statistical event classification, Bayesian inference, and test…
We give an abridged account of a continued string of studies in condensed matter physics and in complex systems that span five decades. We provide links to access abstracts and full texts of a selected list of publications. The studies were…
Bayesian statistics is concerned with conducting posterior inference for the unknown quantities in a given statistical model. Conventional Bayesian inference requires the specification of a probabilistic model for the observed data, and the…
This thesis focuses on the applications of mathematical tools and concepts brought from nonequilibrium statistical physics to the modeling of ecological problems. The first part provides a short introduction where the theoretical concepts…
These notes are based on lectures at the PSSCMP/PiTP summer school that was held at Princeton University and the Institute for Advanced Study in July, 2015. They are devoted largely to topological phases of matter that can be understood in…
This paper demonstrates the advantages of sharing information about unknown features of covariates across multiple model components in various nonparametric regression problems including multivariate, heteroscedastic, and semi-continuous…
In this introductory talk we will establish connections between the statistical analysis of galaxy clustering in cosmology and recent work in mainstream spatial statistics. The lecture will review the methods of spatial statistics used by…
Building on ideas from Castillo and Nickl [Ann. Statist. 41 (2013) 1999-2028], a method is provided to study nonparametric Bayesian posterior convergence rates when "strong" measures of distances, such as the sup-norm, are considered. In…