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Short courses

Short course lecturers and titles

  • Large deviations and sum rules for orthogonal polynomials by Barry Simon, Caltech, USA​
  • Introduction to causal inference by Michael Hudgens, University of North Carolina, USA
  • Introduction to Malliavin calculus and its applications by David Nualart, University of Kansas, USA
  • Bayesian hierarchical models by Gavin Shaddick, University of Bath, UK
  • Big data by Jean-Michel Loubes, Université Toulouse III – Paul Sabatier, France
  • Introduction to Stochastic Models in Finance, by Daniel Hernández Hernández, CIMAT, México

 

Detailed descriptions of the short courses

  • Large deviations and sum rules for orthogonal polynomials

Summary: This course will have four lectures on the subject of the title:

  • Lecture 1: OPRL, OPUC and Sum Rules: I will present the formalism of orthogonal polynomials on the unit circle (OPUC) and real line (OPRL) and explain the Szego-Verblunsky sum rule for OPRL and the Killip-Simon sum rule for OPRL.
  • Lecture 2: Meromorphic Herglotz Functions and Proof of KS Sum Rule: I’ll explain the original proof of the KS sum rule using the Poisson-Jensen formula of complex function theory.
  • Lecture 3: The Theory of Large Deviations: A quick mini-course in the theory of large deviations.
  • Lecture 4: GNR Proof of Sum Rules: The proofs of Gamboa-Nagel-Rouault of the SV (and KS) sum rule using large deviations for certain random matrix models.
  • Introduction to Causal Inference

Summary: This short course will provide an introduction to drawing inference about causal effects using the potential outcomes/counterfactual framework. Causal inference will be discussed in the context of randomized experiments and observational studies. Common approaches to adjusting for confounding, such as inverse probability weighting, will be described. The statistical methods discussed will be illustrated using real data examples, with analyses carried out in R and/or SAS.

A website for the short course has been setup. You can take a look at this link. The slides are password protected so you should ask for it to the lecturer.

  • Introduction to Malliavin calculus and its applications

Resumen: El cálculo de Malliavin es un cálculo estocástico de variaciones respecto de las trayectorias del movimiento Browniano, que fue introducido by Paul Malliavin en la década de los setenta con el propósito de demostrar el teorema de hipoelipticidad de Hörmander mediante métodos de cáculo de probabilidades.  En este curso introduciremos los operadores diferenciales del cáculo de Malliavin: la derivada y la divergencia,  y demostraremos la relación de dualidad que permite introducir los espacios de Sobolev correspondientes. Demostraremos como estos operadores actúan sobre el caos de Wiener y estudiaremos el semigrupo de Ornstein-Uhlenbeck y su generador infinitesimal.

En la segunda parte del curso analizaremos diversas aplicaciones del cálculo de Malliavin. Concretamente, veremos como el cálculo de Malliavin juega un papel fundamental en los siguientes problemas:

  1. Representación integral estocástica de variables aleatorias mediante la fómula de Clark-Ocone. Esta fórmula ha dado lugar a una demostración simple de un resultado de convergencia en ley para el tiempo local del movimiento browniano.
  2. Existencia y regularidad de densidades de funcionales del movimiento Browniano, o de procesos estocásticos Gaussianos generales. El cáculo de Malliavin permite obtener fórmulas explícitas para la densidad, que dan pueden utilizarse para deducir  estimaciones de tipo gaussiano.
  3. Aproximaciones normales  y versiones quantitativas de teoremas centrales del límite, obtenidas mediante técnicas de cálculo de Malliavin

Summary: The course provided an introduction to Bayesian Hierarchical Models. The aim of the course is prove an interactive experience for students and researchers from a variety of fields and to allow them to experience state of the art statistical methodology and it’s application. It will cover modelling relationships in both space and time with particular focus on fitting complex models to big data. The course covered both theory and applied examples, the latter specifically through practical ‘hands-on’ computer sessions, using R and R-INLA, in which participants will be guided through the analyses of real data with both temporal and spatial structure. 

  • Day One - Presentation: An introduction to Bayesian Heirarchical Models 
  • Day Two - Practical session: Implementing Bayesian models using R-INLA 
  • Day Three - Presentation:  Applications of Bayesian Heirarchical Models
  • Day Four - Practical session: Bayesian disease mapping 

Further details of the course, the slides, data, code and further material can be found on the course website.

Summary: This course aims at showing practical use of statistics to solve big data issues. We will provide use cases to see statistics in action for Big Data analysis. We will study theoretical methods and their practical implementation such as kmeans, Non-Negative Matric Factorization.
Management and analysis of big data are often associated with a data distributed architecture in the Hadoop and now Spark frameworks. This course offers an introduction for statisticians to these technologies by comparing the performance obtained by the direct use of three reference environments: R, Python Scikit-learn, Spark MLlib on three public use cases: character recognition, recommending films, categorizing products.

Summary: Basados en herramientas básicas de probabilidad, se presentarán modelos fundamentales  para analizar la evolución de precios de acciones en tiempo discreto. Se iniciará con el modelo binomial y se presentarán algunas generalizaciones al caso de procesos de Markov.  En cada uno de ellos se analizarán probelmas como la existencia de oportunidades de arbitraje y valuación de opciones, tanto para mercados completos como incompletos. Para finalizar, se presentarán algunos elementos que subyacen en la solución de problemas de optimización de portafolios con restricciones de riesgo.

 

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