Applied Bayesian Statistics (with Stan) (July 2 to 6)

Title

Applied Bayesian Statistics (with Stan)

Instructor

Carlos J. Gil Bellosta (gilbellosta@gmail.com / @gilbellosta)

C. J.  Gil Bellosta, Degree in Mathematics from  the Univ. de Zaragoza and Master in Mathematics from the  Washington University  (EE.UU).  From  2005  works as an statistical consultant for spanish as well as international enterprises. In the period 2014-2015  he worked in eBay as a Senior Data Scientist.   He has been a pioneer in the use of Big Data  tools for the data analysis in Spain. He is the president of the R users association in spain, developer of several R packages and promoter of the rOpenSpain project.

Course language

English

Schedule

July 2nd to 6th, from 9:00 to 12:00h.

Description

Many statistical problems have a mathematical structure very well defined: they can be seen as generative models that in some cases have  some unknown parameters.

The traditional statistical methods (hypothesis test, linear models, generalized linear models, etc) and their generalizations (GAM, non-linear, etc) may be used efficiently in particular situations. Nevertheless, it is quite common that they  do not capture the totality of the model (for example, the  a priori  information).

Bayesian statistics allows, at least from the theoretical point of view, to solve the model in its enterity. Moreover, since the  computers are a popular thing and  the programing languages have been extended, as Stan, they also can be reached entirely from a practical point of view.

The course will allow to see how to consider and solve froma  Bayesian prestective a set of real and practical problems, from the more simple ones (hypothesis test) to other more advanced ( hiden markov problems, Kalman filter, etc) very important in its applications.

Course goals

The objective of this course is that the student learn how to set out the probabilistic structure (generative) of an statistical problem, to use Stan to estimate the parameters and to use this information to take decisions based on the information provided for the data.

Course contents

The course is going to be eminently practical, with examples of the consultancy to illustrate and justify the theoretical aspects. The session will cover the following aspects of the Bayesian statistics:

• Generative models
• Statistical engineering: formulation of the generative models in real situations, including the properly formulation of the  a priori   distributions
• Parameter estimation and their  a posteriori distributions; analysis of such distributions
• Decision theory

Each one of the previous points  will be illustrated and analyzed through examples, some of them  simple and some others more sophisticated, along the different sections that will cover:

• Hypothesis testing and their extensions
• Classical models (linear and  GLM’s)
• Hiden Markov models,  Kalman filter
• Attribution models
• Mixed distribution  

Evaluation

Each day the students will have to work on one or two exercices associated to the contents of that day session.

Pre-requisite

• Statistics (degree level)
• R (medium level)

Targeted at

• Students interested in bayesian statistics and their applications
• Researchers

Classroom

PC2