Advanced Statistical Modelling

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Credits
6
Types
Specialization complementary (Data Science)
Requirements
This subject has not requirements, but it has got previous capacities
Department
EIO;DAC
The course covers different statistical regression models: generalized linear model, nonparametric regression, generalized nonparametric regression, Bayesian models. The model selection and validation is emphasized. A fundamental part of the course is the study of real cases, both by teachers and by students at the weekly assignments.

Weekly hours

Theory
3
Problems
0
Laboratory
0
Guided learning
0
Autonomous learning
7

Objectives

  1. At the end of the course the student will be able to propose, estimate, interpret and validate generalized linear models.
    Related competences: CG3, CEC2, CTR4, CTR6,
  2. At the end of the course the student will be able to propose, estimate, interpret and validate non-parametric versions of linear regression models and generalized linear models.
    Related competences: CG3, CEC2, CTR4, CTR5, CTR6,
  3. At the end of the course the student will know properly how to choose the smoothing parameters which in nonparametric regression models control the trade-off between good fit to the observed sample and good generalization.
    Related competences: CG3, CEC2, CTR4, CTR5, CTR6,
  4. At the end of the course the student, facing a real problem of modeling and / or prediction, will know to choose the most suitable regression model (parametric, non-parametric, semi-parametric or Bayesian).
    Related competences: CG3, CEC2, CTR4, CTR5, CTR6,
  5. At the end of the course the student will be able to distinguish the difference between Bayesian and non-Bayesian statistical modelling
    Related competences: CG3, CEC2, CTR4, CTR5, CTR6,
  6. At the end of the course the student will be able to define a prior distribution, and go from prior to posterior distributions
    Related competences: CG3, CEC2, CTR4, CTR5, CTR6,
  7. At the end of the course the student will be able to understand the difference between hierarchical and non-hierarchical Bayesian models
    Related competences: CG3, CEC2, CTR4, CTR5, CTR6,
  8. At the end of the course the student will be able to check a Bayesian model, compare Bayesian models and use them for prediction
    Related competences: CG3, CEC2, CTR4, CTR5, CTR6,
  9. At the end of the course the student will be able to simulate from the posterior distribution by means of the suitable software
    Related competences: CG3, CEC2, CTR4, CTR5, CTR6,

Contents

  1. Parametric Modelling
    1. Introduction. Deterministic models and statistical models. Parametric, nonparametric and semiparametric models.

    2. Generalized linear models. Models for binary response data. Models for count data and contingency tables. Estimation by maximum likelihood and through the Xi^2 statistic. Inference. Model checking.

    3. Regularized estimation of LM and GLM. Ridge regression. LASSO estimation
  2. Nonparametric Modelling
    1. Nonparametric regression model. Local polynomial regression. Kernels. Linear smoothers. Choosing the smoothing parameter: Cross validation, plug-in methods, varying windows.

    2. Generalized nonparametric regression model. Estimation by maximum local likelihood.

    3. Inference with nonparametric regression. Variability bands. Testing for no effects. Checking a parametric model. Comparing curves.

    4. Spline smoothing. Penalized least squares nonparametric regression. Cubic splines and interpolation. Smoothing splines. B-splines and P-splines. Fitting generalized nonparametric regression models with splines.

    5. Generalized additive models and Semiparametric models. Multiple nonparametric regression. The curse of dimensionality. Generalized additive models. Semiparametric models.
  3. Bayesian Data Analysis
    1. Bayesian Model. The statistical model. The Likelihood function. The Bayesian model

    2. Bayesian Inference. Point and Interval estimation.Hypothesis Test

    3. Bayesian Computation. Markov Chain Montecarlo simulation. Monitoring convergence

    4. Hierarchical Models

    5. Checking and defining the model

Activities

Activity Evaluation act


Presentation of Theme 1 (parametric regression models) in class

Presentation of Theme 1 (parametric regression models) in class
Objectives: 1 4
Contents:
Theory
6h
Problems
0h
Laboratory
0h
Guided learning
0h
Autonomous learning
14h

Presentation of Theme 2 (non-parametric regression models) in class

Presentation of Theme 2 (non-parametric regression models) in class
Objectives: 2 3 4
Contents:
Theory
16.5h
Problems
0h
Laboratory
0h
Guided learning
0h
Autonomous learning
38.5h

Presentation of theme 3 (Bayesian models) in class

Presentation of theme 3 (Bayesian models) in class
Objectives: 4 5 6 7 8 9
Contents:
Theory
22.5h
Problems
0h
Laboratory
0h
Guided learning
0h
Autonomous learning
52.5h

Teaching methodology

There is a weekly 3 hours session. The first two hours are devoted to the exposition of the theoretical subjects by the teacher. The last hour is dedicated to implement these contents: Each student has his laptop in class and he or she performs the tasks proposed by the teacher. Each session ends with an assigment to students who must be delivered the following session.

Evaluation methodology

Homeworks will be assigned during the course. Homework grades will be worth 50% of your course grade.

There will be an exam for the first part of the course (first and second themes), during the partial exams week, and another one for the second part (third theme), each one with a weight of 25%.

Course Grade = 0.5 * Hwk Grade + 0.25 * 1st part Exam Grade + 0.25 * 2nd part Exam Grade

Bibliography

Basic:

Previous capacities

Not specified