The subject Advanced Statistical Methods is a second year subject of the Degree in Artificial Intelligence. It is an extension of the statistical methods covered in the first year of the degree. The previously introduced concepts are developed in more detain and the Bayesian paradigm is introduced. Moreover, the knowledge and skills obtained through this subject establish the basis for the understanding of the paradigms introduced in further years, in particular in the data analysis area.



An expert in Artificial Intelligence should be able to conduct a statistical analysis and to understand the underlying models, with the goal of proposing solutions in the domain of Artificial Intelligence.

Understand the Bayesian paradigm in statistical inference



Buid statistical models that solve real-life problems



Draw conclusions justifying them by interpreting the data and evidences.



Learn to develop simple programs for the visualization and analysis of data in R

1. Review of some probability concepts

1.1 Random variables

1.2 Joint, marginal and conditional distributions

2. Estimation

2.1 Properties of the estimators

2.2 Method of moments

2.3 Maximum likelihood

2.4 Non-parametric bootstrap

3. Introduction to Bayesian estimation

3.1 Conjugate distributions

3.2 Monte Carlo approximation

3.3 Normal model

3.4 Gibbs sampling

3.5 Group comparison and linear regression

4. Statistical tests

4.1 Parametric, non-parametric and permutation tests

4.2 Multiple testing correction

Conclusiones y observaciones



2. Estimación bayesiana

Revisión de algunas reglas de probabilidad

Distribuciones conjugadas

La distribución a priori

Modelos normales

Estimación y contraste

Muestras grandes

MMCC

Algoritmo Metropolis-Hasting

Muestreo de Gibbs

Diagonosis de convergencia



3. Teoría de la información

Cantidad de información

Entropía

Información mútua. Pointswise mutual information

Divergencias



4. Diseño de experimentos//Contrastes de hipótesis múltiples

Observaciones

Hipótesis múltiples

Diseño de experimentos

Experimentación

Análisis de resultados

Contraste de hipótesis múltiples

Reproducibilidad

In this subject we will promote the autonomous work of the student using computer and bibliographic resources that will help understanding the topic. Lectures with the conceptual contents of the subject will be complemented with exercises. The computation part will be covered with weekly computer sessions.

• Continuous Assessment System
• Final Assessment System
• Tools and qualification percentages:
  • The assessment types and conditions are indicated below: (%): 100

The subject can be passed with two evaluation systems, continuous assessment and global assessment. The election of the continuous assessment will be at the beginning of the subject and will be confirmed before the established deadline (after the evaluation of 60-80% of the subject), once the lecturer confirms the results obtained by the student.



Continuous assessment:

The continuous assessment involves practical individual and group works (15%), theory and exercises partial exams in the laboratory (85%).

The final mark will be the mean of the results obtained in all the evaluation items, provided that a minimum of 4 has been obtained in each one. The subject will be passed with an average mark of 5 or more.



Global assessment:

The global assessment involves a theory and exercises exam in the laboratory (100%). Not taking part in any of these exams will be considered a withdraw. The subject will be passed with an average mark of 5 or more.

The assessment in extraordinary examination will be the same as the global assessment:



The global assessment involves a theory and exercises exam that will take place in the laboratory (100%). Not taking part in any of these exams will be considered a withdraw. The subject will be passed with an average mark of 5 or more.

Ez dago nahitaez erabili beharreko materialik. Ikaslea bera joango da bere materiala osatzen eskolako jarraipena eginez.

Basic bibliography

Leonard Held, Daniel Sabanés-Bové (2014) Applied Statistical Inference. Springer

Peter D. Hoff (2009) A First Course in Bayesian Statistical Methods. Springer