Statistical Models and Stochastic Processes

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Credits
6
Types
Compulsory
Requirements
This subject has not requirements, but it has got previous capacities
Department
EIO;UAB
This course equips students with the concepts required to understand key statistical methods used in bioinformatics methods such as the Hidden Markov Model (HMM) and the Generalised Linear Model (GLM) used in NGS data analysis. Logistic regression, Poisson regression and Mixed models will treated in detail.
Previously introduced probability and statistical concepts are developed and extended. Main subjects include: probability distributions, convergence concepts and large sample results; stochastic processes, probability transition matrix and Markov chains; maximum likelihood and Bayesian estimation; hypothesis tests, likelihood ratio tests and multiple testing issues.

Teachers

Person in charge

  • Mireia Besalú Mayol ( )
  • Pere Puig Casado ( )

Others

  • Nuria Perez Alvarez ( )

Weekly hours

Theory
2
Problems
2
Laboratory
0
Guided learning
0
Autonomous learning
6

Learning Outcomes

Learning Outcomes

Knowledge

  • K2 - Identify mathematical models and statistical and computational methods that allow for solving problems in the fields of molecular biology, genomics, medical research, and population genetics.
  • K3 - Identify the mathematical foundations, computational theories, algorithmic schemes and information organization principles applicable to the modeling of biological systems and to the efficient solution of bioinformatics problems through the design of computational tools.

Skills

  • S2 - Computationally analyze DNA, RNA and protein sequences, including comparative genome analyses, using computation, mathematics and statistics as basic tools of bioinformatics.
  • S3 - Solve problems in the fields of molecular biology, genomics, medical research and population genetics by applying statistical and computational methods and mathematical models.
  • S4 - Develop specific tools that enable solving problems on the interpretation of biological and biomedical data, including complex visualizations.
  • S8 - Make decisions, and defend them with arguments, in the resolution of problems in the areas of biology, as well as, within the appropriate fields, health sciences, computer sciences and experimental sciences.

Competences

  • C3 - Communicate orally and in writing with others in the English language about learning, thinking and decision making outcomes.
  • C6 - Detect deficiencies in the own knowledge and overcome them through critical reflection and the choice of the best action to expand this knowledge.

Objectives

  1. C3 - Communicate orally and in writing with others in the English language about learning, thinking and decision making outcomes.
    Related competences: C3,
  2. C6 - Detect deficiencies in the own knowledge and overcome them through critical reflection and the choice of the best action to expand this knowledge.
    Related competences: C6,
  3. K2 - Identify mathematical models and statistical and computational methods that allow for solving problems in the fields of molecular biology, genomics, medical research, and population genetics.
    Related competences: K2,
  4. K3 - Identify the mathematical foundations, computational theories, algorithmic schemes and information organization principles applicable to the modeling of biological systems and to the efficient solution of bioinformatics problems through the design of computational tools.
    Related competences: K3,
  5. S2 - Computationally analyze DNA, RNA and protein sequences, including comparative genome analyses, using computation, mathematics and statistics as basic tools of bioinformatics.
    Related competences: S2,
  6. S3 - Solve problems in the fields of molecular biology, genomics, medical research and population genetics by applying statistical and computational methods and mathematical models.
    Related competences: S3,
  7. S4 - Develop specific tools that enable solving problems on the interpretation of biological and biomedical data, including complex visualizations.
    Related competences: S4,
  8. S8 - Make decisions, and defend them with arguments, in the resolution of problems in the areas of biology, as well as, within the appropriate fields, health sciences, computer sciences and experimental sciences.
    Related competences: S8,

Contents

  1. Introduction
    Introduction
  2. Maximum likelihood estimation
    Maximum likelihood estimation
  3. Likelihood ratio tests
    Likelihood ratio tests
  4. GLM: Logistic regression
    GLM: Logistic regression
  5. GLM: Poisson regression
    GLM: Poisson regression
  6. Mixed effects models
    Mixed effects models
  7. Bayesian Inference
    Bayesian Inference
  8. Advanced Bayesian Inference
    Advanced Bayesian Inference
  9. Markov models
    Markov models

Activities

Activity Evaluation act




Mid term exam


Objectives: 1 2 8
Week: 9
Theory
2h
Problems
0h
Laboratory
0h
Guided learning
0h
Autonomous learning
0h

Final term exam


Objectives: 1 2 8
Week: 18
Theory
2h
Problems
0h
Laboratory
0h
Guided learning
0h
Autonomous learning
0h

Practical assignments (2)


Objectives: 1 2 3 4 5 6 7 8
Contents:
Theory
0h
Problems
2h
Laboratory
0h
Guided learning
0h
Autonomous learning
20h

Re-evaluation exam

Only the students that after the evaluation have a grade equal or greater than 3 can perform the re-evaluation exam. In the re-evaluation exam only the theoretic part can be retake.
Objectives: 1 8
Week: 1 (Outside class hours)
Theory
3h
Problems
0h
Laboratory
0h
Guided learning
0h
Autonomous learning
0h

Teaching methodology

Lectures will be mainly of expository type. There will be also problem-based sessions and practical sessions using R.

Evaluation methodology

The course assessment is as follows:
30% corresponds to 2 practical assignments (to be done by pairs),
and 70% consists of a 2 partial theoretical exams taken at mid term (35%) and final term (35%).

Recuperation Information
Only the students that after the evaluation have a grade equal or greater than 3 can perform the re-evaluation exam. In the re-evaluation exam only the theoretic part can be retake.

Bibliography

Basic:

Previous capacities

Basic knowledge of statistics and probability.