Statistical Models and Stochastic Processes

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

Others

Weekly hours

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

Competences

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
    0h
    Problems
    0h
    Laboratory
    0h
    Guided learning
    0h
    Autonomous learning
    0h

    Final term exam


    Objectives: 1 2 8
    Week: 18
    Theory
    0h
    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
    0h
    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.