2023/2024

Degree | Type | Year | Semester |
---|---|---|---|

2500149 Mathematics | OB | 3 | 2 |

- Name:
- Ana Alejandra Cabaņa Nigro
- Email:
- anaalejandra.cabana@uab.cat

You can check it through this link. To consult the language you will need to enter the CODE of the subject. Please note that this information is provisional until 30 November 2023.

- Dorota Mlynarczyk

Linear algebra. Mathematical analysis. Probability.

In this course, the concept of Inference, in its inductive version, must be learned.

The concepts of Modeling, Estimation (point and interval estimation) and Goodness of fit must be introduced.

we shall study:

1. Descriptive and exploratory statistics that will allow to extract and summarize efficiently information of the data.

2. Statistical Inference: how to quantify the uncertainty present in the data.

3. The modeling of populations, parameters estimation, specially maximum likelihood, and parametric and non-parametric hypotheses tests.

3. Basic properties of optimality for estimators: invariance, sufficiency, efficiency, bias, variance and asymptotic properties.

4. How to solve applied problems. Through the resolution of problems and practices with statistical software (R), the student will work with different statistical models and with real data.

- Apply critical spirit and thoroughness to validate or reject both one's own arguments and those of others.
- Distinguish, when faced with a problem or situation, what is substantial from what is purely chance or circumstantial.
- Recognise the presence of Mathematics in other disciplines.
- Students must be capable of applying their knowledge to their work or vocation in a professional way and they should have building arguments and problem resolution skills within their area of study.
- Students must be capable of collecting and interpreting relevant data (usually within their area of study) in order to make statements that reflect social, scientific or ethical relevant issues.
- Students must be capable of communicating information, ideas, problems and solutions to both specialised and non-specialised audiences.
- Students must develop the necessary learning skills to undertake further training with a high degree of autonomy.
- Students must have and understand knowledge of an area of study built on the basis of general secondary education, and while it relies on some advanced textbooks it also includes some aspects coming from the forefront of its field of study.
- Take sex- or gender-based inequalities into consideration when operating within one's own area of knowledge.
- Use computer applications for statistical analysis, numeric and symbolic calculus, graphic display, optimisation or other purposes to experiment with Mathematics and solve problems.
- When faced with real situations of a medium level of complexity, request and analyse relevant data and information, propose and validate models using the adequate mathematical tools in order to draw final conclusions
- Work in teams.

- Apply critical spirit and thoroughness to validate or reject both one's own arguments and those of others.
- Descriptively synthesise and analyse datasets.
- Formulate and solve hypothesis contrast problems in one or two populations
- Identify the main inequalities and discriminations in terms of sex/gender present in society.
- Students must be capable of applying their knowledge to their work or vocation in a professional way and they should have building arguments and problem resolution skills within their area of study.
- Students must be capable of collecting and interpreting relevant data (usually within their area of study) in order to make statements that reflect social, scientific or ethical relevant issues.
- Students must be capable of communicating information, ideas, problems and solutions to both specialised and non-specialised audiences.
- Students must develop the necessary learning skills to undertake further training with a high degree of autonomy.
- Students must have and understand knowledge of an area of study built on the basis of general secondary education, and while it relies on some advanced textbooks it also includes some aspects coming from the forefront of its field of study.
- Understand the basic properties of point and interval estimators.
- Use large datasets with the help of a statistical package.
- Use the maximum verisimilitude, Bayes and least square methods to construct estimators
- Work in teams

**Modelling and estimationa: **Random experiments. Some important distributions.

**Point estimation and Intervals:**

** **Estima**t**ors**. **Bias, mean quadratic error, consistency, sufficiency, asymptotic normality. Estimation methods: moments, maximum likelyhood, Bayesian estimators.

Fisher Information and the Cramér-Rao lower bound. Efficiency.

Asymptotic normality of the MLE .

**Hypothesis Testing:**

Null and alternative hypotheses. Types of errors.

** **Neyman & Pearson lemma and UMP tests.

Likelyhood ratio test, Score and Wald tests.

Permutation and bootstrap tests.

**Unless the requirements enforced by the health authorities demand a prioritization or reduction of these contents.**

We have theoretical classes, problems and computer practices.

New subjects will be introduced primarily in the theretical sessions, but it will be necessary to deepen the teacher's explanations through student's autonomous study, with the support of the bibliography. Student participation will be encouraged. There will be a partial control of theory and problems in the period dessignated by the school. Material to complement the classes will be available through Virtual Campus.

Problems' classes will be devoted to the resolution of proposed problems. Students' participation in these classes will be especially encouraged.

Practical classes will introduce the use of R software through statistical applications. You will see descriptive and inferential methodologies.

** **

**Annotation**: Within the schedule set by the centre or degree programme, 15 minutes of one class will be reserved for students to evaluate their lecturers and their courses or modules through questionnaires.

Title | Hours | ECTS | Learning Outcomes |
---|---|---|---|

Type: Directed | |||

Master classes: theory | 28 | 1.12 | 10, 3, 7, 5, 2, 13, 11, 12 |

Practical work with computer tools | 14 | 0.56 | 10, 7, 5, 2, 12 |

Problem classes | 14 | 0.56 | 10, 3, 7, 12 |

Type: Supervised | |||

Tutorials | 5 | 0.2 | |

Type: Autonomous | |||

Practical work with computer tools | 25 | 1 | |

Problem solving (workshops and classes) | 20 | 0.8 | 10, 3, 7, 5, 2, 13, 11, 12 |

Study and think problems | 39 | 1.56 | 10, 3, 7, 5, 2, 13, 11, 12 |

The assessment is carried out continuously throughout the course.

Continuous assessment has several fundamental objectives: Monitor the teaching and learning process, allowing both the student and the teacher to know the degree of achievement of the competencies and correct, if possible, the deviations that occur. Encourage the students' continued effort in the face of over-effort, often useless, last-minute. Verify that the student has achieved the competences determined in the syllabus. For this, the accreditation of a minimum level in all assessment activities will be requested (3 out of 10).

To carry out this evaluation, the following instruments are available: problem sessions(15%), practical exams (15%) ( in one or more than one session), and a first partial exam (30%).

The continuous assessment is complemented by a written test at the end of the semester( 40%) of the final mark of the subject.

The recovery exam will be directed to students**who have not** passed attained a final mark of 5. The practical part and problems (30%) cannot be recovered.

Continuous assessment has several fundamental objectives: Monitor the teaching and learning process, allowing both the student and the teacher to know the degree of achievement of the competencies and correct, if possible, the deviations that occur. Encourage the students' continued effort in the face of over-effort, often useless, last-minute. Verify that the student has achieved the competences determined in the syllabus. For this, the accreditation of a minimum level in all assessment activities will be requested (3 out of 10).

To carry out this evaluation, the following instruments are available: problem sessions(15%), practical exams (15%) ( in one or more than one session), and a first partial exam (30%).

The continuous assessment is complemented by a written test at the end of the semester( 40%) of the final mark of the subject.

The recovery exam will be directed to students

Title | Weighting | Hours | ECTS | Learning Outcomes |
---|---|---|---|---|

Computer Exam (R) | 15% | 6 | 0.24 | 1, 10, 3, 9, 8, 7, 6, 2, 11, 12 |

Partial Exam 2 | 40% | 7 | 0.28 | 10, 3, 7, 5, 2, 12 |

Partial Exam-1 | 30% | 5 | 0.2 | 10, 3, 7, 5, 2, 11, 12 |

Problems | 15% | 12 | 0.48 | 1, 10, 4, 3, 9, 7, 2, 13, 11, 12 |

**Fundamental**

- Casella, G..and Berger, R. (2002) .
*Statistical Inference, 2º ed*. Wadsworth, Belmont, CA. - Casella, G., Berger, R. and Santana, D. (2002). Solutions Manual for Statistical Inference, Second Edition.
*Morris H. Degroot, Mark J. Schervish, Probability and Statistics ,*https://es1lib.org/book/3606887/3d12fd?id=3606887&secret=3d12fd- Luis Ruiz Maya Pérez, Francisco Javier Martín-Pliego López. (2006). Estadística. II, Inferencia. Editoria AC.
- Millar, R. (2011).
*Maximum Likelihood Estimation and Inference*. Wiley. - Rossi, Richard,Mathematical Statistics: An Introduction to Likelihood Based Inference, https://onlinelibrary.wiley.com/doi/book/10.1002/9781118771075

- Casella, G..and Berger, R. (2002) .

** Complement**

- Das Gupta ("2008) "Asymptotic Theory of Statistics and Porbability", Springer.
- J.A.Rice (2007), Mathematicla Statistics and data analysis, 3rd Ed, Duxbury/Thomson
- Versani, J. "Using R for introductory Statistics", Taylor and Francis.
- M. Kendall and A. Stuart (1983). “The Advanced Theory of Statistics”.Griffin and Co. Limited, London.
- Lehman, E.L. and Romano (2005, 3rd Ed.), J.P, "Testing Statistical Hypotheses", Springer
- C.R. Rao (1973). “Linear Statistical Inference and its Applications”. Wiley, London.
- M.L. Rizzo (2007). "Statisticalcomputing with R". Computer Science and Data Anal Cysis Series". Chapman & Hall / CRC
- Williams, D. (2001) "Weighihg the Odds", Cambridge University Press.

R Core Team (2021). R: A language and environment for statistical computing. R

Foundation for Statistical Computing, Vienna, Austria. URL

https://www.R-project.org/.