Class Probabilities and Statistics

Integrate concepts of probability and statistics in the design, development, and evaluation of models and algorithms for computational biomedicine and artificial intelligence.

Not applicable

1. Descriptive Statistics: Measures of central tendency and measures of dispersion. Graphical representations. 2. Probability Theory: Basic concepts. Conditional probability. Independent events. 3. Random Variables: Probability function, probability density, and distribution. 4. Parameters of Random Variables: Expected value and variance. Covariance and linear correlation coefficient. 5. Discrete Probability Distributions: Discrete uniform, binomial, negative binomial, and Poisson distributions. 6. Continuous Probability Distributions: Continuous uniform, normal, exponential, chi-squared, t, and F distributions. 7. Sampling and Estimation: Sampling distributions. Central Limit Theorem. Properties of estimators. 8. Interval Estimation: Mean, proportion, variance, and difference of means. 9. Hypothesis Testing: Parametric(Mean, proportion, variance, and difference of means) and non-parametric tests. 10. Linear Regression Model.      

In the theoretical component of this course, topics are presented clearly using digital support materials. The presentations are based on literature and provided to students in advance to encourage prior study and class discussions. Case studies will also be presented to stimulate critical thinking and enhance the ability to analyse scientific publications. A balance will be maintained between the presentation of concepts and discussion, fostering active student participation. The theoretical-practical component will adopt a mixed format. Students will be encouraged to solve increasingly complex exercises aligned with the progression of the Curriculum Unit. In addition to individual work, students will be encouraged to collaborate on group exercises. A group assignment will also be proposed.

Daniel, W., & Cross, C. (2018). Biostatistics: A Foundation for Analysis in the Health Sciences (11th ed.). Wiley Series in Probability and Statistics. Hines, W., Montgomery, D., Goldsman, D., & Borror, C. (2003). Probability and Statistics in Engineering and Management Science (4th ed.). John Wiley. Pestana, D., & Velosa, H. (2006). Introdução à Probabilidade e à Estatística. Fundação Calouste Gulbenkian. Reis, E., Melo, P., Andrade, R., & Calapez, T. (2021). Estatística Aplicada (7ª ed., vol. 1 & 2). Ed. Sílabo lda. Ross, S. (2009). Introduction to Probability and Statistics for Engineers and Scientists (4th ed.). Elsevier Academic Press.