STATISTICS

Description

Objectives: Basic understanding of data collection, presentation and analysis, including use of statistical software. The basic notions of statistical analysis include the formulation of statistical models, the point and interval estimation of parameters and the interpretation of significance tests. The essentials of elementary probability theory, including elementary probability calculus formulae, discrete and continuous distributions and their (first and second order) moments, the law of large numbers and the basic central limit theorem. By the end of the course the student will be able to continue the studies with a more advanced course on statistical methods, as well as to manage a first elaboration of a data set. Assessment: Students will be evaluated through the final written exam, covering the whole course program. The final written exam consists of theoretical questions and practical problems aimed at verifying the student’s mastering of the basic notions and their application. In general, the exam will be formed by 5-6 questions. During the semester, there will be an intermediate test covering the first part of the program, which will count for 1/3 of the final grade. NOTE: the intermediate test grade will be effective only if the final exam is taken during the summer session. Teaching Methods: Frontal lectures, exercise sessions with teaching assistant, use of R for data analysis. Prerequisites: One semester of Math prior to taking the course Contents: Basic ideas in statistics: data collection, presentation, summary statistics and plots. Basic probability. Statistical models, and probability based statistical inference: estimation and hypothesis testing. Introduction to the use of statistical software Reference Texts: Ross, S. M. (2017). Introductory statistics (4th ed.). Elsevier/Academic Press. Thesis assignment criteria: Not relevant Extended Program And Reference Reading Material: Week 1: Ch 1/2/3 Introduction, data collection. Statistical models and parameters. The population and the sample. Descriptive statistics: tables, line plots, histograms, etc. Data examples. Summary statistics, mean, median, variance, standard deviation, covariance and correlation coefficient and percentiles Extended Program And Reference Reading Material: Week 10: Ch 12 Linear regression, the basic model and examples. Data examples for regression. Estimation of parameters in linear regression. The Least Squares method. Linear regression with R. Extended Program And Reference Reading Material: Week 11: Ch 12 Regression to the mean. Correlations, residual analysis. (Multiple and logistic regression, demonstration with R. Dummy variables and analysis of variance). Extended Program And Reference Reading Material: Week 12: Review Extended Program And Reference Reading Material: Week 2: Ch 1/2/3 Introduction to the theory of probability. Extended Program And Reference Reading Material: Week 3: Ch 4 Basic probability, events, experiments, conditional probability, independence. Bayes' formula. Uniform spaces and notions of combinatorics. Extended Program And Reference Reading Material: Week 4: Ch 5 Random variables, definition and examples. Discrete and continuous random variables. Distributions (uniform, discrete/continuous; geometric, exponential, Poisson, normal), density, distribution function. Simple transformations of random variables. Bernoulli sequences and the binomial distribution. Joint distributions, the 2x2 table, dependence and independence. Extended Program And Reference Reading Material: Week 5: Ch 5/6/7 Random variables, expectation and variance of random variables, examples. Sums of two uniforms. Rules for expectation and variance. Covariance and correlation coefficient. Simple non-linear transformations. The law of large numbers... Intro to simulation in R Extended Program And Reference Reading Material: Week 6: Ch 5/6/7 The binomial distribution and proportions. The normal distribution and probability tables. Exact properties, normal approximation, the central limit theorem. Normal distribution and applications. : sampling distribution of the mean, normal approximation. Mention of chi-square and t-distribution. Discussion of sample size. Use of R for probability calculations. Extended Program And Reference Reading Material: Week 7: Ch 8 Short introduction to inference questions and answers. Estimation, basic notions. Sampling distributions. Estimation of population mean and variance. Estimation of proportions. Extended Program And Reference Reading Material: Week 8: Ch 8/9 Confidence intervals for means, proportions, etc. Testing. Hypotheses, basic ideas, significance level and related concepts Extended Program And Reference Reading Material: Week 9: Ch 9/10/13 Tests related to means, proportions (also contingency tables and Goodness of Fit tests), and more. Two-sample tests. P-value. Tests in R Intended learning outcomes: Knowledge and understanding: The student - by participating in the lectures and exercise sessions - develops the ability to understand the fundamental notions of Statistics and data analysis. The student will also be introduced to the use of statistical software Applying knowledge and understanding: The student will be able to apply the notions and techniques described during the course and to present the results in a suitable way. Making autonomous judgements: The student will have acquired the ability to identify suitable solution methods for various problems and developed critical thinking and problem solving skills Communication skills: At the end of the course the student will be able to express judgments and present the results of a statistical analysis of problems and/or data, with the required terminological precision and the appropriate technical lexicon. Learning skills: The knowledge acquired during the course will allow the student to autonomously understand and interpret more advanced notions and techniques of the subject and adapt them to a specific reference context. The knowledge of the fundamental aspects of the subject acquired during the course will allow the student to engage in further studies in the subject, even on his/her own, and to participate in future post-graduate training. Objectives: Basic understanding of data collection, presentation and analysis, including use of statistical software. The basic notions of statistical analysis include the formulation of statistical models, the point and interval estimation of parameters and the interpretation of significance tests. The essentials of elementary probability theory, including elementary probability calculus formulae, discrete and continuous distributions and their (first and second order) moments, the law of large numbers and the basic central limit theorem. By the end of the course the student will be able to continue the studies with a more advanced course on statistical methods, as well as to manage a first elaboration of a data set. Assessment: Students will be evaluated through the final written exam, covering the whole course program. The final written exam consists of theoretical questions and practical problems aimed at verifying the student’s mastering of the basic notions and their application. In general, the exam will be formed by 5-6 questions. During the semester, there will be an intermediate test covering the first part of the program, which will count for 1/3 of the final grade. NOTE: the intermediate test grade will be effective only if the final exam is taken during the summer session. Teaching Methods: Frontal lectures, exercise sessions with teaching assistant, use of R for data analysis. Prerequisites: One semester of Math prior to taking the course Contents: Basic ideas in statistics: data collection, presentation, summary statistics and plots. Basic probability. Statistical models, and probability based statistical inference: estimation and hypothesis testing. Introduction to the use of statistical software Reference Texts: Ross, S. M. (2017). Introductory statistics (4th ed.). Elsevier/Academic Press. Thesis assignment criteria: Not relevant Extended Program And Reference Reading Material: Week 1: Ch 1/2/3 Introduction, data collection. Statistical models and parameters. The population and the sample. Descriptive statistics: tables, line plots, histograms, etc. Data examples. Summary statistics, mean, median, variance, standard deviation, covariance and correlation coefficient and percentiles Extended Program And Reference Reading Material: Week 10: Ch 12 Linear regression, the basic model and examples. Data examples for regression. Estimation of parameters in linear regression. The Least Squares method. Linear regression with R. Extended Program And Reference Reading Material: Week 11: Ch 12 Regression to the mean. Correlations, residual analysis. (Multiple and logistic regression, demonstration with R. Dummy variables and analysis of variance). Extended Program And Reference Reading Material: Week 12: Review Extended Program And Reference Reading Material: Week 2: Ch 1/2/3 Introduction to the theory of probability. Extended Program And Reference Reading Material: Week 3: Ch 4 Basic probability, events, experiments, conditional probability, independence. Bayes' formula. Uniform spaces and notions of combinatorics. Extended Program And Reference Reading Material: Week 4: Ch 5 Random variables, definition and examples. Discrete and continuous random variables. Distributions (uniform, discrete/continuous; geometric, exponential, Poisson, normal), density, distribution function. Simple transformations of random variables. Bernoulli sequences and the binomial distribution. Joint distributions, the 2x2 table, dependence and independence. Extended Program And Reference Reading Material: Week 5: Ch 5/6/7 Random variables, expectation and variance of random variables, examples. Sums of two uniforms. Rules for expectation and variance. Covariance and correlation coefficient. Simple non-linear transformations. The law of large numbers... Intro to simulation in R Extended Program And Reference Reading Material: Week 6: Ch 5/6/7 The binomial distribution and proportions. The normal distribution and probability tables. Exact properties, normal approximation, the central limit theorem. Normal distribution and applications. : sampling distribution of the mean, normal approximation. Mention of chi-square and t-distribution. Discussion of sample size. Use of R for probability calculations. Extended Program And Reference Reading Material: Week 7: Ch 8 Short introduction to inference questions and answers. Estimation, basic notions. Sampling distributions. Estimation of population mean and variance. Estimation of proportions. Extended Program And Reference Reading Material: Week 8: Ch 8/9 Confidence intervals for means, proportions, etc. Testing. Hypotheses, basic ideas, significance level and related concepts Extended Program And Reference Reading Material: Week 9: Ch 9/10/13 Tests related to means, proportions (also contingency tables and Goodness of Fit tests), and more. Two-sample tests. P-value. Tests in R Intended learning outcomes: Knowledge and understanding: The student - by participating in the lectures and exercise sessions - develops the ability to understand the fundamental notions of Statistics and data analysis. The student will also be introduced to the use of statistical software Applying knowledge and understanding: The student will be able to apply the notions and techniques described during the course and to present the results in a suitable way. Making autonomous judgements: The student will have acquired the ability to identify suitable solution methods for various problems and developed critical thinking and problem solving skills Communication skills: At the end of the course the student will be able to express judgments and present the results of a statistical analysis of problems and/or data, with the required terminological precision and the appropriate technical lexicon. Learning skills: The knowledge acquired during the course will allow the student to autonomously understand and interpret more advanced notions and techniques of the subject and adapt them to a specific reference context. The knowledge of the fundamental aspects of the subject acquired during the course will allow the student to engage in further studies in the subject, even on his/her own, and to participate in future post-graduate training.