Bioinformatics - Bioinformatica

Syllabus 1. Descriptive statistics: Introduction to statistics and descriptive statistics, subjects, population, census, sample, sample survey, variable, classification of the variables, data matrix, frequency distribution, relative frequency distribution, percentage frequency distribution, introduction to location measures, mode, cumulative frequency distribution, relative and percentage cumulative frequencies, median, quantiles, quartiles, deciles, percentiles, mean value and its properties, partition of a numerical variable into classes, histogram, box plot, pie chart and related variants, barplot, variability, range, interquartile range, variance and its properties, standard deviation, coefficient of variation, shape of a distribution, symmetric cases, positive and negative asymmetry, standardization of a numerical variable, introduction to bivariate distribution and study of association, joint frequencies, relative joint frequencies, conditional relative frequencies, independence and perfect dependence between variables, chi-squared index of association, scatter plot, Bravais-Pearson correlation coefficient and its properties. 2. Probability calculus: Introduction to probability calculus, experiment, sample space, events, event space, sure and impossible events, Venn diagram, operations between events: intersection, union, complement, distributive property of union and intersection, de Morgan rules, relations between events: mutually exclusive events, exhaustive events, mutually exhaustive events, inclusion, axioms of probability and their consequences, additive rule, definitions of probability: classic, frequentist, subjective, conditional probability, multiplicative rule, independence between events, drawings with and without replacement, Bayes' theorem, definition of random variable, types of random variables, probability distribution, probability mass function, density function, cumulative distribution and its properties, expectation and its properties, variance and its properties, standard deviation, standardization of a random variable, discrete uniform distribution, Bernoulli distribution, Binomial distribution, uniform distribution, normal distribution and its properties, standard normal distribution and use of the related table, chi-squared distribution and use of the related table, Student's T distribution and use of the related table, multivariate random variables, discrete and continuous bivariate random variables, joint probability distribution, marginal probability distributions, conditional probability distributions, independence of random variables, expectation of a multivariate random variable, expectation and variance of a linear combination of random variables, covariance and correlation between two random variables. 3. Inferential statistics: Introduction to statistical inference, population, parameter, simple random sampling, simple random sample and its properties, observed sample, point estimation, interval estimation, hypothesis testing, statistic and estimator, estimate, finite properties of an estimator, unbiasedness, bias, mean square error, relative efficiency of an estimator, asymptotic properties of an estimator, asymptotic unbiasedness, consistency, convergence in distribution, central limit theorem, point estimation of the population mean, point estimation of the population proportion, point estimation of the population variance, unbiased sample variance and its properties, biased sample variance and its properties, comparison of the mean square errors of the unbiased and biased sample variances, confidence interval definition, pivotal quantity, confidence interval for the mean of a normal population (with known and unknown variance), approximate confidence interval for the mean of an arbitrary population and large samples, approximated confidence interval for the population proportion and large samples, confidence interval for the variance of a normal population, interpretation of the confidence interval, introduction to hypothesis testing, definition of hypothesis, null hypothesis and alternative hypothesis, simple and composite hypothesis, one-sided and two-sided hypothesis, test, acceptance and rejection region, type I and type II errors, significance level, confidence level and power of a test, test for the mean of a normal population with known variance (with two-sided and one-sided alternative hypothesis), test statistic, critical threshold, response of the test and its interpretation, test for the mean of a normal population with unknown variance, test for the mean of an arbitrary population and large samples, test for the population proportion and large samples, test for population variance of a normal population, chi-squared test of independence, p-value definition and computation, test for the difference of the means of two normal populations with known variances, test for the difference of the means of two normal populations with unknown equal variances, test for the difference of the means of two arbitrary populations with unknown variances and large samples, test for the difference of the proportions of two populations with large samples.

Elementi di teoria degli insiemi, logica elementare, insiemi numerici, funzioni di una variabile reale, disequazioni.

Testi suggeriti 1. Krijnen W P (2009). Applied statistics for bioinformatics using R. - URL: https://cran.r-project.org/doc/contrib/Krijnen-IntroBioInfStatistics.pdf 2. Venables W N, Smith D M and R Development Core Team (2025). An introduction to R - URL: https://www.math.chalmers.se/Stat/Grundutb/CTH/mve186/1415/R-Binder.pdf 3. Agresti A, Franklin C and Klingenberg B (2020). Statistics: The Art and Science of Learning from Data. Pearson.

Le lezioni sono In presenza e la frequenza non è obbligatoria.

L'esame consiste in una prova scritta, che richiede la risoluzione di esercizi pratici e teorici, e una una prova orale previo superamento della parte scritta, che può svolgersi nella stessa giornata o a distanza di pochi giorni.

Testi suggeriti 1. Krijnen W P (2009). Applied statistics for bioinformatics using R. - URL: https://cran.r-project.org/doc/contrib/Krijnen-IntroBioInfStatistics.pdf 2. Venables W N, Smith D M and R Development Core Team (2025). An introduction to R - URL: https://www.math.chalmers.se/Stat/Grundutb/CTH/mve186/1415/R-Binder.pdf 3. Agresti A, Franklin C and Klingenberg B (2020). Statistics: The Art and Science of Learning from Data. Pearson.

Lezioni frontali di tipo laboratoriale condotte con l'utilizzo del software R e l'interfaccia RStudio.