This book was created with the goal of helping students transition from the theoretical and methodological concepts of statistical inference to their implementation on a computer. The first part of the book is primarily focused on exercises to be solved with pen and paper, so that students can apply knowledge derived from lemmas and theorems; while the second part consists of labs, which involve both the manual implementation of algorithms and the learning of built-in tools for efficient analysis of datasets derived from real-world problems. To optimize the understanding of the topics developed and to guide the reader through their studies, the book is organized into chapters, each of which includes an introductory section that reviews the theoretical foundations of statistical inference, followed by a second part with exercises, each accompanied by a comprehensive solution on paper and, when appropriate, using software. This book is aimed at undergraduate students in Statistics, Mathematics, Engineering, and for graduate-level courses in Data Science.

Guided solutions of inferential statistics exercises help in learning statistical method and ability in data analysis The theory summaries and the guided exercises help students in synthesizing the main methods and results of statistics The presence of commented R code helps students learn to perform analysis using dedicated software

Autorentext

Francesca Gasperoni is currently employed in the pharmaceutical sector as trial statistician. Before moving to industry, she was a researcher at the MRC Biostatistics Unit (Cambridge, UK) and her research focussed on advanced statistical modelling for electronic heath records. During her PhD, obtained at Politecnico of Milan (Italy), she worked as teaching assistant for several courses of Probability and Statistics. Francesca Ieva is Associate Professor of Statistics at the Department of Mathematics of the Polytechnic of Milan. She deals with statistical learning in the biomedical field and statistical modeling for complex data coming from the world of healthcare research. Since 2021 she is associate head of the Health Data Science Center of Human Technopole. Anna Maria Paganoni is Full Professor of Statistics at the Department of Mathematics of the Polytechnic of Milan. She deals with statistical modeling and analysis of highly complex data with particular attention to the biomedical field and learning analytics. She is responsible for several competitively funded research projects. She is currently Coordinator of the Course of Studies in Mathematical Engineering, and delegate of the Rector for "Data Strategy".

Inhalt

Part I: Statistical Inference.- 1 Fundamentals of Probability and Statistics.- 2 Sufficient, Minimal, and Complete Statistics.- 3 Point Estimators.- 4 Uniform Minimum Variance Unbiased Estimators (UMVUEs).- 5 Likelihood Ratio Test.- 6 Uniformly Most Powerful Test.- 7 Confidence Intervals.- 8 Asymptotic Statistics.- Part II: Regression Models and Analysis of Variance.- 9 Linear Regression.- 10 Generalized Linear Models.- 11 ANOVA: Analysis of Variance.- 12 Summary Exercises.- Appendix A: Probability Distributions.