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Subjective Well-Being and Social Media shows how, by exploiting the unprecedented amount of information provided by the social networking sites, it is possible to build new composite indicators of subjective well-being. These new social media indicators are complementary to official statistics and surveys, whose data are collected at very low temporary and geographical resolution. The book also explains in full details how to solve the problem of selection bias coming from social media data. Mixing textual analysis, machine learning and time series analysis, the book also shows how to extract both the structural and the temporary components of subjective well-being.Cross-country analysis confirms that well-being is a complex phenomenon that is governed by macroeconomic and health factors, ageing, temporary shocks and cultural and psychological aspects. As an example, the last part of the book focuses on the impact of the prolonged stress due to the COVID-19 pandemic on subjective well-being in both Japan and Italy. Through a data science approach, the results show that a consistent and persistent drop occurred throughout 2020 in the overall level of well-being in both countries. The methodology presented in this book: enables social scientists and policy makers to know what people think about the quality of their own life, minimizing the bias induced by the interaction between the researcher and the observed individuals; being language-free, it allows for comparing the well-being perceived in different linguistic and socio-cultural contexts, disentangling differences due to objective events and life conditions from dissimilarities related to social norms or language specificities; provides a solution to the problem of selection bias in social media data through a systematic approach based on time-space small area estimation models. The book comes also with replication R scripts and data.Stefano M. Iacus is full professor of Statistics at the University of Milan, on leave at the Joint Research Centre of the European Commission. Former R-core member (1999-2017) and R Foundation Member. Giuseppe Porro is full professor of Economic Policy at the University of Insubria. An earlier version of this project was awarded the Italian Institute of Statistics-Google prize for'official statistics and big data'.

The YUIMA package is the first comprehensive R framework based on S4 classes and methods which allows for the simulation of stochastic differential equations driven by Wiener process, Lévy processes or fractional Brownian motion, as well as CARMA, COGARCH, and Point processes. The package performs various central statistical analyses such as quasi maximum likelihood estimation, adaptive Bayes estimation, structural change point analysis, hypotheses testing, asynchronous covariance estimation, lead-lag estimation, LASSO model selection, and so on. YUIMA also supports stochastic numerical analysis by fast computation of the expected value of functionals of stochastic processes through automatic asymptotic expansion by means of the Malliavin calculus. All models can be multidimensional, multiparametric or non parametric.The book explains briefly the underlying theory for simulation and inference of several classes of stochastic processes and then presents both simulation experiments and applications to real data. Although these processes have been originally proposed in physics and more recently in finance, they are becoming popular also in biology due to the fact the time course experimental data are now available. The YUIMA package, available on CRAN, can be freely downloaded and this companion book will make the user able to start his or her analysis from the first page.

Stochastic di?erential equations model stochastic evolution as time evolves. These models have a variety of applications in many disciplines and emerge naturally in the study of many phenomena. Examples of these applications are physics (see, e. g., [176] for a review), astronomy [202], mechanics [147], economics [26], mathematical?nance [115], geology [69], genetic analysis (see, e. g., [110], [132], and [155]), ecology [111], cognitive psychology (see, e. g., [102], and [221]), neurology [109], biology [194], biomedical sciences [20], epidemi- ogy [17], political analysis and social processes [55], and many other?elds of science and engineering. Although stochastic di?erential equations are quite popular models in the above-mentioned disciplines, there is a lot of mathem- ics behind them that is usually not trivial and for which details are not known to practitioners or experts of other?elds. In order to make this book useful to a wider audience, we decided to keep the mathematical level of the book su?ciently low and often rely on heuristic arguments to stress the underlying ideas of the concepts introduced rather than insist on technical details. Ma- ematically oriented readers may?nd this approach inconvenient, but detailed references are always given in the text. As the title of the book mentions, the aim of the book is twofold.