Chapter 2 is devoted to the classical Central Limit Theorem. The initial presentation is based on Lindeberg’s non-Fourier techniques. This is followed by a derivation of the Berry–Esseen estimate based on ideas of C. Stein. Fourier techniques are introduced in §2.3, and in the final section the CLT is used to derive W. Beckner’s sharp Lpestimates for the Fourier transform.

Chapter 6 addresses the problem of error estimation and resampling in both a theoretical and practical manner. The holdout method is reviewed and cast into the bias/variance framework. Simple resampling approaches such as cross-validation are also reviewed and important variations such as stratified cross-validation and leave-one-out are introduced. Multiple resampling approaches such as bootstrapping, randomization, and multiple trials of simple resampling approaches are then introduced and discussed.

Chapter 2 reviews the principles of statistics that are necessary for the discussion of machine learning evaluation methods, especially the statical analysis discussion of Chapter 7. In particular, it reviews the notions of random variables, distributions, confidence intervals, and hypothesis testing.

The discipline of sociology focuses on interactions and group processes from the perspective of emergent phenomena at the social level. Concepts like social embedding, norms, group-level motivation, or status hierarchies can only be defined and conceptualized in contexts in which individuals are involved in social interaction. Such concepts share the property of being social facts that cannot be changed by individual intention alone and that require some element of individual adjustment to the socially given condition. Sociologists study the embeddedness of individual motivations or preferences in the context of social phenomena as such and the impact of these phenomena on individual adaptation. However, these phenomena can only be observed in individual human behavior, and this tension between the substantive focus on the aggregate level and the analytical focus on the individual level is the challenge that sociological experiments confront.

In the introduction, the field of experimental sociology is outlined and the core concepts of manipulation and control, as well as two crucial conditions of control, are introduced. The random allocation of participants to the treatment and the control group ensures that exogenous factors are distributed equally across these groups, which allows to evaluate the effect of the manipulated condition. Incentivization helps operationalizing behavioral assumptions into the experimental condition. The chapter then briefly elaborates on the topics of the following chapters.

Chapter 8 provides an introduction to Gaussian measures on a Banach space from the point of view that originated in the work of N. Wiener and was further developed by L. Gross and I. Segal. The underlying idea is that, even though it cannot fit there, the measure would like to live on the Hilbert space (the Cameron–Martin space) for which it would be the standard Gauss measure, and it is in that Hilbert space that its properties are encoded. A good deal of functional analysis is required to carry out this program, and the estimate that makes the program possible is X. Fernique’s remarkable exponential estimate. Included are derivations of M. Schilder’s large deviations theorem for Brownian motion and V. Strassen’s function space version of the law of the iterated logarithm, both of which confirm the importance of the Cameron–Martin space.

This chapter summarizes the main points of the book and reflects on possible ways ahead for experimental sociology.

This chapter describes three main numerical methods to model hazards which cannot be simplified by analytical expressions (as covered in Chapter 2): cellular automata, agent-based models (ABMs), and system dynamics. Both cellular automata and ABMs are algorithmic approaches while system dynamics is a case of numerical integration. Energy dissipation during the hazard process is a dynamic process, that is, a process that evolves over time. Reanalysing all perils from a dynamic perspective is not always justified, since a static footprint (as defined in Chapter 2) often offers a reasonable approximation for the purpose of damage assessment. However, for some specific perils, the dynamics of the process must be considered for their proper characterization. A variety of dynamic models is presented here, for armed conflicts, blackouts, epidemics, floods, landslides, pest infestations, social unrest, stampedes, and wildfires. Their implementation in the standard catastrophe (CAT) model pipeline is also discussed.