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.

In Chapter 4 I construct the Lévy processes (a.k.a. independent increment processes) corresponding to infinitely divisible laws. Section 4.1 provides the requisite information about the pathspace D(ℝN) of right-continuous paths with left limits, and §4.2 gives the construction of Lévy processes with discontinuous paths, the ones corresponding to infinitely divisible laws having no Gaussian part. Finally, in §4.3 I construct Brownian motion, the Lévy process with continuous paths, following the prescription given by Lévy. This section also contains a derivation of Kolmogorov’s continuity criterion for general Banach space-valued stochastic processes.

Laboratory experiments are the type of study that most people have in mind when talking about experiments. In this chapter, we first discuss the strengths of laboratory experiments, which offer the highest degree of experimental control as compared to other types of experiments. Single factors can be manipulated according to the requirements of theories under highly controlled conditions. As such, laboratory experiments are well-placed to test theories. We then introduce a sociological laboratory experiment as a leading example, which we use as a reference for a discussion of several principles of laboratory research. Furthermore, we discuss a second goal of laboratory experiments, which is the establishment of empirical regularities in situations where theory does not provide sufficient guidance for deriving behavioral expectations. The chapter concludes with a short discussion of caveats for the analysis of sociological data generated in laboratory experiments.

In Chapter 10, the book turns to practical considerations. In particular, it surveys the software engineering discipline with its rigorous software testing methods, and asks how these techniques can be adapted to the subfield of machine learning. The adaptation is not straightforward, as machine learning algorithms behave in non-deterministic ways aggravated by data, algorithm, and platform imperfections. These issues are discussed and some of the steps taken to handle them are reviewed. The chapter then turns to the practice of online testing and addresses the ethics of machine learning deployment. The chapter concludes with a discussion of current industry practice along with suggestions on how to improve the safety of industrial deployment in the future.

The intimate connection between Brownian motion of classical potential theory is described in Chapter 11. The first topic is again the representation of solutions to the Dirichlet problem in terms of the exit distribution of Brownian paths from a region. In particular, it is shown that, with probability 1, Brownian paths exit through regular points. This is followed by a discussion of the Poisson problem and its relationship, depending on dimension, to the transience or recurrence of Brownian paths. Among other things, a proof is given of F. Riesz’s representation theorem for superharmonic functions, and this result is used to introduce the concept of capacity. K. L. Chung’s formula for the capacitory potential in term of the last exit distribution of Brownian paths is derived and used to prove Wiener’s test for regularity in terms of capacity. Finally, the chapter concludes with two interesting connections, one made by F. Spitzer and the other by G. Hunt, between Brownian paths and capacity.

Vignette experiments are vignettes are brief descriptions of social objects including a list of varying characteristics, on the basis of which survey respondents state their evaluations or judgments. The respondents’ evaluations typically concern positive beliefs, normative judgments, or their own intentions or actions. Using a study on the gender pay gap and an analysis of trust problems in the purchase of used cars as examples, we discuss the design characteristics of vignettes. Core issues are the selection of the vignettes that are included out of the universe of possible combinations, the type of dependent variables, such as rating scales or ranking tasks, the presentation style, differentiating text vignettes from a tabular format, and issues related to sampling strategies.

Chapter 5 starts with an analysis of the classification metrics presented in Chapter 4, outlining their strengths and weaknesses. It then presents more advanced metrics such as Cohen’s kappa, Youden’s index, and likelihood ratios. This is followed by a discussion about data and classifier complexities such as the class imbalance problem and classifier uncertainty that require particular scrutiny to ensure that the results are trustworthy. The chapter concludes with a detailed discussion of ROC analysis to complement its introduction in Chapter 4, and a presentation of other visualization metrics.