This chapter focuses on different research designs in experimental sociology. Most definitions of what constitutes an experiment converge on the idea that the experimenter "control" the phenomenon under investigation, thereby setting the conditions under which the phenomenon is observed and analyzed. Typically, the researcher exerts experimental control by creating two situations that are virtually identical, except for one element that the researcher introduces or manipulates in only one of the situations. The purpose of this exercise is to observe the effects of such manipulation by comparing it with the outcomes of the situation in which the manipulation is absent. One way to look at how the implementation of this rather straightforward exercise produces a variety of designs is by focusing on the relationship that experimental design bears with the theory that inspires it. Therefore, we begin this chapter with a discussion of the relationship between theory and experimental design before turning to a description of the most important features of various types of designs. The chapter closes with a short overview of experiments in different settings such as laboratory, field, and multifactorial survey experiments.

Chapter 6 opens with extensions of martingale theory in two directions: to σ-finite measures and to random variables with values in a Banach space. In §6.2 I prove Burkholder’s Inequality for martingales with values in a Hilbert space. The derivation that I give is essentially the same as Burkholder’s second proof, the one that gives optimal constants. Finally, the results in §6.1 are used in §6.3 to derive Birkhoff’s Individual Ergodic Theorem and a couple of its applications.

Section 7.1 provides a brief introduction to the theory of martingales with a continuous parameter. As anyone at all familiar with the topic knows, anything approaching a full account of this theory requires much more space than a book like this can provide. Thus, I deal with only its most rudimentary aspects, which, fortunately, are sufficient for the applications to Brownian motion that I have in mind. Namely, in §7.2 I first discuss the intimate relationship between continuous martingales and Brownian motion (Lévy’s martingale characterization of Brownian motion), then derive the simplest (and perhaps most widely applied) case of the Doob–Meyer Decomposition Theory, and finally show what Burkholder’s Inequality looks like for continuous martingales. In the concluding section, §7.3, the results in §7.1 and §7.2 are applied to derive the Reflection Principle for Brownian motion.

Chapter 12 is the conclusion. It presents a discussion of how the components of performance evaluation for learning algorithms discussed throughout the book unify into an overall framework for in-laboratory evaluation. This is followed by a discussion of how to move from a laboratory setting to a deployment setting based on the material covered in the last part of the book. We then discuss the potential social consequences of machine learning technology deployment together with their causes, and advocate for the consideration of these consequences as part of the evaluation framework. We follow this discussion with a few concluding remarks.

Experimental practices developed in different scientific disciplines following different historical trajectories. Thus, standard experimental procedures differ starkly between disciplines. One of the most controversial issues is the use of deception as a methodological device. Psychologists do not conduct a study involving deception unless they have determined that the use of deceptive techniques is justified by the study’s significant prospective scientific, educational, or applied value and that effective nondeceptive alternative procedures are not feasible. In experimental economics it is strictly forbidden and a ban on experiments involving deception is enforced by all major economic journals. In the sociological scientific community, there is no clear consensus on the matter. Importantly, the disagreement is sometimes based on ethical considerations, but more often it is based on pragmatic grounds: the anti-deception camp argues that deceiving participants leads to invalid results, while the other side argues that deception has little negative impact and, under certain conditions, can even enhance validity. In this chapter, we first discuss the historical reasons leading to the emergence of such different norms in different fields and then analyze and separate ethical and pragmatic concerns. Finally, we propose some guidelines to regulate the use of deception in sociological experiments.

This chapter is devoted to the study of infinitely divisible laws. It begins in §3.1 with a few refinements (especially the Lévy Continuity Theorem) of the Fourier techniques introduced in §2.3. These play a role in §3.2, where the Lévy–Khinchine formula is first derived and then applied to the analysis of stable laws.

This chapter provides the tools to compute catastrophe (CAT) risk, which represents a compound measure of the likelihood and magnitude of adverse consequences affecting structures, individuals, and valuable assets. The process consists of first establishing an inventory of assets (here real or simulated) exposed to potential hazards (exposure module). Estimating the expected damage resulting from a given hazard load (according to Chapter 2) is the second crucial step in the assessment process (vulnerability module). The application of damage functions to exposure data forms the basis for calculating loss estimates (loss module). To ensure consistency across perils, the mean damage ratio is used as the main measure for damage footprints D(x,y), with the final loss footprints simply expressed as L(x,y) = D(x,y) × ν(x,y), where ν(x,y) represents the exposure footprint. Damage functions are provided for various hazard loads: blasts (explosions and asteroid impacts), earthquakes, floods, hail, landslides, volcanic eruptions, and wind.