In 1788, John Marshall made a prediction that was more prescient than he realized: The federal courts the new Constitution called for would be “the means of preventing disputes with foreign nations.” Marshall could not have known it, but for the next several decades international disputes over persons, ships, and goods caught up in maritime war would wash onto American shores, and into federal courtrooms. The courts’ decisions were essential to the United States’ emergence as a sovereign and independent nation. But preoccupation with Marshall’s famous constitutional rulings has obscured this story of judicial nation-building at sea. And while we have grown accustomed to the idea that “foreign affairs” are the domain of the legislative and executive branches, the political leaders who first tried to solve the puzzle of constitutional governance did not hew to such rigid notions of institutional responsibility. If Marshall’s legacy is the establishment of both judicial and national authority, this book shows that he and his contemporaries did so, first and foremost, at sea.

This chapter explores the newspapers anarchists used to create and disseminate an anarchist Latinidad that was a radical, transnational, anti-capitalist, anticlerical, anti-imperial, and Spanish language-based identity forged initially by US-based migrant anarchists from Spain and Cuba. Using the anarchist press in Florida and New York, anarchists rejected the importance of identifying themselves as “Spanish” or “Cuban” and instead forged a cross-border working-class identity. In creating this identity, anarchists focused on their encounters with US capitalism and republican democracy from 1886 to 1898. Such encounters conditioned their perspectives on what an independent Cuba could look like and what it should avoid. Anarchists also debated whether or not to support the Cuban War for Independence. Was it just another nationalist project that would usher in a new, exploitative ruling elite, or could an independent, non-nationalist anarchist society be constructed? These latter debates began in mid-1891– three and a half years before the mambises launched their uprising against Spanish colonialism.

In this chapter, we describe how to jointly model continuous quantities, by representing them as multiple continuous random variables within the same probability space. We define the joint cumulative distribution function and the joint probability density function and explain how to estimate the latter from data using a multivariate generalization of kernel density estimation. Next, we introduce marginal and conditional distributions of continuous variables and also discuss independence and conditional independence. Throughout, we model real-world temperature data as a running example. Then, we explain how to jointly simulate multiple random variables, in order to correctly account for the dependence between them. Finally, we define Gaussian random vectors which are the most popular multidimensional parametric model for continuous data, and apply them to model anthropometric data.

Some of the key messages of this book are reviewed here in the format of ’reminders’ to clarify the concerns of past misunderstandings and to emphasize solutions to perceived challenges. The importance of basic fundamentals, such as visual assessment, awareness of assumptions and potential numerical solutions is described and then the complementarity of the many statistics and their bases is reviewed. The exciting potential of ongoing developments is summarized, featuring hierarchical Bayesian analysis, spatial causal inference, applications of artificial intelligence (AI), knowledge graphs (KG), literature-based discovery (LBD) and geometric algebra. A quick review of future directions concludes this chapter and the book.

This chapter describes how to model multiple discrete quantities as discrete random variables within the same probability space and manipulate them using their joint pmf. We explain how to estimate the joint pmf from data, and use it to model precipitation in Oregon. Then, we introduce marginal distributions, which describe the individual behavior of each variable in a model, and conditional distributions, which describe the behavior of a variable when other variables are fixed. Next, we generalize the concepts of independence and conditional independence to random variables. In addition, we discuss the problem of causal inference, which seeks to identify causal relationships between variables. We then turn our attention to a fundamental challenge: It is impossible to completely characterize the dependence between all variables in a model, unless they are very few. This phenomenon, known as the curse of dimensionality, is the reason why independence assumptions are needed to make probabilistic models tractable. We conclude the chapter by describing two popular models based on such assumptions: Naive Bayes and Markov chains.

This chapter discusses how to build probabilistic models that include both discrete and continuous variables. Mathematically, this is achieved by defining them as random variables within the same probability space. In practice, the variables are manipulated using their marginal and conditional distributions. We define the conditional pmf of a discrete random variable given a continuous variable, and the conditional probability density of a continuous random variable given a discrete variable. We use these objects to build mixture models and apply them to model height in a population. Next, we describe Gaussian discriminant analysis, a classification method based on mixture models with Gaussian conditional distributions, and apply it to diagnose Alzheimer's disease. Then, we explain how to perform clustering using Gaussian mixture models and leverage the approach to cluster NBA players. Finally, we introduce the framework of Bayesian statistics which enables us to explicitly encode our uncertainty about model parameters, and use it to analyze poll data from the 2020 United States presidential election.

This chapter introduces probability. We begin with an informal definition which enables us to build intuition about the properties of probability. Then, we present a more rigorous definition, based on the mathematical framework of probability spaces. Next, we describe conditional probability, a concept that makes it possible to update probabilities when additional information is revealed. In our first encounter with statistics, we explain how to estimate probabilities and conditional probabilities from data, as illustrated by an analysis of votes in the United States Congress. Building upon the concept of conditional probability, we define independence and conditional independence, which are critical concepts in probabilistic modeling. The chapter ends with a surprising twist: In practice, probabilities are often impossible to compute analytically! Fortunately, the Monte Carlo method provides a pragmatic solution to this challenge, allowing us to approximate probabilities very accurately using computer simulations. We apply w 3 × 3 basketball tournament from the 2020 Tokyo Olympics.

This chapter wraps up the arguments and delineates possible avenues ahead for central banks. Central banks may become Banks of the State, financing government deficits as they have done recently. This may imply a retreat from central bank independence. With large holdings of public securities in central bank balance sheets, the pressure to finance governments would increase. Another option is for central banks to change their job profile, becoming Banks for Everybody. This would happen if they decided to issue all-purpose retail central bank digital currencies. This would risk weakening private initiative in the payment industry, a sector where private markets have worked well recently. The third avenue is for central banks to remain Banks of the Banks, the dominant model that prevailed until the Great Financial Crisis of 2008–09. Central banks would continue to exert rigorous surveillance and use their regulatory powers to encourage further progress and foster efficiency and stability in the underlying settlement infrastructures. We express support for this line but also highlight some challenges, first and foremost the regulation of crypto assets and the extension of safety nets and central bank competence on “shadow banking,” the growing unregulated segment of financial markets.

This chapter traces social medicine to Shibli Shumayyil, a medical doctor and key figure of the Nahḍa, an intellectual and cultural movement that spanned from the late nineteenth century to the outbreak of the First World War. He envisioned social medicine as a tool for social reform, diagnosing its social ills, and proposing a cure. Shumayyil and his successors rejected the colonial justification of social medicine, instead promoting social medicine as a means to free people from all kinds of oppression, ignorance, and injustice. Throughout the twentieth century until today, as poverty, authoritarianism, and social conflicts escalated in the Arab world, doctors increasingly became advocates for the marginalized, the poor, and the oppressed. The chapter examines the work of several revolutionary doctors in Tunisia, Sudan, and Egypt, who used their practice as a form of protest, praxis, and critique. Not only did these doctors embody the meaning that Guérin originally gave to social medicine but they also incorporated Shumayyil’s idea of medicine as a form of progressive clinical sociology.

Guarantor institutions (such as electoral commissions and anti-corruption watchdogs, which supposedly comprise the so-called ‘fourth’ or ‘integrity’ branch of the state) are increasingly of interest to constitutional scholars. In a given political context, a guarantor institution is a tailor-made constitutional institution, vested with material as well as expressive capacities, whose function is to provide a credible and enduring guarantee to a specific non-self-enforcing constitutional norm (or any aspect thereof). Arguing that guarantor institutions are more trustee-like than agent-like in character, this chapter defends the claim that the design of any guarantor institutions should seek to ensure that it has: (i) sufficient expertise and capacity to perform its functions effectively; (ii) sufficient independence from political, economic, or social actors with an interest in frustrating the relevant norm it is meant to guarantee; and (iii) sufficient accountability to bodies with an interest in upholding the relevant norm.

The demise of the League of Nations did not lead to the end of colonial membership at international organisations. Chapter Six examines how the League’s legacy of colonial membership continued under the United Nations. Despite not being fully independent, the Indian National Congress would appoint India’s delegation at the first General Assembly in 1946, resulting in a very different international personality. No longer constrained and gagged by British appointees and the imperial conference, India would aggressively pursue its longstanding grievances against South Africa, destroying the ideal of inter se, and effectively ending the British ideal of colonial membership at international organisations. Instead, this chapter reveals how the end of the legacy of colonial membership went beyond the British Empire, and was replicated by the Soviet Union in the accession of Soviet Belorussia and Ukraine. Neither of these member states would become independent until 1991.

As the Irish Free State came into being, Egypt too was declared independent. Whilst in Ireland, League membership was rapidly forthcoming, negotiations for Egypt’s accession were protracted, with Egypt acceding in 1937, the last member state to join the League. Chapter Five investigates why Egypt, which was never formally a colony of the British Empire and from 1922 deemed an independent state, was obstructed by Britain from joining the League for fifteen years. This chapter examines the contested relationship between the Egyptian nationalist Wafd party, that sought Egyptian independence, and Britain, that sought Egyptian acquiescence to a treaty of alliance. Egypt’s contested accession to the League reveals the risks that colonial membership to the League posed to British imperial policy, and how Britian could act as a gatekeeper for the accession of their colonies to the League. Finally, this chapter reveals how the actions of another imperial party, Italy, and its growing encroachment into North-East Africa would ultimately lead to a compromise that would see Egypt’s accession to the League.

We introduce the concepts of a map, a sigma-field generated by a map and the measurability of a map. This leads to the notion of random variable on a probability space, which is just a map being measurable with respect to the considered sigma-field. This guarantees that the distribution of a random variable is well-defined on a given probability space. Next, we review the main families of random variables, discrete (uniform, Bernoulli, binomial) and continuous (uniform, exponential, normal, log-normal), and recall their mass and density functions, as well as their cumulative distribution functions. In particular, we highlight that any random variable can be built by transforming a continuous uniform random variable in an appropriate manner, following the probability integral transform. Finally, we introduce random vectors (vector of random variables), joint and marginal distributions, and the independence property. We illustrate those concepts on toy examples as well as on our stock price model, computing the distribution of prices at various points in time. We explain how correlation can significantly impact the risk of a portfolio of stocks in simple discrete models.

We introduce the concepts of sample space, sigma-field, and probability measure, which are the three components defining a probability space. We explain that, in general, many probability measures can be associated to a given sample space; which one to pick depends on the problem. Similarly, the list of events for which the probability can be computed in a given problem is the smallest sigma-field built from the events for which the probability is known from the problem. The discrete sigma-field corresponds to the special case where the information provided is substantial enough to yield the probability of every event. This establishes the connection between the concept of information and sigma-field, and shows that the latter is the appropriate structure to serve as definition domain of probability measures. We conclude the chapter with the concept of independence between events and between sigma-fields. Those concepts are illustrated on various examples featuring coins and colored dice. We conclude the chapter by proposing a first model to describe future stock prices.

Chapter 7 is the conclusion of the book and traces how trends set by imperial historians of the nineteenth century framed the Tailors’ conspiracy as dangerous and as an isolated phenomenon while championing the 1789 conspiracy in Minas Gerais as foundational to Brazilian independence. Historians of the twentieth century rightly combated those efforts and fought to establish the conspiracy as equally significant as the plot in Minas Gerais. The book ends with the proposition that historians of the Tailors’ Conspiracy no longer need to do this kind of work. Instead, this book demonstrates the richness that comes from studying the conspiracy in an empire-wide context and in studying it from the vantage point of relations and not simply from the vantage points of ideology and rhetoric.

There were practical limits to these political imaginaries and projects. People needed to work, and the war was a source of employment for many displaced people. This chapter explores the parallel systems of governance in Khartoum that southern militia-running businessmen (including Kerubino Kuanyin Bol, Paulino Matip, Abdel Bagi Ayii Akol, and others) organised in Khartoum, including their own prisons, barracks, and offices. Many residents drew on their jobs, sympathetic policing, and ‘traditional’ courts, but these rebel authorities also propagated their own ideas of future structures of political community based on regional zones of ethno-political authority. This is an unrecorded history of militia governance, looking beyond these authorities’ immediate mercenary aims and exploring their leadership’s and members’ own critiques of governance and models of power. This sets a challenge to current studies of rebel governance systems, which rarely examine pro-government proxy militias. It also outlines how the more creative, inclusive, and imaginative intellectual work detailed in this book was undermined (and ultimately buried) by these wartime exigencies and practical (if mercenary) structures of militia work and ethnic self-defence.