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NEW CONCEPTS AND METHODS—PRE-BAYESIAN ERA

Shoutir Kishore Chatterjee

in Statistical Thought: A Perspective and History

After James Bernoulli, the main contributors to probability theory and its applications in the 18th century worked either to solve more intricate problems of games of chance (De Moivre), or to build ... More

After James Bernoulli, the main contributors to probability theory and its applications in the 18th century worked either to solve more intricate problems of games of chance (De Moivre), or to build new probability models (De Moivre, Daniel Bernoulli). Further, some of them used probabilistic arguments to test hypotheses about or to estimate parameters involved in probability models for real life phenomena in the fields of demography, astronomy, and theory of errors. The concept of continuous variables, the tool of generating functions, the normal model approximation to the binomial, and ‘the rational expectation principle’ (in the context of the St. Petersburg Paradox) emerged out of these studies.Less

Heat in the Eighteenth Century

Jennifer Coopersmith

in Energy, the Subtle Concept: The discovery of Feynman's blocks from Leibniz to Einstein

Connections between ‘airs’ and heat emerged. Hales, in Vegetable Staticks, liberated ‘airs’ on heating various substances, and concluded that there was a repulsive force in ‘elastick air’. This was ... More

Connections between ‘airs’ and heat emerged. Hales, in Vegetable Staticks, liberated ‘airs’ on heating various substances, and concluded that there was a repulsive force in ‘elastick air’. This was consistent with a speculation of Newton’s, and with Boyle’s ‘spring of the air’. Thus, a static model of gas pressure was developed. Boerhaave had ‘fire’ as a universal causal agent and established the morphology of heat studies. He initiated the material (substance or subtle-fluid) theory of heat, but rejected the contemporaneous phlogiston theory. Daniel Bernoulli proposed a kinetic theory of gases (in Hydrodynamica) and calculated the ‘live force contained within an elastic fluid’. The iconic formula, PdV, could be glimpsed for the first time. Also, Amontons’ experimental finding—that pressure is proportional to temperature—was given a theoretical underpinning. Newcomen’s revolutionary atmospheric engine was the first true steam engine, with a piston in a cylinder and valves, and truly self-acting.Less

Epidemiology

Paul Schmid-Hempel

in Evolutionary Parasitology: The Integrated Study of Infections, Immunology, Ecology, and Genetics

This chapter discusses ‘epidemiology’, which in medical literature refers to the field that seeks to identify key correlates for a particular disease. In this book, however, it is the study of ... More

This chapter discusses ‘epidemiology’, which in medical literature refers to the field that seeks to identify key correlates for a particular disease. In this book, however, it is the study of host–parasite population dynamics as a branch of population biology and population genetics. Beginning with the Swiss mathematician Daniel Bernoulli, who used a mathematical model to analyse the dynamics of a small-pox epidemic in Paris, epidemiology provides a great help to the study of evolutionary parasitology. The classical Nicholson-Bailey model is one example of an epidemiology model that analyses host–parasitoid systems. The chapter examines other models, such as SIR-models, in order to further analyse the epidemiology of hosts and their microparasites. It also talks about the epidemiology of vectored microparasites, like malaria, which can also similarly be analysed with modified SIR-models such as the classical Ross-Macdonald model.Less

Calculated Collaborations

in Tides of History: Ocean Science and Her Majesty's Navy

It was local tide calculators, not elite theorists, who advanced the study of the tides in the late eighteenth and early nineteenth centuries, perfecting Daniel Bernoulli's equilibrium theory through ... More

It was local tide calculators, not elite theorists, who advanced the study of the tides in the late eighteenth and early nineteenth centuries, perfecting Daniel Bernoulli's equilibrium theory through their own extended observations. In fact, the tide tables in port cities such as Liverpool and Bristol were exceedingly, even exceptionally, accurate. This chapter analyzes William Whewell's close collaboration with those practitioners he termed “subordinate laborers,” a diverse group who worked alongside the scientific servicemen and scientific elite. In particular, it focuses on the contributions of expert calculators to large-scale geophysical research. Not only were these diligent men of numbers the first to bring the data to the natural philosophers, but they first applied the results to the construction of tables, and thus to the testing of theory. Their ingenuity with difficult calculations made them indispensable for Whewell's tidology. Though they began as calculators Whewell desired “to keep at work,” they actively contributed to his tidology: they tested his theories, advanced his methods, and suggested new avenues of research.Less

The Case of Incomplete Markets: Relating Risk Premiums to Economic Fundamentals

Gilles Bénéplanc and Jean-Charles Rochet

in Risk Management in Turbulent Times

This chapter talks about the expected utility criterion, which solves the St Petersburg paradox proposed in the 18th century by Nicolas Bernoulli. The criterion is useful in modeling insurance ... More

This chapter talks about the expected utility criterion, which solves the St Petersburg paradox proposed in the 18th century by Nicolas Bernoulli. The criterion is useful in modeling insurance decisions and modeling equilibrium prices in the markets where risks are exchanged. However, the equilibrium approach to the assessment of risk premiums has its limits and does not match the observed behavior of individuals who are uncertain about the probability distributions of risks.Less