Christian Gollier
- Published in print:
- 2012
- Published Online:
- October 2017
- ISBN:
- 9780691148762
- eISBN:
- 9781400845408
- Item type:
- chapter
- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691148762.003.0006
- Subject:
- Economics and Finance, Development, Growth, and Environmental
This chapter shows how the probability distribution for economic growth is subject to some parametric uncertainty. There is a limited data set for the dynamics of economic growth, and the absence of ...
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This chapter shows how the probability distribution for economic growth is subject to some parametric uncertainty. There is a limited data set for the dynamics of economic growth, and the absence of a sufficiently large data set to estimate the long-term growth process of the economy implies that its parameters are uncertain and subject to learning in the future. This problem is particularly crucial when its parameters are unstable, or when the dynamic process entails low-probability extreme events. Thus, the rarer the event, the less precise the estimate of its likelihood. This builds a bridge between the problem of parametric uncertainty, and the one of extreme events.Less
This chapter shows how the probability distribution for economic growth is subject to some parametric uncertainty. There is a limited data set for the dynamics of economic growth, and the absence of a sufficiently large data set to estimate the long-term growth process of the economy implies that its parameters are uncertain and subject to learning in the future. This problem is particularly crucial when its parameters are unstable, or when the dynamic process entails low-probability extreme events. Thus, the rarer the event, the less precise the estimate of its likelihood. This builds a bridge between the problem of parametric uncertainty, and the one of extreme events.
Stefan Thurner, Rudolf Hanel, and Peter Klimekl
- Published in print:
- 2018
- Published Online:
- November 2018
- ISBN:
- 9780198821939
- eISBN:
- 9780191861062
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780198821939.003.0002
- Subject:
- Physics, Theoretical, Computational, and Statistical Physics
Phenomena, systems, and processes are rarely purely deterministic, but contain stochastic,probabilistic, or random components. For that reason, a probabilistic descriptionof most phenomena is ...
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Phenomena, systems, and processes are rarely purely deterministic, but contain stochastic,probabilistic, or random components. For that reason, a probabilistic descriptionof most phenomena is necessary. Probability theory provides us with the tools for thistask. Here, we provide a crash course on the most important notions of probabilityand random processes, such as odds, probability, expectation, variance, and so on. Wedescribe the most elementary stochastic event—the trial—and develop the notion of urnmodels. We discuss basic facts about random variables and the elementary operationsthat can be performed on them. We learn how to compose simple stochastic processesfrom elementary stochastic events, and discuss random processes as temporal sequencesof trials, such as Bernoulli and Markov processes. We touch upon the basic logic ofBayesian reasoning. We discuss a number of classical distribution functions, includingpower laws and other fat- or heavy-tailed distributions.Less
Phenomena, systems, and processes are rarely purely deterministic, but contain stochastic,probabilistic, or random components. For that reason, a probabilistic descriptionof most phenomena is necessary. Probability theory provides us with the tools for thistask. Here, we provide a crash course on the most important notions of probabilityand random processes, such as odds, probability, expectation, variance, and so on. Wedescribe the most elementary stochastic event—the trial—and develop the notion of urnmodels. We discuss basic facts about random variables and the elementary operationsthat can be performed on them. We learn how to compose simple stochastic processesfrom elementary stochastic events, and discuss random processes as temporal sequencesof trials, such as Bernoulli and Markov processes. We touch upon the basic logic ofBayesian reasoning. We discuss a number of classical distribution functions, includingpower laws and other fat- or heavy-tailed distributions.
Cang Hui and David M. Richardson
- Published in print:
- 2017
- Published Online:
- March 2017
- ISBN:
- 9780198745334
- eISBN:
- 9780191807046
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198745334.003.0004
- Subject:
- Biology, Ecology, Biomathematics / Statistics and Data Analysis / Complexity Studies
The spreading dynamics of invasive species in their novel range is often faster and has greater variability than would be predicted from diffusion-based models, which leads to an underestimation of ...
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The spreading dynamics of invasive species in their novel range is often faster and has greater variability than would be predicted from diffusion-based models, which leads to an underestimation of rates of spread and often to delayed intervention which reduces the efficient of management. Diverse mechanisms that underpin such boosted range expansion and invasion performance are related to either altered biotic interactions with other species (e.g. enemy release) or readjustment of the invader’s life-history strategies, especially due to augmented dispersal and rapid adaptation at the advancing range margin. This chapter deals with boosted range expansion due to the readjustment of life-history strategies. Key mechanisms include long-distance dispersal, human-mediated translocation, the rapid evolution of dispersal and life-history traits, and spatial sorting. An integrated framework based on joint mechanisms of fat-tailed dispersal and spatial selection at the advancing edge is presented to explain boosted range expansion.Less
The spreading dynamics of invasive species in their novel range is often faster and has greater variability than would be predicted from diffusion-based models, which leads to an underestimation of rates of spread and often to delayed intervention which reduces the efficient of management. Diverse mechanisms that underpin such boosted range expansion and invasion performance are related to either altered biotic interactions with other species (e.g. enemy release) or readjustment of the invader’s life-history strategies, especially due to augmented dispersal and rapid adaptation at the advancing range margin. This chapter deals with boosted range expansion due to the readjustment of life-history strategies. Key mechanisms include long-distance dispersal, human-mediated translocation, the rapid evolution of dispersal and life-history traits, and spatial sorting. An integrated framework based on joint mechanisms of fat-tailed dispersal and spatial selection at the advancing edge is presented to explain boosted range expansion.
Gary Smith and Jay Cordes
- Published in print:
- 2019
- Published Online:
- September 2019
- ISBN:
- 9780198844396
- eISBN:
- 9780191879937
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780198844396.003.0004
- Subject:
- Mathematics, Applied Mathematics, Numerical Analysis
Data-mining tools, in general, tend to be mathematically sophisticated, yet often make implausible assumptions. For example, analysts often assume a normal distribution and disregard the fat tails ...
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Data-mining tools, in general, tend to be mathematically sophisticated, yet often make implausible assumptions. For example, analysts often assume a normal distribution and disregard the fat tails that warn of “black swans.” Too often, the assumptions are hidden in the math and the people who use the tools are more impressed by the math than curious about the assumptions. Instead of being blinded by math, good data scientists use explanatory variables that make sense. Good data scientists use math, but do not worship it. They know that math is an invaluable tool, but it is not a substitute for common sense, wisdom, or expertise.Less
Data-mining tools, in general, tend to be mathematically sophisticated, yet often make implausible assumptions. For example, analysts often assume a normal distribution and disregard the fat tails that warn of “black swans.” Too often, the assumptions are hidden in the math and the people who use the tools are more impressed by the math than curious about the assumptions. Instead of being blinded by math, good data scientists use explanatory variables that make sense. Good data scientists use math, but do not worship it. They know that math is an invaluable tool, but it is not a substitute for common sense, wisdom, or expertise.
Neal V. Dawson and Pierpaolo Andriani
- Published in print:
- 2020
- Published Online:
- July 2020
- ISBN:
- 9780190880743
- eISBN:
- 9780190880774
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780190880743.003.0010
- Subject:
- Public Health and Epidemiology, Public Health, Epidemiology
The normal distribution has been useful to the field of population health—appropriately describing the distribution of many outcomes and serving as a foundation for powerful statistical analyses. But ...
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The normal distribution has been useful to the field of population health—appropriately describing the distribution of many outcomes and serving as a foundation for powerful statistical analyses. But not all outcomes are normally distributed, and this chapter reminds readers of the importance of recognizing, empirically testing for this case, and using appropriate distributional functions to characterize outcomes or as the foundation for statistical and other models. The chapter begins by briefly highlighting several common examples in which nonnormal distributions are used in population health research and then describes two examples in more detail where tremendous meaning is found in recognizing nonnormality. The first is focused on “spectral effects,” variables that contextualize—or change—the relationship between predictor variables and outcomes. These relationships are only illuminated when subpopulations are disaggregated. The second example describes power law distributions and the phenomena that generate them—long recognized but understudied in population health.Less
The normal distribution has been useful to the field of population health—appropriately describing the distribution of many outcomes and serving as a foundation for powerful statistical analyses. But not all outcomes are normally distributed, and this chapter reminds readers of the importance of recognizing, empirically testing for this case, and using appropriate distributional functions to characterize outcomes or as the foundation for statistical and other models. The chapter begins by briefly highlighting several common examples in which nonnormal distributions are used in population health research and then describes two examples in more detail where tremendous meaning is found in recognizing nonnormality. The first is focused on “spectral effects,” variables that contextualize—or change—the relationship between predictor variables and outcomes. These relationships are only illuminated when subpopulations are disaggregated. The second example describes power law distributions and the phenomena that generate them—long recognized but understudied in population health.
James Moore and Niels Pedersen
- Published in print:
- 2014
- Published Online:
- December 2014
- ISBN:
- 9780198719243
- eISBN:
- 9780191788505
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198719243.003.0003
- Subject:
- Business and Management, Pensions and Pension Management
While short-run forecasting has value for financial entertainment and speculation, in the United States and much of the developed world, there is perhaps no field where long-run forecasting has wider ...
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While short-run forecasting has value for financial entertainment and speculation, in the United States and much of the developed world, there is perhaps no field where long-run forecasting has wider implications for personal welfare than that of forecasting asset returns. This chapter motivates and describes a regime-switching macro-driven simulation model for the purposes of simulating long horizon asset returns. The paths generated by this model are compared to more common approaches—multivariate normal generators and a block bootstrap simulation. Despite calibration to the same mean and variance in returns, the models display divergent behavior in the tails of long horizon return simulations. Simulations are run through representative defined contribution and defined benefit applications in order to examine the filtered behavior and draw inferences for future applied research and application.Less
While short-run forecasting has value for financial entertainment and speculation, in the United States and much of the developed world, there is perhaps no field where long-run forecasting has wider implications for personal welfare than that of forecasting asset returns. This chapter motivates and describes a regime-switching macro-driven simulation model for the purposes of simulating long horizon asset returns. The paths generated by this model are compared to more common approaches—multivariate normal generators and a block bootstrap simulation. Despite calibration to the same mean and variance in returns, the models display divergent behavior in the tails of long horizon return simulations. Simulations are run through representative defined contribution and defined benefit applications in order to examine the filtered behavior and draw inferences for future applied research and application.
Thomas Noe and H. Peyton Young
- Published in print:
- 2014
- Published Online:
- October 2014
- ISBN:
- 9780198712220
- eISBN:
- 9780191780752
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198712220.003.0003
- Subject:
- Economics and Finance, Financial Economics, Economic Systems
Performance bonuses have become commonplace in financial institutions and now constitute a major part of employee compensation. Such practice followed academic work on principal-agent contracts, ...
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Performance bonuses have become commonplace in financial institutions and now constitute a major part of employee compensation. Such practice followed academic work on principal-agent contracts, which argued that bonuses would better align the interests of managers and shareholders. This chapter argues that such schemes are not well-suited to aligning these interests for two reasons. First, new financial products make it easy to create the appearance of superior performance over long periods of time, with the outsize returns driven by hidden tail risk. Second, the complexity of new products and the size of financial institutions make it extremely difficult (and costly) to monitor risky activities directly. Compensation schemes are inefficient because it is easy to escape detection for long periods of time. A greater emphasis on ethical values, reflecting duty of care to customers, clients, and shareholders, is more likely to produce effective reforms.Less
Performance bonuses have become commonplace in financial institutions and now constitute a major part of employee compensation. Such practice followed academic work on principal-agent contracts, which argued that bonuses would better align the interests of managers and shareholders. This chapter argues that such schemes are not well-suited to aligning these interests for two reasons. First, new financial products make it easy to create the appearance of superior performance over long periods of time, with the outsize returns driven by hidden tail risk. Second, the complexity of new products and the size of financial institutions make it extremely difficult (and costly) to monitor risky activities directly. Compensation schemes are inefficient because it is easy to escape detection for long periods of time. A greater emphasis on ethical values, reflecting duty of care to customers, clients, and shareholders, is more likely to produce effective reforms.
