Probabilistic Risk Analysis and Bayesian Decision Theory
As Bayesians, we try to acknowledge all our uncertainties about data and models, and express them as probability distributions. As we have seen in the preceding chapters, this approach allows us to quantify predictive uncertainty when using our models to
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Bayesian Compendium
Bayesian Compendium
Marcel van Oijen
Bayesian Compendium
123
Marcel van Oijen Edinburgh, UK
ISBN 978-3-030-55896-3 ISBN 978-3-030-55897-0 https://doi.org/10.1007/978-3-030-55897-0
(eBook)
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Preface
Why This Book? The recurring topic during my 35 years in science has been a struggle with uncertainties. My primary field is agricultural, environmental and ecological science using both process-based and statistical models. And in each of my studies, uncertainties in data and models have kept cropping up. I found that the literature contains many ways for classifying and analysing these uncertainties, but they mostly seem based on arbitrary criteria: a confusing menagerie of methods. My encounters with probability theory, and with Bayesian methods in particular, showed that there is no need for confusion; there is a general perspective that can be applied in every case. The online papers by Edwin Jaynes, and his posthumously published book (2003), followed by the more practice-oriented small book by Sivia (2006) did much to clarify matters. Very striking was Jaynes’ explanation of the Cox postulates, which proved that consistent rational thinking requires the use of the rules of probability theory. Jaynes and Sivia took many of their examples from physics, but it was clear that Bayesian probabilistic methods are completely generic and can be applied in any field. It also became clear that the methods do come with some practical problems. They require researchers to think carefully about their prior knowledge before embarking on an analysis. And the Bayesian analysis itself tends to be co
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