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Titlebook: Bayesian Compendium; Marcel van Oijen Textbook 2024Latest edition The Editor(s) (if applicable) and The Author(s), under exclusive license

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发表于 2025-3-21 16:34:02 | 显示全部楼层 |阅读模式
期刊全称Bayesian Compendium
影响因子2023Marcel van Oijen
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发行地址Covers process-based models as well as simple regression and shows how Bayesian algorithms work in an accessible way.Includes chapters on model emulation, graphical modelling, hierarchical modelling,
图书封面Titlebook: Bayesian Compendium;  Marcel van Oijen Textbook 2024Latest edition The Editor(s) (if applicable) and The Author(s), under exclusive license
影响因子.This book describes how Bayesian methods work. Aiming to demystify the approach, it explains how to parameterize and compare models while accounting for uncertainties in data, model parameters and model structures. Bayesian thinking is not difficult and can be used in virtually every kind of research.  How exactly should data be used in modelling? The literature offers a bewildering variety of techniques (Bayesian calibration, data assimilation, Kalman filtering, model-data fusion, …). This book provides a short and easy guide to all these approaches and more. Written from a unifying Bayesian perspective, it reveals how these methods are related to one another. Basic notions from probability theory are introduced and executable R codes for modelling, data analysis and visualization are included to enhance the book’s practical use. The codes are also freely available online...This thoroughly revised second edition has separate chapters on risk analysis and decision theory. It also features an expanded text on machine learning with an introduction to natural language processing and calibration of neural networks using various datasets (including the famous iris and MNIST). Literatur
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Deriving the Posterior Distribution,s the information content of our data. So all that is left is to apply Bayes’ Theorem (Eq. (.)) to derive our desired posterior distribution. Note that when talking about the posterior, we use the phrase ‘deriving the’ distribution rather than ‘assigning a’ distribution. That is because Bayes’ Theor
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Markov Chain Monte Carlo Sampling (MCMC),or—instead we aim to determine the posterior probability distribution for the parameters. Only the full probability distribution adequately represents our state of knowledge. Although this shift in thinking has made rigorous uncertainty quantification possible, it has also created computational prob
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MCMC and Multivariate Models,fundamentally different from the simpler models we studied in the previous chapters; we can still write them as functions . of their input consisting of covariates . and parameters .. But the output . from the models will be multivariate, e.g. time series of different properties of an ecosystem. Tha
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Discrepancy,ertainty translates into predictive uncertainty. And if we get new data, then we can use Bayes’ Theorem to update the parameter distribution and thereby reduce our predictive uncertainty. So far, so good. But a more difficult problem is that of uncertainty about model structure. We know that all mod
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Gaussian Processes and Model Emulation,MC algorithms. MCMC is especially slow when the model of interest is a process-based model (PBM) with a long run-time. In such cases, it may be good to replace the PBM with a faster surrogate model. The surrogate model will take the same inputs as the original model but calculate the output more qui
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