Titlebook: Bayesian Compendium; Marcel van Oijen Textbook 20201st edition Springer Nature Switzerland AG 2020 Bayesian methods.Multidimensionality.Sa

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Introduction to Bayesian Science,In science, we use models to help us learn from data. But we always work with incomplete theory and measurements that contain errors.

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Assigning a Likelihood Function,As scientists, we want to know how to parameterise our models, make comparisons with other models, and quantify model predictive uncertainty. For all these purposes, measurement data are needed, but how exactly should we use the data? The answer is always the same: in the ..

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Sampling from Any Distribution by MCMC,The Bayesian approach to parameter estimation requires modellers to make a major mental shift: we no longer aim to find a single ‘best’ parameter vector—instead we aim to determine the posterior probability distribution for the parameters.

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MCMC and Complex Models,In this chapter we focus on models with multivariate output. That includes most process-based models (PBMs). Models with multivariate output are not 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 ..

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After the Calibration: Interpretation, Reporting, Visualization,This chapter discusses what needs to be done after your Bayesian calibration: how to interpret your results, what to report and how to report it with emphasis on visualization.

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Model Ensembles: BMC and BMA,In this chapter, we discuss how multiple ‘competing’ models can be used simultaneously. There are advantages to having multiple different models, as was already recognized by Chamberlin in the 19th century (Chamberlin 1890).