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標(biāo)題: Titlebook: Bayesian Compendium; Marcel van Oijen Textbook 2024Latest edition The Editor(s) (if applicable) and The Author(s), under exclusive license [打印本頁]

作者: CULT    時間: 2025-3-21 16:34
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作者: CAMEO    時間: 2025-3-21 21:46

作者: 善于騙人    時間: 2025-3-22 03:24

作者: 遠(yuǎn)地點(diǎn)    時間: 2025-3-22 07:07
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 ‘a(chǎn)ssigning a’ distribution. That is because Bayes’ Theor
作者: Magisterial    時間: 2025-3-22 10:45
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
作者: 記憶法    時間: 2025-3-22 15:17
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
作者: Adherent    時間: 2025-3-22 18:20

作者: Contracture    時間: 2025-3-22 21:52
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
作者: 被詛咒的人    時間: 2025-3-23 01:41

作者: Substance-Abuse    時間: 2025-3-23 09:07
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
作者: Custodian    時間: 2025-3-23 11:59
Graphical Modelling,(2) information about the nodes. So the graph is just the visible part of the model. GMs do not represent a new kind of statistical model; they are just helpful tools for analysing joint probability distributions. Every distribution can be represented by a GM, so whatever your research problem or mo
作者: catagen    時間: 2025-3-23 17:19

作者: 大方不好    時間: 2025-3-23 18:42

作者: 要控制    時間: 2025-3-24 00:35
Bayesian Decision Theory,red, . (BDT) (Berger, . (2nd ed.). Springer Series in Statistics. Springer, 1985; Jaynes, .. Cambridge University Press, 2003; Lindley, . (2nd ed.). Wiley, 1991; Van Oijen and Brewer, ., SpringerBriefs in Statistics. Springer International Publishing, 2022; Williams and Hooten (Ecol Appl 26:1930–194
作者: EPT    時間: 2025-3-24 05:25
Graphs, Hypergraphs, and Metagraphst does not affect the principles of Bayesian calibration in any way but may complicate its execution. In this chapter, we illustrate these issues with a quite simple PBM that as output produces two time series: the growth over time of the biomass and leaf area of vegetation.
作者: Ballad    時間: 2025-3-24 09:04
Integrated Series in Information Systemsckly. However, its output cannot be exactly the same as that of the original model, so it just provides an approximation. If the surrogate model is a statistical model that produces not just the approximative prediction of what the original model would have produced, but a whole probability distribution, then it is called a ., or just . for short.
作者: KEGEL    時間: 2025-3-24 11:17
del emulation, graphical modelling, hierarchical modelling, .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
作者: Provenance    時間: 2025-3-24 16:36
Integrated Series in Information Systems(or more succinctly as .), where as usual . can be multi-dimensional. It is the answer to the question: ’what is the probability of measuring . if the true value is .?’. This can be written formally as follows:
作者: Ebct207    時間: 2025-3-24 21:01

作者: 壯麗的去    時間: 2025-3-25 01:08
Image Segmentation by Gaussian Mixture,er vector was always a fully specified distribution, e.g. the product of known univariate Gaussians. In . (BHM), we do not specify the prior that directly. Instead we make the prior distribution depend on other parameters, which we call .. Here is a table of the differences:
作者: OWL    時間: 2025-3-25 04:45
Prajna Kunche,K. V. V. S. Reddyiley, 1991; Van Oijen and Brewer, ., SpringerBriefs in Statistics. Springer International Publishing, 2022; Williams and Hooten (Ecol Appl 26:1930–1942, 2016). In BDT, every decision problem has three main ingredients:
作者: GLUE    時間: 2025-3-25 10:40

作者: Gustatory    時間: 2025-3-25 13:43
Deriving the Posterior Distribution,t when talking about the posterior, we use the phrase ‘deriving the’ distribution rather than ‘a(chǎn)ssigning a’ distribution. That is because Bayes’ Theorem tells us exactly what the posterior distribution should be once we have defined our prior and likelihood.
作者: Custodian    時間: 2025-3-25 18:55
Bayesian Hierarchical Modelling,er vector was always a fully specified distribution, e.g. the product of known univariate Gaussians. In . (BHM), we do not specify the prior that directly. Instead we make the prior distribution depend on other parameters, which we call .. Here is a table of the differences:
作者: BILK    時間: 2025-3-25 21:10

作者: CYT    時間: 2025-3-26 03:29
Textbook 2024Latest editionfor 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,
作者: happiness    時間: 2025-3-26 06:02
Metagraphs and Their Applicationsrom probability distributions that are not in closed form was provided by Metropolis et al. (J Chem Phys 21:1087–1092, 1953). They introduced the so-called Markov Chain Monte Carlo (MCMC) method. MCMC is the workhorse of computational Bayesian statistics, and by now, many different MCMC algorithms exist.
作者: Soliloquy    時間: 2025-3-26 11:56
https://doi.org/10.1007/978-0-387-37234-1 have no clear idea which of the available models is the best for a given research question. So how can Bayesian thinking help with these issues? Well, as you will expect, the proper Bayesian approach is to quantify our uncertainty about model structure. One way to do that is by following Chamberlin’s advice to use multiple models.
作者: recede    時間: 2025-3-26 16:38

作者: 斷斷續(xù)續(xù)    時間: 2025-3-26 16:50
Model Ensembles: BMC and BMA, have no clear idea which of the available models is the best for a given research question. So how can Bayesian thinking help with these issues? Well, as you will expect, the proper Bayesian approach is to quantify our uncertainty about model structure. One way to do that is by following Chamberlin’s advice to use multiple models.
作者: HALL    時間: 2025-3-26 22:42

作者: 表兩個    時間: 2025-3-27 02:18

作者: 單純    時間: 2025-3-27 05:17

作者: 繁重    時間: 2025-3-27 10:33

作者: 積云    時間: 2025-3-27 13:43
MCMC and Multivariate Models,t does not affect the principles of Bayesian calibration in any way but may complicate its execution. In this chapter, we illustrate these issues with a quite simple PBM that as output produces two time series: the growth over time of the biomass and leaf area of vegetation.
作者: Chronic    時間: 2025-3-27 21:37
Gaussian Processes and Model Emulation,ckly. However, its output cannot be exactly the same as that of the original model, so it just provides an approximation. If the surrogate model is a statistical model that produces not just the approximative prediction of what the original model would have produced, but a whole probability distribution, then it is called a ., or just . for short.
作者: Cardioversion    時間: 2025-3-28 00:04

作者: 摻和    時間: 2025-3-28 02:55
Metagraphs and Their Applications. A prior expresses uncertainty arising from incomplete knowledge, and whatever the subject is, people have different knowledge and expertise. So instead of speaking of ’the prior probability of .’, each of us should say ’my prior probability for .’. We . a prior probability distribution; we do not
作者: defeatist    時間: 2025-3-28 07:31

作者: neutral-posture    時間: 2025-3-28 11:58
Metagraphs in Data and Rule Managements 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 ‘a(chǎn)ssigning a’ distribution. That is because Bayes’ Theor
作者: 發(fā)電機(jī)    時間: 2025-3-28 15:00

作者: PANT    時間: 2025-3-28 19:15
Graphs, Hypergraphs, and Metagraphsfundamentally 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
作者: THROB    時間: 2025-3-28 23:12

作者: Aqueous-Humor    時間: 2025-3-29 06:21

作者: Colonnade    時間: 2025-3-29 08:25
Metagraphs in Workflow and Process Analysisata likelihood function. The posterior distribution is then fully determined, and it encapsulates everything of interest. With the posterior in hand, we can make predictions with proper uncertainty quantification, we can carry out risk analysis and provide decision support. So the basic ideas are ex
作者: 暗諷    時間: 2025-3-29 15:13

作者: 捐助    時間: 2025-3-29 16:48
The Algebraic Structure of Metagraphs(2) information about the nodes. So the graph is just the visible part of the model. GMs do not represent a new kind of statistical model; they are just helpful tools for analysing joint probability distributions. Every distribution can be represented by a GM, so whatever your research problem or mo
作者: LAVA    時間: 2025-3-29 21:42

作者: Tractable    時間: 2025-3-30 02:30
Erik Cuevas,Alberto Luque,Beatriz Riverapproach allows us to quantify predictive uncertainty when we use our models for prediction. And this is of course important for the user of these predictions, whether that user is us or someone to whom we report our results. Our probabilistic predictions allow calculation of risks and, more generall
作者: BACLE    時間: 2025-3-30 07:01
Prajna Kunche,K. V. V. S. Reddyred, . (BDT) (Berger, . (2nd ed.). Springer Series in Statistics. Springer, 1985; Jaynes, .. Cambridge University Press, 2003; Lindley, . (2nd ed.). Wiley, 1991; Van Oijen and Brewer, ., SpringerBriefs in Statistics. Springer International Publishing, 2022; Williams and Hooten (Ecol Appl 26:1930–194
作者: 沒花的是打擾    時間: 2025-3-30 09:15
Marcel van OijenCovers 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,
作者: 召集    時間: 2025-3-30 16:23

作者: Paradox    時間: 2025-3-30 17:47

作者: OVERT    時間: 2025-3-30 23:31
The Algebraic Structure of MetagraphsIn the examples of MCMC in the preceding chapter, no prior or likelihood was specified, nor was there any talk of a posterior distribution. So why is MCMC important for Bayesian analysis?
作者: 摻假    時間: 2025-3-31 01:27
Metagraphs in Workflow and Process AnalysisThis chapter answers a number of common questions about Bayesian calibration in general and MCMC in particular. Many topics are addressed elsewhere in this book at greater length (and pointers to the chapters are then given), but some are only addressed briefly here.
作者: 斗爭    時間: 2025-3-31 06:34
Metagraphs in Workflow and Process AnalysisThis 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 visualisation.
作者: 滑動    時間: 2025-3-31 11:58
Metagraphs in Data and Rule ManagementFitting a straight line through data can be done in many ways that may seem different at first, but after closer inspection prove to be based on the same mathematics. In this chapter, we shall fit a line to data in 13 different ways and compare the resulting parameter estimates. So our goal is to estimate the intercept and the slope of the line.
作者: SAGE    時間: 2025-3-31 17:22

作者: 新奇    時間: 2025-3-31 17:43

作者: 產(chǎn)生    時間: 2025-3-31 22:45

作者: 啪心兒跳動    時間: 2025-4-1 05:29





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