From bbe7d710e9abac63823ab45a2a6a05ebe5cfb0bc Mon Sep 17 00:00:00 2001 From: thurber Date: Tue, 1 Mar 2022 16:19:07 -0800 Subject: [PATCH] fixes #22 --- docs/source/A1.4_Markov_Chain_Monte_Carlo.rst | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/docs/source/A1.4_Markov_Chain_Monte_Carlo.rst b/docs/source/A1.4_Markov_Chain_Monte_Carlo.rst index 7147469..afc3a23 100644 --- a/docs/source/A1.4_Markov_Chain_Monte_Carlo.rst +++ b/docs/source/A1.4_Markov_Chain_Monte_Carlo.rst @@ -5,7 +5,7 @@ Markov chain Monte Carlo (MCMC) is a “gold standard” approach to full uncert MCMC algorithms construct a Markov chain of samples from a parameter space (the combination of model and statistical parameters). This Markov chain is constructed so that the stationary distribution is a target distribution, in this case the (Bayesian) posterior distribution. As a result, after the transient period, the resulting samples can be viewed as a set of dependent samples from the posterior (the dependence is due to the autocorrelation between samples resulting from the Markov chain transitions). Expected values can be computed from these samples (for example, using batch-means estimators :cite:p:`flegal_markov_2008`), or the chain can be sub-sampled or thinned and the resulting samples used as independent Monte Carlo samples due to the reduced or eliminated autocorrelation. -A general workflow for MCMC is shown in :numref:`Figure_A1_4`. The first decision is whether to use the full model or a surrogate model (or emulator). Typical surrogates include Gaussian process emulation :cite:p:`currin_bayesian_1991, sacks_design_1989`, polynomial chaos expansions :cite:p:`ghanem_spectral_1991,xiu_wiener--askey_2002`, support vector machines :cite:p`ciccazzo_svm_2016, pruett_creation_2016`, and neural networks :cite:p:`eason_adaptive_2014, gorissen_sequential_2009`. Surrogate modeling can be faster, but requires a sufficient number of model evaluations for the surrogate to accurately represent the model’s response surface, and this typically limits the number of parameters which can be included in the analysis. +A general workflow for MCMC is shown in :numref:`Figure_A1_4`. The first decision is whether to use the full model or a surrogate model (or emulator). Typical surrogates include Gaussian process emulation :cite:p:`currin_bayesian_1991, sacks_design_1989`, polynomial chaos expansions :cite:p:`ghanem_spectral_1991, xiu_wiener--askey_2002`, support vector machines :cite:p:`ciccazzo_svm_2016, pruett_creation_2016`, and neural networks :cite:p:`eason_adaptive_2014, gorissen_sequential_2009`. Surrogate modeling can be faster, but requires a sufficient number of model evaluations for the surrogate to accurately represent the model’s response surface, and this typically limits the number of parameters which can be included in the analysis. .. _Figure_A1_4: .. figure:: _static/figureA1_4_mcmc_workflow.png