add all other schema

docs/source/6.1_understanding_risk_how_probable_are_extreme_events.rst

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+Understanding Risk: How Probable Are Extreme Events?
+####################################################

docs/source/6.2_understanding_tails_statistical_modeling_of_extreme_events.rst

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+Understanding Tails: Statistical Modeling of Extreme Events
+###########################################################

docs/source/6.3_how_to_choose_an_appropriate_method.rst

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+How to Choose an Appropriate Method?
+####################################

docs/source/6.4_how_to_select_a_prior_distribution.rst

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+How to Select a Prior Distribution?
+###################################

docs/source/6.5_posterior_predictive_checking.rst

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+Posterior Predictive Checking
+#############################

docs/source/6.6_model_selection_and_comparison.rst

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+Model Selection and Comparison
+##############################

docs/source/6.7.1_scenario_discovery.rst

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+Scenario Discovery
+******************

docs/source/6.7.2_pre_calibration_glue.rst

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+Pre-calibration/GLUE
+********************

docs/source/6.7.3.1_metropolis_hastings.rst

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+Metropolis-Hastings
+===================

docs/source/6.7.3.2_gibbs_sampling.rst

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+Gibbs Sampling
+==============

docs/source/6.7.3.3_hamiltonian_monte_carlo.rst

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+Hamiltonian Monte Carlo
+=======================

docs/source/6.7.3_markov_chain_monte_carlo.rst

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+Markov Chain Monte Carlo
+************************
+
+Markov chain Monte Carlo (MCMC) is a “gold standard” approach to full uncertainty quantification. MCMC refers to a category of algorithms which systematically sample from a target distribution (in this case, the posterior distribution) by constructing a Markov chain. MCMC algorithms rely on the mixing properties of the resulting Markov chain to guarantee asymptotic convergence to the posterior distribution, as the chain is constructed so that the posterior is its stationary distribution. It should be stressed that this guarantee exists only asymptotically. Studies use heuristics to test for signs of misconvergence and to assess the skill of the approximation (xx)
+
+MCMC algorithms begin with the choice of some initial value for the Markov chain. This value can be randomly determined, or can be some other quantity such as a maximum likelihood or maximum a posteriori estimates. While the Markov chain will eventually converge to the posterior regardless of the choice of initial value, the amount of time required to escape the transient dynamics of the Markov chain is dependent on this value. Typically, transient samples are discarded as burn-in, as they may skew the sample distribution if the burn-in is relatively long compared to the number of iterations spent exploring the posterior, though this practice is not universal and has been questioned by some statisticians (Geyer, 2011). However, when not discarding the transient area, the chain must be run for a larger number of iterations to ensure that these samples do not bias the sample distribution.
+
+Diagnosing the convergence of the Markov chain to the posterior is more art than science, relying on heuristics and judgement. One example heuristic is to run many Markov chains from different initial conditions, ideally well-dispersed across the parameter space; one may be able to conclude that the chains have not yet converged if the resulting marginal parameter distributions are sufficiently different when plotted. The Gelman-Rubin diagnostic formalizes this idea by comparing the within-chain and pooled variances of multiple chains (Gelman and Rubin, 1992). The ratio of these two quantities, called the potential scale reduction factor, can diagnose a lack of convergence if it is sufficiently far from 1 (typically using a threshold such as 1.1 or 1.05). Thus, it is generally good practice to use several MCMC runs to facilitate the diagnoses of non-convergence.
+
+Another key value is the effective sample size (ESS). Due to the Markovian property, the samples obtained using MCMC are autocorrelated, and therefore not independent. As a result, the number of samples obtained using MCMC are not directly useful when interpreting the extent of exploration (or computing quantities such as the Monte Carlo standard error (Flegal et al., 2008)). For example, it may not be appropriate to draw inferences about tail properties for a small  ESS.
+
+Many MCMC algorithms exist, with varying strengths and weaknesses, discussed below. For example, some require more tuning to improve the ESS than others. All of these algorithms involve the evaluation of the model at various parameter settings. Once a Markov chain is constructed and deemed to suitably represent the posterior distribution, parameter values can be sampled from it with replacement as a proxy for directly sampling from the posterior.
+
+..include:: 6.7.3.1_metropolis_hastings.rst
+
+..include:: 6.7.3.2_gibbs_sampling.rst
+
+..include:: 6.7.3.3_hamiltonian_monte_carlo.rst

docs/source/6.7.4_particle_based_methods.rst

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+Particle-based Methods
+**********************

docs/source/6.7_what_are_common_methods.rst

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+What are Common Methods?
+########################

docs/source/6.8.1_markov_chain_monte_carlo_with_the_true_model.rst

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+Markov Chain Monte Carlo with the True Model
+********************************************

docs/source/6.8.2_markov_chain_monte_carlo_with_surrogate_models.rst

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+Markov Chain Monte Carlo with Surrogate Models
+**********************************************

docs/source/6.8_what_are_example_software_implementations.rst

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+What are Example Software Implementations?
+##########################################

docs/source/6_uncertainty_quantification_a_tool_for_capturing_risks_and_extremes.rst

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+*****************************************************************
+Uncertainty Quantification: A Tool For Capturing Risks & Extremes
+*****************************************************************
+
+.. include:: 6.1_understanding_risk_how_probable_are_extreme_events.rst
+
+.. include:: 6.2_understanding_tails_statistical_modeling_of_extreme_events.rst
+
+.. include:: 6.3_how_to_choose_an_appropriate_method.rst
+
+.. include:: 6.4_how_to_select_a_prior_distribution.rst
+
+.. include:: 6.5_posterior_predictive_checking.rst
+
+.. include:: 6.6_model_selection_and_comparison.rst
+
+.. include:: 6.7_what_are_common_methods.rst
+
+.. include:: 6.8_what_are_example_software_implementations.rst

docs/source/7_conclusion.rst

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+**********
+Conclusion
+**********
+
+As noted in the Introduction (Section 1.0), the computational and conceptual challenges of the multi-model, transdisciplinary workflows that characterize ambitious projects such as IM3 have limited UC and UQ analyses. Moreover, the very nature and purpose of modeling and diagnostic model evaluation can have very diverse philosophical framings depending on the disciplines involved (see Figure 1 and Section 2.0). The guidance provided in this text  can be used to frame consistent and rigorous experimental designs for better understanding the consequences and insights from our modeling choices when seeking to capture complex human-natural systems. The progression of sections of this text provide a thorough introduction of the concepts and definitions of diagnostic model evaluation, sensitivity analysis, UC, and UQ. In addition, we comprehensively discuss how specific modeling objectives and applications should guide the selection of appropriate techniques; broadly, these can include model diagnostics, in-depth analysis of the behavior of the abstracted system, and projections under conditions of deep uncertainty. This text also contains a detailed presentation of the main sensitivity analysis, UC, and UQ analysis methods and a discussion of their features and main limitations. Readers are also provided with an overview of computer tools and platforms that have been developed and could be considered in addressing IM3 scientific questions. The appendices of this text include a terminology glossary of the key concepts as well as example test cases and scripts to showcase various UC related capabilities.
+
+Although we distinguish the UC and UQ model diagnostics, the reader should note that we suggest an overall consistent approach to both in this text by emphasizing “exploratory modeling” (see review add citation). Although data support, model complexity, and computational limits strongly distinguish the feasibility and appropriateness of the UC and UQ diagnostic tools (e.g., see Figure 18), we overall recommend that modelers view their work through the lens of cycles of learning. Iterative and deliberative exploration of model-based hypotheses and inferences for transdisciplinary teams is non-trivial and ultimately critical for mapping where innovations or insights are most consequential. Overall, we recommend approaching modeling with an openness to the diverse disciplinary perspectives such as those mirrored by the IM3 family of models in a progression from evaluating models relative to observed history to advanced formalized analyses to make inferences on multi-sector, multi-scale vulnerabilities and resilience. Exploratory modeling approaches can help fashion experiments with large numbers of alternative hypotheses on the co-evolutionary dynamics of influences, stressors, as well as path-dependent changes in the form and function of coupled human-natural systems (Weaver et al., 2013). This text guides the reader through the use of sensitivity analysis and uncertainty methods across the diverse perspectives that have shaped modern diagnostic and exploratory modeling.