This repository contains the necessary directories and files to perform the Bayesian uncertainty
anlaysis presented in "Uncertainty Quantification Accounting for Model Discrepancy Within 
a Random Effects Bayesian Framework" - Denielle E. Ricciardi, Oksana A. Chkrebtii, Stephen R. Niezgoda, IMMI (2020)

Uncertainty in the unknown Voce hardening parameters within the VPSC crystal platicity code 
are determined by calibrating to simulated data. The posterior distribution over all unknown parameters
is determined numerically through an MCMC simulation using an adaptive Metropolis-Hastings algorithm with Gibbs updates
where appropriate. Full details on the statistical model and derivations of full-conditional distribtuions
can be found in the publication. This code is written for MATLAB.

vpsc7d_virgin - contains all necessary files to run the VPSC crystal plastiticy code
MCMC - contains all necessary files to perform simulation targeting the posterior distribution
figures - all diagnostic plots and files will be saved to this directory
FFT_Simulated_Data - file containing simulated data used for calibration
MCMC.m - in the MCMC directory is the main source file to be run in MATLAB

Example Usage
 	Parameter estimation for the VPSC model (Tome and Lebensohn)
 	taking into account various sources of uncertainty stemming 
 	from noisy and/or inconsistent data (both epistemic and
    aleatoric) and model-form error

Unknown Parameters
	theta^[s]: VPSC model parameters for the random effects
		sampled in MH steps (blocks 1:S)
	theta: VPSC model parameters for overall effect
		sampled in MH steps (block S+1)
	Lambda: Random effects precision - not sampled directly
	R: Decomposed correlation of Lambda
		sampled in Gibbs step
	t2: Decomposed variance of Lambda
		sampled in MH step (block S+2)
	de1ta: Error precision
		sampled in Gibbs step
	Delta: Discrepancy (Model-form error)
		sampled in Gibbs step

 Output
	k = 'num_iter' samples targeting the posterior distribution of 
	all relavent parameters as well as posterior and posterior
    predictive samples


Copyright (c) 2020, Denielle Ricciardi
All rights reserved.