Bayesian analysis for uncertainty estimation of a canopy transpiration model

We present a statistical framework for model calibration and uncertainty estimation for complex deterministic models. A Bayesian approach is used to combine data from observations, the deterministic model, and prior parameter distributions to obtain forecast distributions. A case study is presented in which the statistical framework is applied using the hydrogeochemical model (MAGIC) for an assessment of recovery from acidification of soils and surface waters at a long-term study site in Norway under different future acid deposition conditions. The water quality parameters are coupled with a simple dose-response model for trout population health. Uncertainties in model output parameters are estimated and forecast results are presented as probability distributions for future water chemistry and as probability distributions of future healthy trout populations. The forecast results are examined for three different scenarios of future acid deposition corresponding to three different emissions control strategies for Europe. Despite the explicit consideration of uncertainties propagated into the future forecasts, there are clear differences among the scenarios. The case study illustrates how inclusion of uncertainties in model predictions can strengthen the inferences drawn from model results in support of decision making and assessments.

A conceptual CSO emission model: SEWSIM

Process-based forest models generally have many parameters, multiple outputs of interest and a small underlying empirical database. These characteristics hamper parameterization. Bayesian calibration offers a solution to the calibration problem because it applies to models of any type or size. It provides parameter estimates, with measures of uncertainty and correlation among the parameters. The procedure begins by quantifying the uncertainty about parameter values in the form of a prior probability distribution. Then data on the output variables are used to update the parameter distribution by means of Bayes' Theorem. This yields a posterior calibrated distribution for the parameters, which can be summarized in the form of a mean vector and variance matrix. The predictive uncertainty of the model can be quantified by running it with different parameter settings, sampled from the posterior distribution. In a further step, one may evaluate the posterior probability of the model itself (rather than that of the parameters) and compare that against the probability of other models, to aid in model selection or improvement. Bayesian calibration of process-based models cannot be performed analytically, so the posterior parameter distribution must be approximated in the form of a representative sample of parameter values. This can be achieved by means of Markov Chain Monte Carlo simulation, which is suitable for process-based models because of its simplicity and because it does not require advance knowledge of the shape of the posterior distribution. Despite the suitability of Bayesian calibration, the technique has rarely been used in forestry research. We introduce the method, using the example of a typical forest model. Further, we show that reductions in parameter uncertainty, and thus in output uncertainty, can be effected by increasing the variety of data, increasing the accuracy of measurements and increasing the length of time series.

A new method is proposed based on the finite difference method (FDM), differential evolution algorithm and Markov Chain Monte Carlo (MCMC) simulation to identify water quality model parameters of an open channel in a long distance water transfer project. Firstly, this parameter identification problem is considered as a Bayesian estimation problem and the forward numerical model is solved by FDM, and the posterior probability density function of the parameters is deduced. Then these parameters are estimated using a sampling method with differential evolution algorithm and MCMC simulation. Finally this proposed method is compared with FDM-MCMC by a twin experiment. The results show that the proposed method can be used to identify water quality model parameters of an open channel in a long distance water transfer project under different scenarios better with fewer iterations, higher reliability and anti-noise capability compared with FDM-MCMC. Therefore, it provides a new idea and method to solve the traceability problem in sudden water pollution accidents.

Dynamic analysis of growth of Salmonella spp. in raw ground beef – Estimation of kinetic parameters, sensitivity analysis, and Markov Chain Monte Carlo simulation

SummaryThe paper demonstrates how cost-effectiveness decision analysis may be implemented from a Bayesian perspective, using Markov chain Monte Carlo simulation methods for both the synthesis of relevant evidence input into the model and the evaluation of the model itself. The desirable aspects of a Bayesian approach for this type of analysis include the incorporation of full parameter uncertainty, the ability to perform all the analysis, including each meta-analysis, in a single coherent model and the incorporation of expert opinion either directly or regarding the relative credibility of different data sources. The method is described, and its ease of implementation demonstrated, through a practical example to evaluate the cost-effectiveness of using taxanes for the second-line treatment of advanced breast cancer compared with conventional treatment. For completeness, the results from the Markov chain Monte Carlo simulation model are compared and contrasted with those from a classical Monte Carlo simulation model.

In many application domains, it is impossible or impractical to perform full-scale experiments on a system in the regime of interest. Instead, data may be collected via experiments at lower levels of the system on individual materials, components, or subsystems. As a result, physics-based models are the only available tool at the full system level and must be used to make predictions in the regime of interest. This scenario poses difficulty when attempting to characterize the uncertainty in the model prediction since no further data is available. This problem has commonly been addressed by characterizing aleatory uncertainty in input variables with probability distributions and then performing calibration to characterize epistemic uncertainty stemming from parameter uncertainty. Calibrated models are then validated by any of a number of available metrics by utilizing a new set of independent data, typically at a higher level of the system hierarchy. Once the models are validated at the subsystem level, the input variability and parameter uncertainty can be propagated through a system-level model to make a prediction in the regime of interest. Standard propagation techniques will yield a probability distribution for a quantity of interest which can then be used to perform reliability analysis and make system assessments. However, common implementations of this approach largely ignore model uncertainty, which may be a leading source of uncertainty in the prediction. The approach presented in this study accounts for the fact that models never perform perfectly in the validation activities. Model validation is typically posed as a single pass/fail decision, but it can instead be viewed probabilistically. The model reliability metric is utilized in this study because it readily allows this probabilistic treatment by computing the probability of model errors exceeding a specified tolerance. We assert that parameters which are calibrated from models which are later partially invalidated should not be fully carried forward to the prediction. Calibration can be performed jointly with all available subsystem models or by using only a subset of them. Thus, from a Bayesian calibration approach we can obtain several posterior distributions of the parameters in addition to the prior distribution. These parameter distributions can then be weighted by the corresponding model probabilities computed in the

We survey Bayesian methods for estimating dynamic stochastic general equilibrium (DSGE) models in this article. We focus on New Keynesian (NK) DSGE models because of the interest shown in this class of models by economists in academic and policy-making institutions. This interest stems from the ability of this class of DSGE model to transmit real, nominal, and fiscal and monetary policy shocks into endogenous fluctuations at business cycle frequencies. Intuition about these propagation mechanisms is developed by reviewing the structure of a canonical NKDSGE model. Estimation and evaluation of the NKDSGE model rests on being able to detrend its optimality and equilibrium conditions, to construct a linear approximation of the model, to solve for its linear approximate decision rules, and to map from this solution into a state space model to generate Kalman filter projections. The likelihood of the linear approximate NKDSGE model is based on these projections. The projections and likelihood are useful inputs into the Metropolis-Hastings Markov chain Monte Carlo simulator that we employ to produce Bayesian estimates of the NKDSGE model. We discuss an algorithm that implements this simulator. This algorithm involves choosing priors of the NKDSGE model parameters and fixing initial conditions to start the simulator. The output of the simulator is posterior estimates of two NKDSGE models, which are summarized and compared to results in the existing literature. Given the posterior distributions, the NKDSGE models are evaluated with tools that determine which is most favored by the data. We also give a short history of DSGE model estimation as well as pointing to issues that are at the frontier of this research.

Bayesian Estimation of DSGE Models

Stochastic constitutive modeling of elastic-plastic materials with uncertain properties

Groundwater flow and mass transport predictions are subjected to uncertainty due to heterogeneity of hydraulic conductivity, whose variability in space is considerably higher than that of other hydraulic properties relevant to groundwater flow. To characterize the distribution of hydraulic conductivity, random space function (RSF) is often used. The Bayesian approach was applied to quantitatively study the effect of parameter uncertainty in RSF on a hypothetical two-dimensional uniform groundwater flow and mass transport. Specifically, the parameter uncertainty transmitted to macrodispersion in mass transport model was also inferred. The results showed that the posterior probability distributions of parameters were updated after Bayesian inference. The numerical experiments indicated that the overall predictive uncertainty was increased with simulating time along the flow direction. As to the relative contribution of the two types of uncertainty, it indicated that parametric uncertainty was a little more important than stochastic uncertainty for the predictive uncertainty of hydraulic head. When the uncertainty of hydraulic head as well as macrodispersion was transported to mass transport model, a much bigger contribution of stochastic uncertainty was observed. Therefore, parametric uncertainty should not be neglected during the process of subsurface simulation.

Thermodynamic modeling and uncertainty quantification of CO2-loaded aqueous MEA solutions

Diagnostic tests are of vital importance in a number of veterinary fields and are essential for decision-making by veterinary practioners, researchers and the veterinary authorities. The development and evaluation of laboratory diagnostic tests as well as the interpretation of test results engage a number of different veterinary disciplines including virologists, parasitologists, bacteriologists, laboratory experts, clinicians as well as epidemiologists and biostatisticians. This thesis was devised shortly after the section of epidemiology came into existence at the Vetsuisse Faculty end of 2009. The aim is to interrelate veterinary epidemiology - being closely linked to virology, parasitology, bacteriology and clinical medicine - with biostatistics. Thus allowing innovative concepts and recent software developments to provide solutions and answers in our veterinary field. After a brief introduction into diagnostic tests, the thesis is structured into three main parts. First, from a laboratory perspective, aspects of analytical sensitivity and specificity are illustrated by three peer-reviewed papers presenting practical applications of veterinary diagnostic tests for feline calicivirus and porcine parvovirus. Second, in the context of assessing agreement and method comparison studies, categorical test results are compared by Cohen’s k and continuous measurements by linear mixed effects models extending the classical use of Bland-Altman plots with limits of agreement. The former is illustrated in a publication on the diagnostic test Interferon-Gamma to classify bovines being infected with Mycobacterium bovis when analysing samples from the same animals in five different laboratories and from different anatomical locations. Two peer-reviewed papers aim to assess the agreement of serumspecific lipase, as a diagnostic test for feline pancreatitis with a commercial test kit and ultrasonographic findings. In the context of comparing continuous measurements, i.e. cardiac output and blood pressure measured directly and indirectly, two peer-reviewed paper illustrate the application of linear mixed effects models to simultaneously assess bias, precision and covariate information. Typical pitfalls arising in method comparison studies are summarised in a review paper. Building upon the previous parts, the third part adds to the existing knowledge by presenting novel and innovative approaches when assessing the performance of diagnostic tests in the absence of a perfect gold standard. So-called no gold standard models (NGS) are applied to assess the diagnostic test accuracies in the context of zoonotic diseases such as bovine tuberculosis, porcine toxoplasmosis as well as canine and vulpine echinococcosis. Additionally, these models are applied to assess diagnostic test accuracies to diagnose Brachyspira hyodysenteriae, an economically important disease in pigs. Furthermore, they are also utilised to assess diagnostic accuracies of diagnostic tools for subclinical mastitis in dairy cattle. In this part, Bayesian approaches are presented, together with technical aspects including conditional dependencies, Markov Chain Monte Carlo simulations and aspects of model selection. The innovative aspects and main novelty of the work presented in this thesis pertain to the incorporation of covariate information and random effects. Whereas covariate information in the form of risk factors has been included in statistical analyses since decades, considering random effects to account for clustering of animals at herd level just became possible with increased computational power. Nowadays dealing appropriately with the hierarchical structure of animal data is considered as good statistical practice and warranted in epidemiological studies to avoid biased results. However, diagnostic test studies including covariate information and random effects are scarce. The aim of this thesis is to fill this gap by showcasing a number of Bayesian latent class analyses for various infectious diseases in animals.

Application of spherical subset simulation method and auxiliary domain method on a benchmark reliability study

Parameter identification and uncertainty quantification in stochastic state space models and its application to texture analysis