scholarly journals Uncertainty Quantification in Epidemiological Models for COVID-19 Pandemic

2020 ◽  
Author(s):  
Leila Taghizadeh ◽  
Ahmad Karimi ◽  
Clemens Heitzinger
Keyword(s):  
Inverse Modeling ◽  
Posteriori Probability ◽  
Model Parameters ◽  
Epidemiological Models ◽  
Unknown Parameters ◽  
Protective Measures ◽  
A Posteriori Probability ◽  
Estimated Parameters ◽  
Forward And Inverse Modeling ◽  
Inversion Techniques

AbstractThe main goal of this paper is to develop the forward and inverse modeling of the Coronavirus (COVID-19) pandemic using novel computational methodologies in order to accurately estimate and predict the pandemic. This leads to governmental decisions support in implementing effective protective measures and prevention of new outbreaks. To this end, we use the logistic equation and the SIR system of ordinary differential equations to model the spread of the COVID-19 pandemic. For the inverse modeling, we propose Bayesian inversion techniques, which are robust and reliable approaches, in order to estimate the unknown parameters of the epidemiological models. We use an adaptive Markov-chain Monte-Carlo (MCMC) algorithm for the estimation of a posteriori probability distribution and confidence intervals for the unknown model parameters as well as for the reproduction number. Furthermore, we present a fatality analysis for COVID-19 in Austria, which is also of importance for governmental protective decision making. We perform our analyses on the publicly available data for Austria to estimate the main epidemiological model parameters and to study the effectiveness of the protective measures by the Austrian government. The estimated parameters and the analysis of fatalities provide useful information for decision makers and makes it possible to perform more realistic forecasts of future outbreaks.

scholarly journals Parameter Estimation of DC Motor using Adaptive Transfer Function Based on Nelder-Mead Optimisation

2018 ◽  
Vol 9 (3) ◽  
pp. 696 ◽  
Author(s):  
Byamakesh Nayak ◽  
Sangeeta Sahu ◽  
Tanmoy Roy Choudhury
Keyword(s):  
Experimental Data ◽  
Transfer Function ◽  
Adaptive Method ◽  
Dc Motor ◽  
Model Parameters ◽  
Current Response ◽  
Adaptive Model ◽  
Unknown Parameters ◽  
Dc Motors ◽  
Estimated Parameters

<p>This paper explains an adaptive method for estimation of unknown parameters of transfer function model of any system for finding the parameters. The transfer function of the model with unknown model parameters is considered as the adaptive model whose values are adapted with the experimental data. The minimization of error between the experimental data and the output of the adaptive model have been realised by choosing objective function based on different error criterions. Nelder-Mead optimisation Method is used for adaption algorithm. To prove the method robustness and for students learning, the simple system of separately excited dc motor is considered in this paper. The experimental data of speed response and corresponding current response are taken and transfer function parameters of  dc motors are adapted based on Nelder-Mead optimisation to match with the experimental data. The effectiveness of estimated parameters with different objective functions are compared and validated with machine specification parameters.</p>

Inverse Modeling Techniques for Parameter Estimation in Engineering Simulation Models

2006 ◽  
Author(s):  
Srikanth Akkaram ◽  
Don Beeson ◽  
Harish Agarwal ◽  
Gene Wiggs
Keyword(s):  
Heat Transfer ◽  
Parameter Estimation ◽  
Inverse Modeling ◽  
Simulation Models ◽  
Posteriori Probability ◽  
Design System ◽  
Model Parameters ◽  
Input And Output ◽  
Ill Posed ◽  
Well Posed

Computational simulation models are extensively used in the development, design and analysis of an aircraft engine and its components to represent the physics of an underlying phenomenon. The use of such a model-based simulation in engineering often necessitates the need to estimate model parameters based on physical experiments or field data. This class of problems, referred to as inverse problems [1] in the literature can be classified as well-posed or ill-posed dependent on the quality (uncertainty) and quantity (amount) of data that is available to the engineer. The development of a generic inverse modeling solver in a probabilistic design system [2] requires the ability to handle diverse characteristics in various models. These characteristics include (a) varying fidelity in model accuracy with simulation times from a couple of seconds to many hours (b) models being black-box with the engineer having access to only the input and output (c) non-linearity in the model (d) time-dependent model input and output. The paper demonstrates methods that have been implemented to handle these features with emphasis on applications in heat transfer and applied mechanics. A practical issue faced in the application of inverse modeling for parameter estimation is ill-posedness that is characterized by instability and non-uniqueness in the solution. Generic methods to deal with ill-posedness include (a) model development, (b) optimal experimental design and (c) regularization methods. The purpose of this paper is to communicate the development and implementation of an inverse method that provides a solution for both well-posed as well as ill-posed problems using regularization based on the prior values of the parameters. In the case of an ill-posed problem, the method provides two solution schemes — a most probable solution closest to the prior, based on the singular value decomposition (SVD) and a maximum a-posteriori probability solution (MAP). The inverse problem is solved as a finite dimensional non-linear optimization problem using the SVD and/or MAP techniques tailored to the specifics of the application. The paper concludes with numerical examples and applications demonstrating the scope as well as validating the developed method. Engineering applications include heat transfer coefficient estimation for disk quenching in process modeling, material model parameter estimation, sparse clearance data modeling, steady state and transient engine high-pressure compressor heat transfer estimation.

OBJECTIVE FUNCTIONS FOR OCEAN ACOUSTIC INVERSION DERIVED BY LIKELIHOOD METHODS

2000 ◽  
Vol 08 (02) ◽  
pp. 259-270 ◽  
Author(s):  
CHRISTOPH F. MECKLENBRÄUKER ◽  
PETER GERSTOFT
Keyword(s):  
Inverse Problem ◽  
Objective Function ◽  
Likelihood Function ◽  
Point Of View ◽  
Single Frequency ◽  
Posteriori Probability ◽  
A Posteriori ◽  
Objective Functions ◽  
Unknown Parameters ◽  
A Posteriori Probability

Selection of a suitable objective function is an integral part of the inverse problem, and poor selection can have a strong influence on the inverse result. Objective functions are here derived for many practical occasions such as for single frequency and broadband, with and without knowledge of source strength, and with and without the received signal phase. These objective functions are all derived from a unified approach based on maximum likelihood and additive Gaussian noise models. The assumptions for the objective function are thus clear and the resulting estimator has good properties. From a Bayesian point of view, the solution to the inverse problem is the a posteriori probability distribution of the unknown parameters, which can be found from the likelihood function. Thus using objective functions based on likelihood functions facilitates computing the a posteriori distributions.

Some practical aspects of prestack waveform inversion using a genetic algorithm: An example from the east Texas Woodbine gas sand

Geophysics ◽  
1999 ◽  
Vol 64 (2) ◽  
pp. 326-336 ◽  
Author(s):  
Subhashis Mallick
Keyword(s):  
Genetic Algorithm ◽  
Biological Evolution ◽  
Synthetic Data ◽  
Posteriori Probability ◽  
Inversion Method ◽  
Model Parameters ◽  
East Texas ◽  
Data Set ◽  
A Posteriori Probability ◽  
Prestack Inversion

In this paper, a prestack inversion method using a genetic algorithm (GA) is presented, and issues relating to the implementation of prestack GA inversion in practice are discussed. GA is a Monte‐Carlo type inversion, using a natural analogy to the biological evolution process. When GA is cast into a Bayesian framework, a priori information of the model parameters and the physics of the forward problem are used to compute synthetic data. These synthetic data can then be matched with observations to obtain approximate estimates of the marginal a posteriori probability density (PPD) functions in the model space. Plots of these PPD functions allow an interpreter to choose models which best describe the specific geologic setting and lead to an accurate prediction of seismic lithology. Poststack inversion and prestack GA inversion were applied to a Woodbine gas sand data set from East Texas. A comparison of prestack inversion with poststack inversion demonstrates that prestack inversion shows detailed stratigraphic features of the subsurface which are not visible on the poststack inversion.

STUDYING THE IDENTIFIABILITY OF EPIDEMIOLOGICAL MODELS USING MCMC

2013 ◽  
Vol 06 (02) ◽  
pp. 1350008 ◽  
Author(s):  
ANTTI SOLONEN ◽  
HEIKKI HAARIO ◽  
JEAN MICHEL TCHUENCHE ◽  
HERIETH RWEZAURA
Keyword(s):  
Real Life ◽  
Simulated Data ◽  
Mcmc Methods ◽  
Infection Model ◽  
Model Parameters ◽  
Epidemiological Models ◽  
Unknown Parameters ◽  
Design And Optimization ◽  
Numerical Studies ◽  
Complex Models

Studying different theoretical properties of epidemiological models has been widely addressed, while numerical studies and especially the calibration of models, which are often complicated and loaded with a high number of unknown parameters, against measured data have received less attention. In this paper, we describe how a combination of simulated data and Markov Chain Monte Carlo (MCMC) methods can be used to study the identifiability of model parameters with different type of measurements. Three known models are used as case studies to illustrate the importance of parameter identifiability: a basic SIR model, an influenza model with vaccination and treatment and a HIV–Malaria co-infection model. The analysis reveals that calibration of complex models commonly studied in mathematical epidemiology, such as the HIV–Malaria co-dynamics model, can be difficult or impossible, even if the system would be fully observed. The presented approach provides a tool for design and optimization of real-life field campaigns of collecting data, as well as for model selection.

A Neural Network for Nonlinear Bayesian Estimation in Drug Therapy

1990 ◽  
Vol 2 (2) ◽  
pp. 216-225 ◽  
Author(s):  
Reza Shadmehr ◽  
David Z. D'Argenio
Keyword(s):  
Neural Network ◽  
Bayesian Estimation ◽  
Bayesian Estimator ◽  
Posteriori Probability ◽  
Model Parameters ◽  
Prediction Errors ◽  
A Posteriori ◽  
Likelihood Estimator ◽  
A Posteriori Probability ◽  
Trained Neural Network

The feasibility of developing a neural network to perform nonlinear Bayesian estimation from sparse data is explored using an example from clinical pharmacology. The problem involves estimating parameters of a dynamic model describing the pharmacokinetics of the bronchodilator theophylline from limited plasma concentration measurements of the drug obtained in a patient. The estimation performance of a backpropagation trained network is compared to that of the maximum likelihood estimator as well as the maximum a posteriori probability estimator. In the example considered, the estimator prediction errors (model parameters and outputs) obtained from the trained neural network were similar to those obtained using the nonlinear Bayesian estimator.

Transdimensional inversion of ambient seismic noise for 3D shear velocity structure of the Tasmanian crust

Geophysics ◽  
2013 ◽  
Vol 78 (3) ◽  
pp. WB49-WB62 ◽  
Author(s):  
Mallory K. Young ◽  
Nicholas Rawlinson ◽  
Thomas Bodin
Keyword(s):  
Seismic Noise ◽  
Velocity Structure ◽  
Shear Velocity ◽  
Wave Dispersion ◽  
Posteriori Probability ◽  
Ambient Seismic Noise ◽  
Model Parameters ◽  
Surface Wave Dispersion ◽  
Two Stage ◽  
A Posteriori Probability

Ambient seismic noise tomography has proven to be a valuable tool for imaging 3D crustal shear velocity using surface waves; however, conventional two-stage inversion schemes are severely limited in their ability to properly quantify solution uncertainty and account for inhomogeneous data coverage. In response to these challenges, we developed a two-stage hierarchical, transdimensional, Bayesian scheme for inverting surface wave dispersion information for a 3D shear velocity structure and apply it to ambient seismic noise data recorded in Tasmania, southeast Australia. The key advantages of our Bayesian approach are that the number and distribution of model parameters are implicitly controlled by the data and that the standard deviation of the data noise is treated as an unknown in the inversion. Furthermore, the use of Bayesian inference — which combines prior model information and observed data to quantify the a posteriori probability distribution — means that model uncertainty information can be correctly propagated from the dispersion curves to the phase velocity maps and finally onward to the 1D shear models that are combined to form a composite 3D image. We successfully applied the new method to ambient noise dispersion data (1–12-s period) from Tasmania. The results revealed an east-dipping anomalously low shear velocity zone that extends to at least a 15-km depth and can be related to the accretion of oceanic crust onto the eastern margin of Proterozoic Tasmania during the mid-Paleozoic.

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