Likelihood-based estimation and prediction for a measles outbreak in Samoa.

Modular Algorithms for Scientific Computing in Julia

Epidemic modeling is a key component in the assessment of infectious diseases transmission and guiding the public health response. This report explores two primary approaches to epidemic modeling: It has categorized the models into deterministic model where the disease spread is depicted using differential equations and stochastic models where probability forms the basis of modeling the spread of the diseases. These approaches offer essential information about the nature of epidemic behaviors, for example, the ability to forecast the trends of epidemic curves, and calculation of the basic reproduction number (R0), assessment of child and caregiver, identification of protective/environmental factors, and assessment of intervention approaches. The SIR and SEIR models based on ordinary differential equations that trace the shifting between Susceptible, Infected and Recovered populations. They are especially good in large data scenarios where randomness, or the lack of it, has negligible or no bearing and are fast in providing long-term trends. But they do not target small or more heterogenic groups and do not account for stochastic fluctuations. On the other hand, stochastic models take into consideration the variability of the disease’s transmission as well as the recovery time for disease, they are used for small population size or variable conditions. These models, frequently calibrated through computations involving Monte Carlo simulation or stochastic differential equations, allow for a wider envisaged set of outcomes and shed light on such scenarios as disease wiping out or super spread events. However, they present higher computational costs and are sensitive with parameter estimates as well. It highlights how problematic mathematical modeling is for evidence-informed decision making in public health, as evidenced by COVID-19 pandemic. This highlights the need for constant refinement of the models – data streaming, population variability, and adaptation of the model to real-world emerging issues such as climatic change and zoonotic diseases. Applying the respective strengths of deterministic and stochastic models, further research is encouraged as well as policy implications associated with the interaction between these models and infectious disease outbreaks

The aim of the study is to condition stochastic generated realizations on well test data in order to improve simulation of fades and petrophysics in fluvial reservoirs. First we have used the pressure data to estimate the shortest distance from the well to a possible channel boundary and thereby simulate the channel structures. The well test also provides the permeability average in the part of the channel intersected by the well. Together with core/log data and general knowledge of the reservoir this have been used to simulate permeability. These permeability realizations is input to a numerical flow simulator and compared with experimental results of the well test.

A Primer on Bootstrap Testing of Hypotheses in Time Series Models: With an Application to Double Autoregressive Models

HiFlow3 Version 2.0 continues the path as a multi-purpose finite element software, which provides powerful tools for efficient and accurate solution of a wide range of problems modeled by partial differen- tial equations (PDEs). New features and functionalities, which allow to run numerical simulations with more advanced solution algorithms and discretizations in comparison to previous releases of HiFlow3, have been implemented. These comprise Uncertainty Quantification (UQ), energy-efficient multigrid techniques, Schur complement solvers for saddle-point problems, extended third-party library support, and adaptive local mesh refinement in a parallel computing environment. Furthermore, HiFlow3 has been successfully integrated into advanced and state-of-the-art simulation environments by means of the Medical Simulation Markup Language (MSML), for example.The presented new algorithms and features as well as general under-the-hood improvements have enabled excellent and relevant research activities in the fields of both medical engineering and meteorol- ogy and environmental sciences. The described show cases demonstrate the potential and advantages, which HiFlow3 can offer in performing a numerical simulation by means of finite element methods. Especially, the high performance computing capabilities of HiFlow3 – not only in the mentioned fields of applications, but also in general – have been significantly improved in Version 2.0.

ObjectiveWe present a mathematical framework for non-parametric estimation of the force of infection, together with statistical upper and lower confidence bands. The resulting estimates allow to assess how well simpler models, such as SEIR, fit the observed time series of incidence data.IntroductionUncertainty Quantification (UQ), the ability to quantify the impact of sample-to-sample variations and model misspecification on predictions and forecasts, is a critical aspect of disease surveillance. While quantifying the impact of stochastic uncertainty in the data is well understood, quantifying the impact of model misspecification is significantly harder. For the latter, one needs a "universal model" to which more restrictive parametric models are compared too.MethodsThis talk presents a useful modeling framework for time series of incidence data from contagious diseases that enables one to identify and quantify the impact of model form uncertainty. Specifically, we propose to focus on estimating the timedependent force of infection. The latter is a universal parameters for all contagious disease model. Using a machine learning technique for estimating monotone functions, i.e., isotonic regression and its variants, one can estimate the force ofinfection without addtional assumptions. We note that most contagious disease model do satisfy this monotonicity assumption, due to a combination of factors: depletion of susceptibles, implementation of mitigation strategies, behavior change, etc. Comparing the resulting "non-parametric" estimate with parametric estimates, obtained by fitting an SEIR for example, can reveal model deficiencies and help quantify model form uncertainties.Finally, we discuss how ideas from "strict bound theory" can be used to develop upper and lower uncertainty bands for force of infection that acknowledge the intrinsic stochasticity in the data.ResultsWe demonstrate the application of the methodology to weekly Influenza Like Illness (ILI) incidence data from France andcompare the results to fitted SIR and SEIR models. This comparison can be seen as a nonparametric goodness of fit test, providing one with tools to do simple model selection.ConclusionsWe present a novel and flexible model to statistically describe the force of infection as a function of time. Comparing the fit to incidence data of that model with the fit of simpler parametric models enables the quantification of model form uncertainty and associated model selection.

Accurate contaminant prediction is very important for risk assessment and site remediation. Several predictive tools in the form of mathematical models have been used to model the movement and behavior of contaminants in groundwater. These deterministic models do not account for the heterogeneity and uncertainties in the subsurface environment. Discretization of the models spatially and temporally introduces approximation and truncation errors. In this research, to improve the accuracy of subsurface contaminant prediction in time and space and to assess the impact of first-order decay rate parameter estimation, Kalman filter coupled with Monte Carlo sampling was used in a specified three-dimensional domain space. The filter is perturbed with random Gaussian noise to reflect real life case of contaminant movement. Set of sparse observation points selected at specific locations are used to guide the filter at every time step to improve the accuracy of the prediction. The first-order decay rate parameter is estimated using Monte Carlo sampling method. The algorithms to generate the simulation results were run on Matlab 7.1. The efficacy of the Kalman filter coupled with Monte Carlo sampling, Kalman filter without Parameter Estimation and the numerical method were tested using Mean Absolute Error (MAE) and Maximum Absolute Error (Emax) equations. The results show that the Kalman filter coupled with Monte Carlo sampling performs better than both the Kalman filter without Parameter Estimation and the numerical method. Also, the Kalman filter coupled with Monte Carlo sampling is capable of reducing the error in the numerical solution by approximately 75% when Mean Absolute Error equation is used to estimate the prediction error. The error reduction is due to the adaptive nature of the Kalman filter to the observation data used in the simulation.

Handling uncertainty is one of the most important challenges in real physical systems. In this article, we study an approximate optimal magnetic control strategy for a one-dimensional (1-D) magnetohydrodynamic (MHD) system with uncertainty quantification within the learning framework of the underlying MHD model. First, the MHD flow system is modeled by coupled partial differential equations (PDEs) wherein the Reynolds number is not deterministic but random. Then, the optimal magnetic control problem is formulated and reduced to a parameter selection problem with stochastic PDE constraints by means of the control parameterization method. Significantly different from the conventional sensitivity analysis and adjoint methods, a polynomial chaos expansion (PCE) based on a multifidelity model is developed to construct the underlying PDEs model by polynomial functions. Thus, the relationship between the objective function and the control sequence is derived explicitly, which, in turn, transforms the optimal parameter selection problem with stochastic PDE constraints into a typical algebraic optimization problem that can be easily solved by the existing nonlinear programming algorithm. Numerical simulations are illustrated to demonstrate the high performance of our proposed method.

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

We study a multiple group model with ordinal categorical observed variables that are manifestations of underlying normal variables. When the objective of an analysis is to compare the locations and dispersions of the underlying continuous variables in different groups, traditional approaches use exact linear constraints on thresholds across groups to identify the model. Though the resultant model facilitates interpretation in multiple group analysis, in some cases the exact linear relationships on thresholds are not appropriate for describing the reality. However, these constraints must be imposed to identify the model. In view of this, we propose to apply across group stochastic constraints on thresholds to identify the model. Stochastic constraints are more practical and flexible than exact constraints, and subsume exact constraints as a special case, and therefore enable the structure of the data to be described in a more realistic way. Using stochastic constraints, we can achieve an identified model that allows the comparison of underlying continuous variables in different groups relatively, and at the same time accommodate the possible differences in thresholds. A Bayesian approach is employed to analyze the model, and prior knowledge can be incorporated into the analysis. It is demonstrated that the parameter estimates can be produced conveniently using the Mx software program, and an illustrative sample Mx input script is presented. A real data set is analyzed with the proposed approach, and results are compared to those obtained by using other prevailing approaches.

Effects of physical correlations on long-distance GPS positioning and zenith tropospheric delay estimates

When modeling multilevel data, it is important to accurately represent the interdependence of observations within clusters. Ignoring data clustering may result in parameter misestimation. However, it is not well established to what degree parameter estimates are affected by model misspecification when applying missing data techniques (MDTs) to incomplete multilevel data. We compare the performance of three MDTs with incomplete hierarchical data. We consider the impact of imputation model misspecification on the quality of parameter estimates by employing multiple imputation under assumptions of a normal model (MI/NM) with two-level cross-sectional data when values are missing at random on the dependent variable at rates of 10%, 30%, and 50%. Five criteria are used to compare estimates from MI/NM to estimates from MI assuming a linear mixed model (MI/LMM) and maximum likelihood estimation to the same incomplete data sets. With 10% missing data (MD), techniques performed similarly for fixed-effects estimates, but variance components were biased with MI/NM. Effects of model misspecification worsened at higher rates of MD, with the hierarchical structure of the data markedly underrepresented by biased variance component estimates. MI/LMM and maximum likelihood provided generally accurate and unbiased parameter estimates but performance was negatively affected by increased rates of MD.

This chapter describes how Markov chain Monte Carlo methods can be used to analyze data from outbreaks of infectious disease. Specifically, methods are described for Bayesian estimation of the parameters of stochastic disease transmission models. The methods are highly flexible in nature, being applicable to a wide range of models and types of data. The methods also can cater for missing data, particularly in the sense that the actual process of infection need not be observed, as is typical in practice. As well as providing details of the Markov chain Monte Carlo methods, practical guidelines are given in the chapter. The methods are illustrated in detail for a simple example featuring a simple susceptible-infective-removed model, and also a more complex example of a real-life data set on a measles outbreak.

The Linear Regression Model is a useful prediction tool. In this paper, a linear regression model was used to analyze and predict the death toll of the novel corona virus (2019-nCov) outbreaks in 2019. Besides, an improved linear regression method was proposed to obtain a more accurate epidemic prediction model. In this paper, the author used one parameter to predict the data. Therefore, in the further research, more factors will be added to conduct a more accurate prediction.

BackgroundIdentifying a proper model structure, using methods that address both structural and parameter uncertainty, is a crucial problem within the systems approach to biology. And yet, it has a marginal presence in the recent literature. While many existing approaches integrate methods for simulation and parameter estimation of a single model to address parameter uncertainty, only few of them address structural uncertainty at the same time. The methods for handling structure uncertainty often oversimplify the problem by allowing the human modeler to explicitly enumerate a relatively small number of alternative model structures. On the other hand, process-based modeling methods provide flexible modular formalisms for specifying large classes of plausible model structures, but their scope is limited to deterministic models. Here, we aim at extending the scope of process-based modeling methods to inductively learn stochastic models from knowledge and data.ResultsWe combine the flexibility of process-based modeling in terms of addressing structural uncertainty with the benefits of stochastic modeling. The proposed method combines search trough the space of plausible model structures, the parsimony principle and parameter estimation to identify a model with optimal structure and parameters. We illustrate the utility of the proposed method on four stochastic modeling tasks in two domains: gene regulatory networks and epidemiology. Within the first domain, using synthetically generated data, the method successfully recovers the structure and parameters of known regulatory networks from simulations. In the epidemiology domain, the method successfully reconstructs previously established models of epidemic outbreaks from real, sparse and noisy measurement data.ConclusionsThe method represents a unified approach to modeling dynamical systems that allows for flexible formalization of the space of candidate model structures, deterministic and stochastic interpretation of model dynamics, and automated induction of model structure and parameters from data. The method is able to reconstruct models of dynamical systems from synthetic and real data.