scholarly journals Assessing model mismatch and model selection in a Bayesian uncertainty quantification analysis of a fluid-dynamics model of pulmonary blood circulation

2020 ◽  
Vol 17 (173) ◽  
pp. 20200886
Author(s):  
L. Mihaela Paun ◽  
Mitchel J. Colebank ◽  
Mette S. Olufsen ◽  
Nicholas A. Hill ◽  
Dirk Husmeier
Keyword(s):  
Model Selection ◽  
Mean Squared Error ◽  
Formal Model ◽  
Circulation Model ◽  
Noise Model ◽  
Parameter Estimates ◽  
Model Parameters ◽  
Imaging Data ◽  
Micro Computed Tomography ◽  
Model Mismatch

This study uses Bayesian inference to quantify the uncertainty of model parameters and haemodynamic predictions in a one-dimensional pulmonary circulation model based on an integration of mouse haemodynamic and micro-computed tomography imaging data. We emphasize an often neglected, though important source of uncertainty: in the mathematical model form due to the discrepancy between the model and the reality, and in the measurements due to the wrong noise model (jointly called ‘model mismatch’). We demonstrate that minimizing the mean squared error between the measured and the predicted data (the conventional method) in the presence of model mismatch leads to biased and overly confident parameter estimates and haemodynamic predictions. We show that our proposed method allowing for model mismatch, which we represent with Gaussian processes, corrects the bias. Additionally, we compare a linear and a nonlinear wall model, as well as models with different vessel stiffness relations. We use formal model selection analysis based on the Watanabe Akaike information criterion to select the model that best predicts the pulmonary haemodynamics. Results show that the nonlinear pressure–area relationship with stiffness dependent on the unstressed radius predicts best the data measured in a control mouse.

scholarly journals Approximate Bayesian computation reveals the importance of repeated measurements for parameterising cell-based models of growing tissues

2017 ◽  
Author(s):  
Jochen Kursawe ◽  
Ruth E. Baker ◽  
Alexander G. Fletcher
Keyword(s):  
Computational Models ◽  
Imaging Techniques ◽  
Quantitative Model ◽  
Repeated Measurements ◽  
Parameter Estimates ◽  
Model Parameters ◽  
Summary Statistics ◽  
Imaging Data ◽  
Reliable Parameter ◽  
Approximate Bayesian

AbstractThe growth and dynamics of epithelial tissues govern many morphogenetic processes in embryonic development. A recent quantitative transition in data acquisition, facilitated by advances in genetic and live-imaging techniques, is paving the way for new insights to these processes. Computational models can help us understand and interpret observations, and then make predictions for future experiments that can distinguish between hypothesised mechanisms. Increasingly, cell-based modelling approaches such as vertex models are being used to help understand the mechanics underlying epithelial morphogenesis. These models typically seek to reproduce qualitative phenomena, such as cell sorting or tissue buckling. However, it remains unclear to what extent quantitative data can be used to constrain these models so that they can then be used to make quantitative, experimentally testable predictions. To address this issue, we perform an in silico study to investigate whether vertex model parameters can be inferred from imaging data, and explore methods to quantify the uncertainty of such estimates. Our approach requires the use of summary statistics to estimate parameters. Here, we focus on summary statistics of cellular packing and of laser ablation experiments, as are commonly reported from imaging studies. We find that including data from repeated experiments is necessary to generate reliable parameter estimates that can facilitate quantitative model predictions.

scholarly journals Parameter Calibration in Crowd Simulation Models using Approximate Bayesian Computation

2020 ◽  
Vol 5 ◽  
Author(s):  
Nikolai Bode
Keyword(s):  
Model Selection ◽  
Approximate Bayesian Computation ◽  
Model Fitting ◽  
Simulation Models ◽  
Parameter Estimates ◽  
Model Parameters ◽  
Bayesian Computation ◽  
Continuous Space ◽  
Pedestrian Dynamics ◽  
Approximate Bayesian

Simulation models for pedestrian crowds are a ubiquitous tool in research and industry. It is crucial that the parameters of these models are calibrated carefully and ultimately it will be of interest to compare competing models to decide which model is best suited for a particular purpose. In this contribution, I demonstrate how Approximate Bayesian Computation (ABC), which is already a popular tool in other areas of science, can be used for model fitting and model selection in a pedestrian dynamics context. I fit two different models for pedestrian dynamics to data on a crowd passing in one direction through a bottleneck. One model describes movement in continuous-space, the other model is a cellular automaton and thus describes movement in discrete-space. In addition, I compare models to data using two metrics. The first is based on egress times and the second on the velocity of pedestrians in front of the bottleneck. My results show that while model fitting is successful, a substantial degree of uncertainty about the value of some model parameters remains after model fitting. Importantly, the choice of metric in model fitting can influence parameter estimates. Model selection is inconclusive for the egress time metric but supports the continuous-space model for the velocity-based metric. These findings show that ABC is a flexible approach and highlights the difficulties associated with model fitting and model selection for pedestrian dynamics. ABC requires many simulation runs and choosing appropriate metrics for comparing data to simulations requires careful attention. Despite this, I suggest ABC is a promising tool, because it is versatile and easily implemented for the growing number of openly available crowd simulators and data sets.

An Information-theoretical Model for Breast Cancer Detection

2008 ◽  
Vol 47 (04) ◽  
pp. 322-327 ◽  
Author(s):  
D. Blokh ◽  
N. Zurgil ◽  
I. Stambler ◽  
E. Afrimzon ◽  
Y. Shafran ◽  
...  
Keyword(s):  
Breast Cancer ◽  
Cancer Detection ◽  
Hamming Distance ◽  
Formal Model ◽  
Methodological Approach ◽  
Breast Cancer Detection ◽  
Receptor Expression ◽  
Diagnostic Model ◽  
Model Parameters ◽  
Two Stages

Summary Objectives: Formal diagnostic modeling is an important line of modern biological and medical research. The construction of a formal diagnostic model consists of two stages: first, the estimation of correlation between model parameters and the disease under consideration; and second, the construction of a diagnostic decision rule using these correlation estimates. A serious drawback of current diagnostic models is the absence of a unified mathematical methodological approach to implementing these two stages. The absence of aunified approach makesthe theoretical/biomedical substantiation of diagnostic rules difficult and reduces the efficacyofactual diagnostic model application. Methods: The present study constructs a formal model for breast cancer detection. The diagnostic model is based on information theory. Normalized mutual information is chosen as the measure of relevance between parameters and the patterns studied. The “nearest neighbor” rule is utilized for diagnosis, while the distance between elements is the weighted Hamming distance. The model concomitantly employs cellular fluorescence polarization as the quantitative input parameter and cell receptor expression as qualitative parameters. Results: Twenty-four healthy individuals and 34 patients (not including the subjects analyzed for the model construction) were tested by the model. Twenty-three healthy subjects and 34 patients were correctly diagnosed. Conclusions: The proposed diagnostic model is an open one,i.e.it can accommodate new additional parameters, which may increase its effectiveness.

scholarly journals Parameter stability and consistency in an alongshore-current model determined with Markov chain Monte Carlo

2008 ◽  
Vol 10 (2) ◽  
pp. 153-162 ◽  
Author(s):  
B. G. Ruessink
Keyword(s):  
Monte Carlo ◽  
Markov Chain ◽  
Markov Chain Monte Carlo ◽  
Parameter Estimates ◽  
Model Parameters ◽  
Parameter Stability ◽  
Small Uncertainty ◽  
Best Fit ◽  
Stability And Consistency

When a numerical model is to be used as a practical tool, its parameters should preferably be stable and consistent, that is, possess a small uncertainty and be time-invariant. Using data and predictions of alongshore mean currents flowing on a beach as a case study, this paper illustrates how parameter stability and consistency can be assessed using Markov chain Monte Carlo. Within a single calibration run, Markov chain Monte Carlo estimates the parameter posterior probability density function, its mode being the best-fit parameter set. Parameter stability is investigated by stepwise adding new data to a calibration run, while consistency is examined by calibrating the model on different datasets of equal length. The results for the present case study indicate that various tidal cycles with strong (say, >0.5 m/s) currents are required to obtain stable parameter estimates, and that the best-fit model parameters and the underlying posterior distribution are strongly time-varying. This inconsistent parameter behavior may reflect unresolved variability of the processes represented by the parameters, or may represent compensational behavior for temporal violations in specific model assumptions.

Multi-day flow forecasting using the Kalman filter

1991 ◽  
Vol 18 (2) ◽  
pp. 320-327 ◽  
Author(s):  
Murray A. Fitch ◽  
Edward A. McBean
Keyword(s):  
Kalman Filter ◽  
Prediction Model ◽  
Linear Prediction ◽  
Measured Data ◽  
System Model ◽  
Parameter Estimates ◽  
Model Parameters ◽  
Forecasting Performance ◽  
Optimal Forecasting ◽  
Linear Prediction Model

A model is developed for the prediction of river flows resulting from combined snowmelt and precipitation. The model employs a Kalman filter to reflect uncertainty both in the measured data and in the system model parameters. The forecasting algorithm is used to develop multi-day forecasts for the Sturgeon River, Ontario. The algorithm is shown to develop good 1-day and 2-day ahead forecasts, but the linear prediction model is found inadequate for longer-term forecasts. Good initial parameter estimates are shown to be essential for optimal forecasting performance. Key words: Kalman filter, streamflow forecast, multi-day, streamflow, Sturgeon River, MISP algorithm.

Renal function measurements from MR renography and a simplified multicompartmental model

2007 ◽  
Vol 292 (5) ◽  
pp. F1548-F1559 ◽  
Author(s):  
Vivian S. Lee ◽  
Henry Rusinek ◽  
Louisa Bokacheva ◽  
Ambrose J. Huang ◽  
Niels Oesingmann ◽  
...  
Keyword(s):  
Low Dose ◽  
Random Noise ◽  
Compartment Model ◽  
Parameter Estimates ◽  
Imaging Data ◽  
Tracer Injection ◽  
Multicompartmental Model ◽  
Enhancement Curve ◽  
Reference Measurements ◽  
Single Kidney

The purpose of this study was to determine the accuracy and sources of error in estimating single-kidney glomerular filtration rate (GFR) derived from low-dose gadolinium-enhanced T1-weighted MR renography. To analyze imaging data, MR signal intensity curves were converted to concentration vs. time curves, and a three-compartment, six-parameter model of the vascular-nephron system was used to analyze measured aortic, cortical, and medullary enhancement curves. Reliability of the parameter estimates was evaluated by sensitivity analysis and by Monte Carlo analyses of model solutions to which random noise had been added. The dominant sensitivity of the medullary enhancement curve to GFR 1–4 min after tracer injection was supported by a low coefficient of variation in model-fit GFR values (4%) when measured data were subjected to 5% noise. These analyses also showed the minimal effects of bolus dispersion in the aorta on parameter reliability. Single-kidney GFR from MR renography analyzed by the three-compartment model (4.0–71.4 ml/min) agreed well with reference measurements from 99mTc-DTPA clearance and scintigraphy ( r = 0.84, P < 0.001). Bland-Altman analysis showed an average difference of 11.9 ml/min (95% confidence interval = 5.8–17.9 ml/min) between model and reference values. We conclude that a nephron-based multicompartmental model can be used to derive clinically useful estimates of single-kidney GFR from low-dose MR renography.

Generalised DOPs with Consideration of the Influence Function of Signal-in-Space Errors

2011 ◽  
Vol 64 (S1) ◽  
pp. S3-S18 ◽  
Author(s):  
Yuanxi Yang ◽  
Jinlong Li ◽  
Junyi Xu ◽  
Jing Tang
Keyword(s):  
Least Squares ◽  
Stochastic Models ◽  
Influence Function ◽  
A Priori ◽  
Functional Model ◽  
Global Navigation Satellite Systems ◽  
Parameter Estimates ◽  
Model Parameters ◽  
Integrated Navigation ◽  
Satellite Systems

Integrated navigation using multiple Global Navigation Satellite Systems (GNSS) is beneficial to increase the number of observable satellites, alleviate the effects of systematic errors and improve the accuracy of positioning, navigation and timing (PNT). When multiple constellations and multiple frequency measurements are employed, the functional and stochastic models as well as the estimation principle for PNT may be different. Therefore, the commonly used definition of “dilution of precision (DOP)” based on the least squares (LS) estimation and unified functional and stochastic models will be not applicable anymore. In this paper, three types of generalised DOPs are defined. The first type of generalised DOP is based on the error influence function (IF) of pseudo-ranges that reflects the geometry strength of the measurements, error magnitude and the estimation risk criteria. When the least squares estimation is used, the first type of generalised DOP is identical to the one commonly used. In order to define the first type of generalised DOP, an IF of signal–in-space (SIS) errors on the parameter estimates of PNT is derived. The second type of generalised DOP is defined based on the functional model with additional systematic parameters induced by the compatibility and interoperability problems among different GNSS systems. The third type of generalised DOP is defined based on Bayesian estimation in which the a priori information of the model parameters is taken into account. This is suitable for evaluating the precision of kinematic positioning or navigation. Different types of generalised DOPs are suitable for different PNT scenarios and an example for the calculation of these DOPs for multi-GNSS systems including GPS, GLONASS, Compass and Galileo is given. New observation equations of Compass and GLONASS that may contain additional parameters for interoperability are specifically investigated. It shows that if the interoperability of multi-GNSS is not fulfilled, the increased number of satellites will not significantly reduce the generalised DOP value. Furthermore, the outlying measurements will not change the original DOP, but will change the first type of generalised DOP which includes a robust error IF. A priori information of the model parameters will also reduce the DOP.

Optimized blood sampling protocols and sequential design of kinetic experiments

1981 ◽  
Vol 240 (5) ◽  
pp. R259-R265 ◽  
Author(s):  
J. J. DiStefano
Keyword(s):  
Endocrine System ◽  
Primary Objective ◽  
Blood Sampling ◽  
Optimal Designs ◽  
Parameter Estimates ◽  
Model Parameters ◽  
Reverse T3 ◽  
Model Parameter ◽  
Maximum Accuracy ◽  
Sampling Protocols

Design of optimal blood sampling protocols for kinetic experiments is discussed and evaluated, with the aid of several examples--including an endocrine system case study. The criterion of optimality is maximum accuracy of kinetic model parameter estimates. A simple example illustrates why a sequential experiment approach is required; optimal designs depend on the true model parameter values, knowledge of which is usually a primary objective of the experiment, as well as the structure of the model and the measurement error (e.g., assay) variance. The methodology is evaluated from the results of a series of experiments designed to quantify the dynamics of distribution and metabolism of three iodothyronines, T3, T4, and reverse-T3. This analysis indicates that 1) the sequential optimal experiment approach can be effective and efficient in the laboratory, 2) it works in the presence of reasonably controlled biological variation, producing sufficiently robust sampling protocols, and 3) optimal designs can be highly efficient designs in practice, requiring for maximum accuracy a number of blood samples equal to the number of independently adjustable model parameters, no more or less.

scholarly journals Operational ocean models in the Adriatic Sea: a skill assessment

Ocean Science ◽  
2008 ◽  
Vol 4 (1) ◽  
pp. 61-71 ◽  
Author(s):  
J. Chiggiato ◽  
P. Oddo
Keyword(s):  
General Circulation ◽  
Mean Squared Error ◽  
Three Dimensional ◽  
Circulation Model ◽  
Remote Sensing Data ◽  
Skill Assessment ◽  
Regional Models ◽  
Operational Systems ◽  
Forecasting System ◽  
The Mediterranean

Abstract. In the framework of the Mediterranean Forecasting System (MFS) project, the performance of regional numerical ocean forecasting systems is assessed by means of model-model and model-data comparison. Three different operational systems considered in this study are: the Adriatic REGional Model (AREG); the Adriatic Regional Ocean Modelling System (AdriaROMS) and the Mediterranean Forecasting System General Circulation Model (MFS-GCM). AREG and AdriaROMS are regional implementations (with some dedicated variations) of POM and ROMS, respectively, while MFS-GCM is an OPA based system. The assessment is done through standard scores. In situ and remote sensing data are used to evaluate the system performance. In particular, a set of CTD measurements collected in the whole western Adriatic during January 2006 and one year of satellite derived sea surface temperature measurements (SST) allow to asses a full three-dimensional picture of the operational forecasting systems quality during January 2006 and to draw some preliminary considerations on the temporal fluctuation of scores estimated on surface quantities between summer 2005 and summer 2006. The regional systems share a negative bias in simulated temperature and salinity. Nonetheless, they outperform the MFS-GCM in the shallowest locations. Results on amplitude and phase errors are improved in areas shallower than 50 m, while degraded in deeper locations, where major models deficiencies are related to vertical mixing overestimation. In a basin-wide overview, the two regional models show differences in the local displacement of errors. In addition, in locations where the regional models are mutually correlated, the aggregated mean squared error was found to be smaller, that is a useful outcome of having several operational systems in the same region.

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