10,058 research outputs found
Understanding predictive uncertainty in hydrologic modeling: The challenge of identifying input and structural errors
Meaningful quantification of data and structural uncertainties in conceptual rainfall-runoff modeling is a major scientific and engineering challenge. This paper focuses on the total predictive uncertainty and its decomposition into input and structural components under different inference scenarios. Several Bayesian inference schemes are investigated, differing in the treatment of rainfall and structural uncertainties, and in the precision of the priors describing rainfall uncertainty. Compared with traditional lumped additive error approaches, the quantification of the total predictive uncertainty in the runoff is improved when rainfall and/or structural errors are characterized explicitly. However, the decomposition of the total uncertainty into individual sources is more challenging. In particular, poor identifiability may arise when the inference scheme represents rainfall and structural errors using separate probabilistic models. The inference becomes illâposed unless sufficiently precise prior knowledge of data uncertainty is supplied; this illâposedness can often be detected from the behavior of the Monte Carlo sampling algorithm. Moreover, the priors on the data quality must also be sufficiently accurate if the inference is to be reliable and support meaningful uncertainty decomposition. Our findings highlight the inherent limitations of inferring inaccurate hydrologic models using rainfallârunoff data with large unknown errors. Bayesian total error analysis can overcome these problems using independent prior information. The need for deriving independent descriptions of the uncertainties in the input and output data is clearly demonstrated.Benjamin Renard, Dmitri Kavetski, George Kuczera, Mark Thyer, and Stewart W. Frank
Parameter Estimation and Uncertainty Quantication for an Epidemic Model
We examine estimation of the parameters of Susceptible-Infective-Recovered (SIR) models in the context of least squares. We review the use of asymptotic statistical theory and sensitivity analysis to obtain measures of uncertainty for estimates of the model parameters and the basic reproductive number (R0 )âan epidemiologically signiïŹcant parameter grouping. We ïŹnd that estimates of diïŹerent parameters, such as the transmission parameter and recovery rate, are correlated, with the magnitude and sign of this correlation depending on the value of R0. Situations are highlighted in which this correlation allows R0 to be estimated with greater ease than its constituent parameters. Implications of correlation for parameter identiïŹability are discussed. Uncertainty estimates and sensitivity analysis are used to investigate how the frequency at which data is sampled aïŹects the estimation process and how the accuracy and uncertainty of estimates improves as data is collected over the course of an outbreak. We assess the informativeness of individual data points in a given time series to determine when more frequent sampling (if possible) would prove to be most beneïŹcial to the estimation process. This technique can be used to design data sampling schemes in more general contexts
Identifiability issues of age-period and age-period-cohort models of the Lee-Carter type
The predominant way of modelling mortality rates is the Lee-Carter model and
its many extensions. The Lee-Carter model and its many extensions use a latent
process to forecast. These models are estimated using a two-step procedure that
causes an inconsistent view on the latent variable. This paper considers
identifiability issues of these models from a perspective that acknowledges the
latent variable as a stochastic process from the beginning. We call this
perspective the plug-in age-period or plug-in age-period-cohort model. Defining
a parameter vector that includes the underlying parameters of this process
rather than its realisations, we investigate whether the expected values and
covariances of the plug-in Lee-Carter models are identifiable. It will be seen,
for example, that even if in both steps of the estimation procedure we have
identifiability in a certain sense it does not necessarily carry over to the
plug-in models
Spatial two tissue compartment model for DCE-MRI
In the quantitative analysis of Dynamic Contrast-Enhanced Magnetic Resonance
Imaging (DCE-MRI) compartment models allow to describe the uptake of contrast
medium with biological meaningful kinetic parameters. As simple models often
fail to adequately describe the observed uptake behavior, more complex
compartment models have been proposed. However, the nonlinear regression
problem arising from more complex compartment models often suffers from
parameter redundancy. In this paper, we incorporate spatial smoothness on the
kinetic parameters of a two tissue compartment model by imposing Gaussian
Markov random field priors on them. We analyse to what extent this spatial
regularisation helps to avoid parameter redundancy and to obtain stable
parameter estimates. Choosing a full Bayesian approach, we obtain posteriors
and point estimates running Markov Chain Monte Carlo simulations. The proposed
approach is evaluated for simulated concentration time curves as well as for in
vivo data from a breast cancer study
Adaptive optimal operation of a parallel robotic liquid handling station
Results are presented from the optimal operation of a fully automated robotic liquid handling station where parallel experiments are performed for calibrating a kinetic fermentation model. To increase the robustness against uncertainties and/or wrong assumptions about the parameter values, an iterative calibration and experiment design approach is adopted. Its implementation yields a stepwise reduction of parameter uncertainties together with an adaptive redesign of reactor feeding strategies whenever new measurement information is available. The case study considers the adaptive optimal design of 4 parallel fed-batch strategies implemented in 8 mini-bioreactors. Details are given on the size and complexity of the problem and the challenges related to calibration of over-parameterized models and scarce and non-informative measurement data. It is shown how methods for parameter identifiability analysis and numerical regularization can be used for monitoring the progress of the experimental campaigns in terms of generated information regarding parameters and selection of the best fitting parameter subset.BMBF, 02PJ1150, Verbundprojekt: Plattformtechnologien fĂŒr automatisierte Bioprozessentwicklung (AutoBio); Teilprojekt: Automatisierte Bioprozessentwicklung am Beispiel von neuen Nukleosidphosphorylase
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