Statistics of Parameter Estimates: A Concrete Example

Aguilar, Oscar Manuel; Allmaras, Moritz; Bangerth, Wolfgang

doi:10.1137/130929230

Cited by 21 publications

(15 citation statements)

References 15 publications

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“…A more formal way to determine

{boldC}_{z z}

using a proxy model instead of the modeler's drafting is described in Aguilar et al . [], even though we argue that direct drafting is a better way to represent the modeler's knowledge about the desired fidelity of the model. More sophisticated error models may be developed in a precalibration study [e.g., Kaipio and Somersalo , ; Cooley and Christensen , ; Lehikoinen et al ., ], or their stochastic parameters estimated as part of the inversion itself [ Carrera and Neuman , ; Schoups and Vrugt , ; Finsterle and Zhang , ].…”

Section: Theoretical Backgroundmentioning

confidence: 98%

Practical notes on local data‐worth analysis

Finsterle

2015

Water Resources Research

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These notes discuss the usefulness, limitations, and potential pitfalls of using sensitivity indices as a means to evaluate data worth and to guide the formulation and solution of inverse problems. A sensitivity analysis examines changes in model output variables with respect to changes in model input parameters. It appears straightforward to use this information to select influential parameters that should be subjected to estimation by inverse modeling and to identify the observations that contain information about these parameters and thus may be useful as calibration points. However, the results of such a sensitivity analysis do not account for parameter correlations and redundancies in observations and may not properly separate between calibration and prediction targets if used as criteria that guide inverse modeling; they may thus yield misleading recommendations about parameter identifiability and data worth. These issues (and some remedies) are discussed using an illustrative example, in which we examine the value of data sets potentially used for the calibration of a geothermal reservoir model. These notes highlight the importance of carefully formulating the objectives of a simulation study, which controls the setup of the inverse problem and related data needs.

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“…A more formal way to determine

{boldC}_{z z}

Section: Theoretical Backgroundmentioning

confidence: 98%

Practical notes on local data‐worth analysis

Finsterle

2015

Water Resources Research

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“…Parameter inference is approached generally in one of two ways, either through a frequentist approach or a Bayesian approach [2,6]. In frequentist inference, one generally seeks a point estimate of a parameter through maximum likelihood estimation, and captures uncertainty in the estimate through the generation of confidence intervals.…”

Section: Approximate Bayesian Computation and Summary Statisticsmentioning

confidence: 99%

The impact of experimental design choices on parameter inference for models of growing cell colonies

Parker

Simpson

Baker

2017

Preprint

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To better understand development, repair and disease progression it is useful to quantify the behaviour of proliferative and motile cell populations as they grow and expand to fill their local environment. Inferring parameters associated with mechanistic models of cell colony growth using quantitative data collected from carefully designed experiments provides a natural means to elucidate the relative contributions of various processes to the growth of the colony. In this work we explore how experimental design impacts our ability to infer parameters for simple models of the growth of proliferative and motile cell populations. We adopt a Bayesian approach, which allows us to characterise the uncertainty associated with estimates of the model parameters. Our results suggest that experimental designs that incorporate initial spatial heterogeneities in cell positions facilitate parameter inference without the requirement of cell tracking, whilst designs that involve uniform initial placement of cells require cell tracking for accurate parameter inference. As cell tracking is an experimental bottleneck in many studies of this type, our recommendations for experimental design provide for significant potential time and cost savings in the analysis of cell colony growth.

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“…The statistical measures used here provide a superficial glimpse into the dimer exchange data. Much deeper analyses of parameter estimates are common [1]. Future work aims to reduce the variance in k + by collecting more data from the first hour of the assay, to address the peak parameter sensitivities described in section 4.3.…”

Section: Data Modelingmentioning

confidence: 99%

Modeling, Simulating, and Parameter Fitting of Biochemical Kinetic Experiments

Goulet¹

2016

SIAM Rev.

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Abstract. In many chemical and biological applications, systems of differential equations containing unknown parameters are used to explain empirical observations and experimental data. 1. Introduction. The empirical study of many current biological problems generates large and complex data sets. How best to use this data to generate and improve scientific hypotheses is a subject of great interest to biologists, mathematicians, statisticians, and computational scientists. Combining these various scientific and quantitative disciplines requires careful communication. Figure 1 illustrates the flow of information for a typical problem in quantitative biology.The modeling process described in the present work began with the formation of a scientific hypothesis based on laboratory experiments and intuition. This theory was used by biochemists to construct an experimental protocol and generate data. The same theory was used by mathematicians to develop a mathematical model, which was studied analytically and simulated computationally. Both models were intended to confirm or improve hypotheses. The theory and experiments are described in section 2, while the mathematical and computational models are described in sections 3 and 4, respectively.For the biological model to feed back on theory, its output data needed to be analyzed. For the quantitative model to feed back on theory, its unknown parameter

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Statistics of Parameter Estimates: A Concrete Example

Abstract: Abstract. Most mathematical models include parameters that need to be determined from measurements.

Cited by 21 publications

References 15 publications

Practical notes on local data‐worth analysis

Practical notes on local data‐worth analysis

The impact of experimental design choices on parameter inference for models of growing cell colonies

Modeling, Simulating, and Parameter Fitting of Biochemical Kinetic Experiments

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