@article{banks_meade_schacht_catenacci_thompson_abate-daga_enderling_2020, title={Parameter estimation using aggregate data}, volume={100}, ISSN={["0893-9659"]}, DOI={10.1016/j.aml.2019.105999}, abstractNote={In biomedical/physiological/ecological experiments, it is common for measurements in time series data to be collected from multiple subjects. Often it is the case that a subject cannot be measured or identified at multiple time points (often referred to as aggregate population data). Due to a lack of alternative methods, this form of data is typically treated as if it is collected from a single individual. As we show by examples, this assumption leads to an overconfidence in model parameter (means, variances) values and model based predictions. We discuss these issues in the context of a mathematical model to determine T-cell behavior with cancer chimeric antigen receptor (CAR) therapies where during the collection of data cancerous mice are sacrificed at each measurement time.}, journal={APPLIED MATHEMATICS LETTERS}, author={Banks, H. . T. and Meade, Annabel E. and Schacht, Celia and Catenacci, Jared and Thompson, W. Clayton and Abate-Daga, Daniel and Enderling, Heiko}, year={2020}, month={Feb} }
 @article{banks_baraldi_catenacci_myers_2016, title={Parameter Estimation Using Unidentified Individual Data in Individual Based Models}, volume={11}, ISSN={["1760-6101"]}, DOI={10.1051/mmnp/201611602}, abstractNote={In physiological experiments, it is common for measurements to be collected from multiple subjects. Often it is the case that a subject cannot be measured or identified at multiple time points (referred to as unidentified individual data in this work but often referred to as aggregate population data [5, Chapter 5]). Due to a lack of alternative methods, this form of data is typically treated as if it is collected from a single individual. This assumption leads to an overconfidence in model parameter values and model based predictions. We propose a novel method which accounts for inter-individual variability in experiments where only unidentified individual data is available. Both parametric and nonparametric methods for estimating the distribution of parameters which vary among individuals are developed. These methods are illustrated using both simulated data, and data taken from a physiological experiment. Taking the approach outlined in this paper results in more accurate quantification of the uncertainty attributed to inter-individual variability.}, number={6}, journal={MATHEMATICAL MODELLING OF NATURAL PHENOMENA}, author={Banks, H. T. and Baraldi, R. and Catenacci, J. and Myers, N.}, year={2016}, pages={9–27} }
 @article{banks_catenacci_criner_2016, title={Quantifying the degradation in thermally treated ceramic matrix composites}, volume={52}, ISSN={["1875-8800"]}, DOI={10.3233/jae-162168}, abstractNote={Reflectance spectroscopy obtained from a thermally treated silicon nitride carbon based ceramic matrix composite is used to quantity the oxidation products SiO2 and SiN. The data collection is described in detail in order to point out the potential biasing present in the data processing. A probability distribution is imposed on select model parameters, and then non-parametrically estimated. A non-parametric estimation is chosen since the exact composition of the material is unknown due to the inherent heterogeneity of ceramic composites. The probability distribution is estimated using the Prohorov metric framework in which the infinite dimensional optimization is reduced to a finite dimensional optimization using an approximating space composed of linear splines. A weighted least squares estimation is carried out, and uncertainty quantification is performed on the model parameters, including a piecewise asymptotic confidence band for the estimated probability density. Our estimation results indicate a distinguishable increase in the SiO2 present in the samples which were heat treated for 100 hours compared to 10 hours.}, number={1-2}, journal={INTERNATIONAL JOURNAL OF APPLIED ELECTROMAGNETICS AND MECHANICS}, author={Banks, H. T. and Catenacci, Jared and Criner, Amanda}, year={2016}, pages={3–24} }
 @article{banks_catenacci_hu_2016, title={Use of difference-based methods to explore statistical and mathematical model discrepancy in inverse problems}, volume={24}, number={4}, journal={Journal of Inverse and Ill-Posed Problems}, author={Banks, H. T. and Catenacci, J. and Hu, S. H.}, year={2016}, pages={413–433} }
 @article{banks_catenacci_hu_2015, title={Estimation of distributed parameters in permittivity models of composite dielectric materials using reflectance}, volume={23}, number={5}, journal={Journal of Inverse and Ill-Posed Problems}, author={Banks, H. T. and Catenacci, J. and Hu, S. H.}, year={2015}, pages={491–509} }
 @inproceedings{criner_cherry_cooney_katter_banks_hu_catenacci_2015, title={Identification of thermal degradation using probabilistic models in reflectance spectroscopy}, volume={1650}, booktitle={41st annual review of progress in quantitative nondestructive evaluation, vol 34}, author={Criner, A. K. and Cherry, A. J. and Cooney, A. T. and Katter, T. D. and Banks, H. T. and Hu, S. H. and Catenacci, J.}, year={2015}, pages={1898–1906} }
 @inproceedings{banks_catenacci_hu_kenz_2014, title={Decomposition of permittivity contributions from reflectance using mechanism models}, booktitle={2014 american control conference (acc)}, author={Banks, H. T. and Catenacci, J. and Hu, S. H. and Kenz, Z. R.}, year={2014}, pages={367–372} }