@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{stemkovski_baraldi_flores_banks_2016, title={Validation of a mathematical model for green algae (Raphidocelis Subcapitata) growth and implications for a coupled dynamical system with Daphnia magna}, volume={6}, number={5}, journal={Applied Sciences-Basel}, author={Stemkovski, M. and Baraldi, R. and Flores, K. B. and Banks, H. T.}, year={2016} }
 @article{banks_baraldi_cross_flores_mcchesney_poag_thorpe_2015, title={UNCERTAINTY QUANTIFICATION IN MODELING HIV VIRAL MECHANICS}, volume={12}, ISSN={["1551-0018"]}, DOI={10.3934/mbe.2015.12.937}, abstractNote={We consider an in-host model for HIV-1 infection dynamics developed and validated with patient data in earlier work [7]. We revisit the earlier model in light of progress over the last several years in understanding HIV-1 progression in humans. We then consider statistical models to describe the data and use these with residual plots in generalized least squares problems to develop accurate descriptions of the proper weights for the data. We use recent parameter subset selection techniques [5,6] to investigate the impact of estimated parameters on the corresponding selection scores. Bootstrapping and asymptotic theory are compared in the context of confidence intervals for the resulting parameter estimates.}, number={5}, journal={MATHEMATICAL BIOSCIENCES AND ENGINEERING}, author={Banks, H. T. and Baraldi, Robert and Cross, Karissa and Flores, Kevin and Mcchesney, Christina and Poag, Laura and Thorpe, Emma}, year={2015}, month={Oct}, pages={937–964} }
 @inproceedings{baraldi_cross_mcchesney_poag_thorpe_flores_banks_2014, title={Uncertainty quantification for a model of HIV-1 patient response to antiretroviral therapy interruptions}, booktitle={2014 american control conference (acc)}, author={Baraldi, R. and Cross, K. and McChesney, C. and Poag, L. and Thorpe, E. and Flores, K. B. and Banks, H. T.}, year={2014}, pages={2753–2758} }