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1	Information Content in Data Sets: A Review of Methods for Interrogation and Model Comparison Banks, H. Thomas, Joyner, Michele L. 01 January 2018 (has links) In this reviewwe discuss methodology to ascertain the amount of information in given data sets with respect to determination of model parameters with desired levels of uncertainty.We do this in the context of least squares (ordinary,weighted, iterative reweightedweighted or "generalized", etc.) based inverse problem formulations. The ideas are illustrated with several examples of interest in the biological and environmental sciences. akaike information criterion information content model comparison techniques sensitivity weighted least squares Mathematics and Statistics
2	Parameter Estimation in Random Differential Equation Models Banks, H. T., Joyner, M. L. 01 January 2017 (has links) We consider two distinct techniques for estimating random parameters in random differential equation (RDE) models. In one approach, the solution to a RDE is represented by a collection of solution trajectories in the form of sample deterministic equations. In a second approach we employ pointwise equivalent stochastic differential equation (SDE) representations for certain RDEs. Each of the approaches is tested using deterministic model comparison techniques for a logistic growth model which is viewed as a special case of a more general Bernoulli growth model. We demonstrate efficacy of the preferred method with experimental data using algae growth model comparisons. model comparison techniques parameter estimation random differential equations Mathematics and Statistics
3	Adaption of Akaike Information Criterion Under Least Squares Frameworks for Comparison of Stochastic Models Banks, H. T., Joyner, Michele L. 01 January 2019 (has links) In this paper, we examine the feasibility of extending the Akaike information criterion (AIC) for deterministic systems as a potential model selection criteria for stochastic models. We discuss the implementation method for three different classes of stochastic models: continuous time Markov chains (CTMC), stochastic differential equations (SDE), and random differential equations (RDE). The effectiveness and limitations of implementing the AIC for comparison of stochastic models is demonstrated using simulated data from the three types of models and then applied to experimental longitudinal growth data for algae. AIC akaike information criterion continuous time Markov chain models CTMC inverse problems model comparison techniques random differential equations RDE SDE stochastic differential equations Mathematics and Statistics

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