ArticleCommunications in applied analysis2019
Estimation of the Distribution of Random Parameters in Discrete Time Abstract Parabolic Systems with Unbounded Input and Output: Approximation and Convergence.
Article in Communications in applied analysis, 2019. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Cited by 12 papers.
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Who cites it
12 citing papers in PubMed.
- REAL-TIME RECURSIVE ESTIMATION OF, AND UNCERTAINTY QUANTIFICATION FOR, BREATH ALCOHOL CONCENTRATION VIA LQ TRACKING CONTROL-BASED INVERSE FILTERING OF TRANSDERMAL ALCOHOL BIOSENSOR SIGNALS.Applied mathematics for modern challenges · 2024Article
- Computation of nonparametric, mixed effects, maximum likelihood, biosensor data based-estimators for the distributions of random parameters in an abstract parabolic model for the transdermal transport of alcohol.Mathematical biosciences and engineering : MBE · 2023Article
- Uncertainty Quantification in Estimating Blood Alcohol Concentration From Transdermal Alcohol Level With Physics-Informed Neural Networks.IEEE transactions on neural networks and learning systems · 2023Article
- Article
- Effects of stomach content on the breath alcohol concentration-transdermal alcohol concentration relationship.Drug and alcohol review · 2021Article
- Deconvolving breath alcohol concentration from biosensor measured transdermal alcohol level under uncertainty: a Bayesian approach.Mathematical biosciences and engineering : MBE · 2021Article
- Applying a novel population-based model approach to estimating breath alcohol concentration (BrAC) from transdermal alcohol concentration (TAC) biosensor data.Alcohol (Fayetteville, N.Y.) · 2019Article
- Estimating the Distribution of Random Parameters in a Diffusion Equation Forward Model for a Transdermal Alcohol Biosensor.Automatica : the journal of IFAC, the International Federation of Automatic Control · 2019Article
- Estimating intratumoral heterogeneity from spatiotemporal data.Journal of mathematical biology · 2018Article
- Deconvolving the input to random abstract parabolic systems: a population model-based approach to estimating blood/breath alcohol concentration from transdermal alcohol biosensor data.Inverse problems · 2018Article
- THE PROHOROV METRIC FRAMEWORK AND AGGREGATE DATA INVERSE PROBLEMS FOR RANDOM PDEs.Communications in applied analysis · 2018Article
- A population model-based linear-quadratic Gaussian compensator for the control of intravenously infused alcohol studies and withdrawal symptom prophylaxis using transdermal sensing.Optimal control applications & methodsArticle
Corrections and comments
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Authors and funding
3 authors.
Funding
Abstract
A finite dimensional abstract approximation and convergence theory is developed for estimation of the distribution of random parameters in infinite dimensional discrete time linear systems with dynamics described by regularly dissipative operators and involving, in general, unbounded input and output operators. By taking expectations, the system is re-cast as an equivalent abstract parabolic system in a Gelfand triple of Bochner spaces wherein the random parameters become new space-like variables. Estimating their distribution is now analogous to estimating a spatially varying coefficient in a standard deterministic parabolic system. The estimation problems are approximated by a sequence of finite dimensional problems. Convergence is established using a state space-varying version of the Trotter-Kato semigroup approximation theorem. Numerical results for a number of examples involving the estimation of exponential families of densities for random parameters in a diffusion equation with boundary input and output are presented and discussed.
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