Academic Appointments

Lecturer, Mathematics
202324 Courses
 Differential Equations with Linear Algebra, Fourier Methods, and Modern Applications
MATH 53 (Spr)  Foundations for Calculus
MATH 18 (Aut)  Partial Differential Equations
MATH 131P (Win)  Preparation for Success in Mathematics at Stanford
SOAR 10MA (Aut)  Proofs and Modern Mathematics
MATH 56 (Win) 
Prior Year Courses
202223 Courses
 Calculus
MATH 19 (Aut)  Calculus
MATH 20 (Win)  Calculus, ACE
MATH 19ACE (Aut)  Calculus, ACE
MATH 20ACE (Win)  Differential Equations with Linear Algebra, Fourier Methods, and Modern Applications
MATH 53 (Spr)  Foundations for Calculus
MATH 18 (Aut)  Preparation for Success in Mathematics at Stanford
SOAR 10MA (Aut)
202122 Courses
 Calculus
MATH 19 (Win)  Calculus, ACE
MATH 19A (Win)  Integral Calculus of Several Variables
MATH 52 (Spr)  Integral Calculus of Several Variables, ACE
MATH 52A (Spr)  Linear Algebra, Multivariable Calculus, and Modern Applications
MATH 51 (Aut)
 Calculus
All Publications

Computation of nonparametric, mixed effects, maximum likelihood, biosensor data basedestimators for the distributions of random parameters in an abstract parabolic model for the transdermal transport of alcohol.
Mathematical biosciences and engineering : MBE
2023; 20 (11): 2034520377
Abstract
The existence and consistency of a maximum likelihood estimator for the joint probability distribution of random parameters in discretetime abstract parabolic systems was established by taking a nonparametric approach in the context of a mixed effects statistical model using a Prohorov metric framework on a set of feasible measures. A theoretical convergence result for a finite dimensional approximation scheme for computing the maximum likelihood estimator was also established and the efficacy of the approach was demonstrated by applying the scheme to the transdermal transport of alcohol modeled by a random parabolic partial differential equation (PDE). Numerical studies included show that the maximum likelihood estimator is statistically consistent, demonstrated by the convergence of the estimated distribution to the "true" distribution in an example involving simulated data. The algorithm developed was then applied to two datasets collected using two different transdermal alcohol biosensors. Using the leaveoneout crossvalidation (LOOCV) method, we found an estimate for the distribution of the random parameters based on a training set. The input from a test drinking episode was then used to quantify the uncertainty propagated from the random parameters to the output of the model in the form of a 95 error band surrounding the estimated output signal.
View details for DOI 10.3934/mbe.2023900
View details for PubMedID 38052648