Research

My interests lie in applied and computational statistics. A lot of my work is motivated by problems in Bayesian modeling. More precisely:

  • Simulation algorithms and the computation of high-dimensional integrals. This encompasses Markov chains Monte Carlo, Gibbs and Hamiltonian Monte Carlo sampling, and approximate methods such as embedded Laplace approximations.
  • Automatic differentiation, meaning the computation of derivatives to supports gradient based algorithms. Emphasis on the differentiation of implicit functions, such as solutions to differential equations.
  • Hierarchical and latent Gaussian models, the geometry of their posteriors, and how this interacts with simulation algorithms.
  • Bayesian modeling workflows with applications in pharmacometrics, epidimeology, and physics.
  • Ising and Spin glass models, graph models, and more generally high-dimensional discrete spaces.

Writing

I try to post formal articles on research gate. Here, I’ll also lay out other projects and resources.

Preprint and publications:

  • (2020) Hamiltonian Monte Carlo using an adjoint-differentiated Laplace approximation. Charles C. Margossian, Aki Vehtari, Daniel Simpson and Raj Agrawal. accepted for NeurIPS 2020. [preprint, code]

  • (2020) Approximate Bayesian inference for latent Gaussian models in Stan. Charles C. Margossian, Aki Vehtari, Daniel Simpson and Raj Agrawal. presented at Stan Con 2020. [article, code, talk]

  • (2020) Bayesian Workflow for disease transmission modeling in Stan. Leo Grinsztajn, Elizaveta Semenova, Charles C. Margossian and Julien Riou. preprint. [preprint, html file, code, talk]

  • (2020) Estimation of SARS-CoV-2 mortality during the early stages of an epidemic: a modelling study in Hubei, China and six regions of Europe. Julien Riou et al. PLOS Medicine. [article, preprint]

  • (2020) The Discrete adjoint method: efficient derivatives for functions of discrete sequences. Michael Betancourt, Charles C. Margossian and Vianey Leos-Barajas. preprint. [preprint]

  • (2019) A Review of automatic differentiation and its efficient implementation. Charles C. Margossian. Wiley interdisciplinary reviews: data mining and knowledge discovery. [article, preprint]
  • (2018) Computing Steady states with Stan’s nonlinear algebraic solver. Charles C. Margossian. Stan Con Asilomar 2018. [article, code, talk]
  • (2017) Gaining Efficiency by combining analytical and numerical methods to solve ODEs: implementation in Stan and application to Bayesian PK/PD modeling. Charles C. Margossian and Bill Gillespie. Journal of Pharmacokinetics and Pharmacodynamics, presented at the American Conference on Pharmacometrics 8. [poster]
  • (2017) Differential equation based models in Stan. Charles C. Margossian and Bill Gillespie. Stan Con 2017. [article, code, talk]
  • (2016) Stan functions for pharmacometrics. Charles C. Margossian and Bill Gillespie. _Journal of Pharmacokinetics and Pharmacodynamics, presented at the American Conference on Pharmacometrics 7. [poster]
  • (2014) Planet Hunters. VII. Discovery of a new low-mass, low-density (PH3 C) orbiting Kepler-289 with mass measurements of two additional plamets of two additional planets (PH3 B and D). Joseph Schmitt et al. Astrophysical Journal. [article]

Software documentation (manuals, technical reports, and short articles):

  • The Stan Book. Stan development team. [manual]
  • Torsten User Manual. Charles C. Margossian, Yi Zhang, Bill Gillespie and Metrum Research Group. [manual]
  • (2018) Technical appendix for Torsten. Charles C. Margossian. in progress. [technical report]
  • Contributing New Functions to Stan. Stan development team. [wiki page]

Softwares

  • Stan: a probabilistic programing language. Stan development team. [Home page]
  • Torsten: a pharmacometrics library for Stan. Charles C Margossian, Yi Zhang, Bill Gillespie and Metrum Research Group. [GitHub]
  • mrgsolve: pharmacometrics and quantitative systems pharmacology simulation in R. Kyle Baron and contributors. [Home page]

Others

With Sumit Mukherjee, I’m working on simulation methods for spin glass models, of which the Ising model is a special case.

In 2018, I worked on an econometrics model with Shosh Vasserman. The data generating process of the model involved the solution to a constrained optimization problem, resulting in a discontinuous posterior. Finding an appropriate sampler remains an open problem. See this discussion on non-smooth posterior and KKT.

In 2018, I did a class project in population genetics with Elliott Gordon Rodriguez, working with Guy Sella and his lab in the Department of Biological Sciences.

As an undergraduate at Yale, I worked with the exoplanet group, in the Department of Astronomy.