Bayesian Inference for Linear Inverse Models
Linear Inverse Models are popular in atmospheric science studies in order to estimate linear stochastic dynamical models describing the evolution of state variables. Often, the parameters of these models are estimated with Maximum Likelihood approximations made to the transition distribution. In an upcoming paper, I formulate a fully Bayesian scheme to estimate the parameters, and discuss the advantages over simple ML estimation.
Non-parametric Multi-Scale Bayesian Network Modeling
Inspired from “Multiresolution Optimal Interpolation and Statistical Analysis of TOPEXPOSEIDON Satellite Altimetry” by Fieguth et al and “Multiresolution Markov Models for Signal and Image Processing” by Willsky. Multi-Scale models using Bayesian networks is attractive because of the resulting tree structure is easy to perform inference on. These papers use linear functions between nodes, we consider non-parametric models that are fitted between scales.
Estimating Posterior Distribution of Chaotic Dynamics
There are several methods for analyzing the statistics of a random ordinary differential equation. In this note, we compare two spectral methods’ ability to capture the statistics for a solution to the classic 1963 Lorenz system with random initial conditions.
The document Finite Element Solvers: A MATLAB and FEniCS Review provides a brief introduction and tutorial on solving 2 and 3 dimensional Poisson and Heat Equation problems using software packages for MATLAB and FEniCS (Python).
As an undergraduate, I assisted in research with Professor of Mathematics Ken Golden and Professor of Atmospheric Science Courtney Strong. As a part of his research group, we studied sea ice floes in a multi-scale framework. There, I focused on analyzing the Marginal Ice Zone from a macroscopic viewpoint.
Some of my other miscellaneous projects includes a review of rogue wave research and my own algorithm for computing nth roots. You can find them here:
I’ve written several research papers in the political science. These topics range from environmental policy to international political theory (files to be added).