This repository will contain the work of a Masters project in statistics.
- Background and motivation: Hidden Markov Models versus stopping time problems; such as finite birth-death processes, and phase type distributions (maybe mention latest PNAS article on accelerated failure time models in C. Elegans, to contrast with mainstay of proportional hazard models being used). The Frechet derivative of the matrix exponential has been used extensively in non-linear system control to determine stability and sensitivity via the condition number.
- Abstract definition of the Lie group of invertible stochastic linear maps
- Computation of structure coefficients of the generators of the Lie algebra of stochastic linear maps
- Representations of the Frechet derivative of the exponential map
- Pade approximation of the Frechet derivative of the exponential map and Kroenecker product expansion of the adjoint
- Representations of the second Frechet derivative of the exponential map
- Multi-variable Pade approximation of the second Frechet derivative of the exponential map
- Construction of a Newton-Raphson method for maximum likelihood estimation of the generator of a continuous Markov process
- Projection maps in the computation of first passage time distributions
- Application to survival data in continuing care settings