Statistical Inference of Discretely Observed Compound Poisson Processes and Related Jump Processes

Code for reproducing the simulations from my Part III Essay.

This folder contains

demos

Folder containing four subfolders, one for each estimator in the essay.

• spectralconv

  • spectralconvdemo.py --- runs spectralconv estimator and plots against true density
  • plots --- output plots

• spectralkde

  • spectralkdedemo.py --- runs spectralkde estimator and plots against true density
  • plots --- output plots

• bayesianmixture

  • bayesianmixturedemo.py --- runs bayesianmixture estimator and plots against true density
  • plots --- output plots

• bayesiandirichlet

  • bayesiandirichlet.py --- runs bayesiandirichlet estimator and plots against true density
  • plots --- output plots

utils

Folder with utility classes and functions.

• distributions.py--- Distributions used during the simulations

• simulation.py--- Simulates the CPP and observes points at discrete points in time

• charfunctions.py--- Characteristic functions of kernels/other functions required for the estimators

• spectralconv.py--- Kernel density estimator via computing estimators of convolution powers

• spectralkde.py--- Kernel density estimator via suitable inversion of characteristic functions

• bayesianmixture.py--- Parametric Bayesian density estimator via data augmentation scheme

• bayesiandirichlet.py--- Non-parametric Bayesian density estimator via Dirichlet Process Mixture prior