Filtering through many options – an introduction to optical filters

An Introduction to Exotic Options

Options or “privileges” as they were known in early 19th Century America actually appeared on the financial scene around the same times as stocks. Initially, there were numerous problems with the trading of options. The terms of the contract were different from contract to contract, contracts had to be exercised in person, and there really was no secondary market to trade. Options were eventual...

An introduction to particle filters

Aims The aim of this tutorial is to introduce particle filters to those with a background in “classical” recursive estimation based on variants of the Kalman filter. We describe the principles behind the basic particle filter algorithm and provide a detailed worked example. We also show that the basic algorithm is a special case of a more general particle filter that greatly extends the filter ...

An Introduction to Quantum Filtering

This paper provides an introduction to quantum filtering theory. An introduction to quantum probability theory is given, focusing on the spectral theorem and the conditional expectation as a least squares estimate, and culminating in the construction of Wiener and Poisson processes on the Fock space. We describe the quantum Itô calculus and its use in the modeling of physical systems. We use bo...

An Introduction to Particle Filtering

This report introduces the ideas behind particle filters, looking at the Kalman filter and the SIS and SIR filters to learn about the latent state of state space models. It then introduces particle MCMC as a way of learning about the parameters behind these models. Finally, the SIR filter and particle MCMC algorithms are applied to reaction networks, in particular the Lotka Volterra model.

An Introduction to Sociolinguistics