Particle filter-based Gaussian process optimisation for parameter inference

We propose a novel method for maximum likelihood-based parameter inference in nonlinear and/or non-Gaussian state space models. The method is an iterative procedure with three steps. At each iteration a particle filter is used to estimate the value of the log-likelihood function at the current parameter iterate. Using these log-likelihood estimates, a surrogate objective function is created by utilizing a Gaussian process model. Finally, we use a heuristic procedure to obtain a revised parameter iterate, providing an automatic trade-off between exploration and exploitation of the surrogate model. The method is profiled on two state space models with good performance both considering accuracy and computational cost.Comment: Accepted for publication in proceedings of the 19th World Congress of the International Federation of Automatic Control (IFAC), Cape Town, South Africa, August 2014. 6 pages, 4 figure

Getting Started with Particle Metropolis-Hastings for Inference in Nonlinear Dynamical Models

This tutorial provides a gentle introduction to the particle Metropolis-Hastings (PMH) algorithm for parameter inference in nonlinear state-space models together with a software implementation in the statistical programming language R. We employ a step-by-step approach to develop an implementation of the PMH algorithm (and the particle filter within) together with the reader. This final implementation is also available as the package pmhtutorial in the CRAN repository. Throughout the tutorial, we provide some intuition as to how the algorithm operates and discuss some solutions to problems that might occur in practice. To illustrate the use of PMH, we consider parameter inference in a linear Gaussian state-space model with synthetic data and a nonlinear stochastic volatility model with real-world data.Comment: 41 pages, 7 figures. In press for Journal of Statistical Software. Source code for R, Python and MATLAB available at: https://github.com/compops/pmh-tutoria

Particle Metropolis-Hastings using gradient and Hessian information

Particle Metropolis-Hastings (PMH) allows for Bayesian parameter inference in nonlinear state space models by combining Markov chain Monte Carlo (MCMC) and particle filtering. The latter is used to estimate the intractable likelihood. In its original formulation, PMH makes use of a marginal MCMC proposal for the parameters, typically a Gaussian random walk. However, this can lead to a poor exploration of the parameter space and an inefficient use of the generated particles. We propose a number of alternative versions of PMH that incorporate gradient and Hessian information about the posterior into the proposal. This information is more or less obtained as a byproduct of the likelihood estimation. Indeed, we show how to estimate the required information using a fixed-lag particle smoother, with a computational cost growing linearly in the number of particles. We conclude that the proposed methods can: (i) decrease the length of the burn-in phase, (ii) increase the mixing of the Markov chain at the stationary phase, and (iii) make the proposal distribution scale invariant which simplifies tuning.Comment: 27 pages, 5 figures, 2 tables. The final publication is available at Springer via: http://dx.doi.org/10.1007/s11222-014-9510-

Quasi-Newton particle Metropolis-Hastings

Particle Metropolis-Hastings enables Bayesian parameter inference in general nonlinear state space models (SSMs). However, in many implementations a random walk proposal is used and this can result in poor mixing if not tuned correctly using tedious pilot runs. Therefore, we consider a new proposal inspired by quasi-Newton algorithms that may achieve similar (or better) mixing with less tuning. An advantage compared to other Hessian based proposals, is that it only requires estimates of the gradient of the log-posterior. A possible application is parameter inference in the challenging class of SSMs with intractable likelihoods. We exemplify this application and the benefits of the new proposal by modelling log-returns of future contracts on coffee by a stochastic volatility model with $\alpha$-stable observations.Comment: 23 pages, 5 figures. Accepted for the 17th IFAC Symposium on System Identification (SYSID), Beijing, China, October 201

Autonomous Ground Vehicle

WildCat is an autonomous ground vehicle (AGV). AGVs were first developed for military purposes: Intelligent Transportation Systems (ITS), Manufacturing, Search and Rescue operations, Mining, etc. WildCat will be entered in the Intelligent Ground Vehicle competition (IGVC) held in June 2016 at Oakland University in Rochester, Michigan. Teams from major universities not only in the U.S., but also India, France, the UK, China, and around the world will be competing. The IGVC offers a design experience that is at the very cutting edge of engineering education. It is multidisciplinary, theory-based, hands-on, team implemented, and outcome assessed competition. It encompasses the very latest technologies impacting industrial development and taps subjects of high interest to students. The objective of the competition is to challenge students to think creatively as a team about the evolving technologies of vehicle electronic controls, sensors, computer science, robotics, and system integration throughout the design, fabrication, and field testing of autonomous intelligent mobile robots. The vehicle will compete to: 1) autonomously navigate an outdoor obstacle course as quickly as possible, keeping within the speed limit and reaching all GPS waypoints, 2) complete a course with remote (user) control, and 3) have ingenuity and uniqueness in design