Dirichlet Process Mixtures for Density Estimation in Dynamic Nonlinear Modeling: Application to GPS Positioning in Urban Canyons

International audienceIn global positioning systems (GPS), classical localization algorithms assume, when the signal is received from the satellite in line-of-sight (LOS) environment, that the pseudorange error distribution is Gaussian. Such assumption is in some way very restrictive since a random error in the pseudorange measure with an unknown distribution form is always induced in constrained environments especially in urban canyons due to multipath/masking effects. In order to ensure high accuracy positioning, a good estimation of the observation error in these cases is required. To address this, an attractive flexible Bayesian nonparametric noise model based on Dirichlet process mixtures (DPM) is introduced. Since the considered positioning problem involves elements of non-Gaussianity and nonlinearity and besides, it should be processed on-line, the suitability of the proposed modeling scheme in a joint state/parameter estimation problem is handled by an efficient Rao-Blackwellized particle filter (RBPF). Our approach is illustrated on a data analysis task dealing with joint estimation of vehicles positions and pseudorange errors in a global navigation satellite system (GNSS)-based localization context where the GPS information may be inaccurate because of hard reception conditions

Bayesian semiparametric stochastic volatility modeling

This paper extends the existing fully parametric Bayesian literature on stochastic volatility to allow for more general return distributions. Instead of specifying a particular distribution for the return innovation, nonparametric Bayesian methods are used to flexibly model the skewness and kurtosis of the distribution while the dynamics of volatility continue to be modeled with a parametric structure. Our semiparametric Bayesian approach provides a full characterization of parametric and distributional uncertainty. A Markov chain Monte Carlo sampling approach to estimation is presented with theoretical and computational issues for simulation from the posterior predictive distributions. The new model is assessed based on simulation evidence, an empirical example, and comparison to parametric models.Dirichlet process mixture, MCMC, block sampler

Sequential Modelling and Inference of High-frequency Limit Order Book with State-space Models and Monte Carlo Algorithms

The high-frequency limit order book (LOB) market has recently attracted increasing research attention from both the industry and the academia as a result of expanding algorithmic trading. However, the massive data throughput and the inherent complexity of high-frequency market dynamics also present challenges to some classic statistical modelling approaches. By adopting powerful state-space models from the field of signal processing as well as a number of Bayesian inference algorithms such as particle filtering, Markov chain Monte Carlo and variational inference algorithms, this thesis presents my extensive research into the high-frequency limit order book covering a wide scope of topics. Chapter 2 presents a novel construction of the non-homogeneous Poisson process to allow online intensity inference of limit order transactions arriving at a central exchange as point data. Chapter 3 extends a baseline jump diffusion model for market fair-price process to include three additional model features taken from real-world market intuitions. In Chapter 4, another price model is developed to account for both long-term and short-term diffusion behaviours of the price process. This is achieved by incorporating multiple jump-diffusion processes each exhibiting a unique characteristic. Chapter 5 observes the multi-regime nature of price diffusion processes as well as the non-Markovian switching behaviour between regimes. As such, a novel model is proposed which combines the continuous-time state-space model, the hidden semi-Markov switching model and the non-parametric Dirichlet process model. Additionally, building upon the general structure of the particle Markov chain Monte Carlo algorithm, I further propose an algorithm which achieves sequential state inference, regime identification and regime parameters learning requiring minimal prior assumptions. Chapter 6 focuses on the development of efficient parameter-learning algorithms for state-space models and presents three algorithms each demonstrating promising results in comparison to some well-established methods. The models and algorithms proposed in this thesis not only are practical tools for analysing high-frequency LOB markets, but can also be applied in various areas and disciplines beyond finance

Imitating Human Responses via a Dual-Process Model Approach

Human-autonomous system teaming is becoming more prevalent in the Air Force and in society. Often, the concept of a shared mental model is discussed as a means to enhance collaborative work arrangements between a human and an autonomous system. The idea being that when the models are aligned, the team is more productive due to an increase in trust, predictability, and apparent understanding. This research presents the Dual-Process Model using multivariate normal probability density functions (DPM-MN), which is a cognitive architecture algorithm based on the psychological dual-process theory. The dual-process theory proposes a bipartite decision-making process in people. It labels the intuitive mode as “System 1” and the reflective mode as “System 2”. The current research suggests by leveraging an agent which forms decisions based on a dual-process model, an agent in a human-machine team can maintain a better shared mental model with the user. Evaluation of DPM-MN in a game called Space Navigator shows that DPM-MN presents a successful dual-process theory motivated model