In this paper, we propose a new particle filter based on sequential importance sampling. The algorithm uses a bank of unscented filters to obtain the importance proposal distribution. This proposal has two very "nice" properties. Firstly, it makes efficient use of the latest available information and, secondly, it can have heavy tails. As a result, we find that the algorithm outperforms standard particle filtering and other nonlinear filtering methods very substantially. This experimental finding is in agreement with the theoretical convergence proof for the algorithm. The algorithm also includes resampling and (possibly) Markov chain Monte Carlo (MCMC) steps.

We discuss a novel strategy for training neural networks using sequential Monte Carlo algorithms and propose a new hybrid gradient descent/sampling importance resampling algorithm (HySIR). In terms of both computational time and accuracy, the hybrid SIR is a clear improvement over conventional sequential Monte Carlo techniques. The new algorithm may be viewed as a global optimisation strategy, which allows us to learn the probability distributions of the network weights and outputs in a sequential framework. It is well suited to applications involving on-line, nonlinear and non-Gaussian signal processing. We show how the new algorithm outperforms extended Kalman filter training on several problems. In particular, we address the problem of pricing option contracts, traded in financial markets. In this context, we are able to estimate the one-step-ahead probability density functions of the options prices. i Contents 1 Introduction 1 2 State Space Neural Network Modelling 2 3 The Bayes...

Summary The application of the Bayesian learning paradigm to neural networks results in a flexi-ble and powerful nonlinear modelling framework that can be used for regression, den-sity estimation, prediction and classification. Within this framework, all sources of uncertainty are expressed and measured by probabilities. This formulation allows for a probabilistic treatment of our a priori knowledge, domain specific knowledge, model selection schemes, parameter estimation methods and noise estimation techniques. Many researchers have contributed towards the development of the Bayesian learn-ing approach for neural networks. This thesis advances this research by proposing several novel extensions in the areas of sequential learning, model selection, optimi-sation and convergence assessment. The first contribution is a regularisation strategy for sequential learning based on extended Kalman filtering and noise estimation via evidence maximisation. Using the expectation maximisation (EM) algorithm, a similar algorithm is derived for batch learning. Much of the thesis is, however, devoted to Monte Carlo simulation methods. A robust Bayesian method is proposed to estimate,

Prices and liquidity on distributed dealer markets are known to market participants but not to external observers. Hence, the strategy of polling n respondents, coupled with data reduction using a robust location estimator, has been widely employed, especially in the context of cash–settled futures contracts. In this paper, we offer a market microstructure interpretation of the information obtained by polling, and propose improvements for many elements of the polling process. The choice of estimator in this context reflects a tradeoff between statistical efficiency and vulnerability to manipulation. We offer empirical evidence about this tradeoff. The results suggest that the adaptive trimmed mean (ATM) has significant advantages over the fixed trimming procedures which are widely used by futures exchanges today.