Local robustness of Bayesian parametric inference and observed likelihoods

Here a new class of local separation measures over prior densities is studied and their usefulness for examining prior to posterior robustness under a sequence of observed likelihoods, possibly erroneous, illustrated. It is shown that provided an approximation to a prior distribution satisfies certain mild smoothness and tail conditions then prior to posterior inference for large samples is robust, irrespective of whether the priors are grossly misspecified with respect to variation distance and irrespective of the form or the validity of the observed likelihood. Furthermore it is usually possible to specify error bounds explicitly in terms of statistics associated with the posterior associated with the approximating prior and asumed prior error bounds. These results apply in a general multivariate setting and are especially easy to interpret when prior densities are approximated using standard families or multivariate prior densities factorise

Regulating autonomous agents facing conflicting objectives : a command and control example

UK military commanders have a degree of devolved decision authority delegated from command and control (C2) regulators, and they are trained and expected to act rationally and accountably. Therefore from a Bayesian perspective they should be subjective expected utility maximizers. In fact they largely appear to be so. However when current tactical objectives conflict with broader campaign objective there is a strong risk that fielded commanders will lose rationality and coherence. By systematically analysing the geometry of their expected utilities, arising from a utility function with two attributes, we demonstrate in this paper that even when a remote C2 regulator can predict only the likely broad shape of her agents' marginal utility functions it is still often possible for her to identify robustly those settings where the commander is at risk of making inappropriate decisions

Second Order Filter Distribution Approximations for Financial Time Series with Extreme Outliers

Particle Filters are now regularly used to obtain the filter distributions associated with state space financial time series. Most commonly used nowadays is the auxiliary particle filter method in conjunction with a first order Taylor expansion of the log-likelihood. We argue in this paper that for series such as stock returns, which exhibit fairly frequent and extreme outliers, filters based on this first order approximation can easily break down. However, an auxiliary particle filter based on the much more rarely used second order approximation appears to perform well in these circumstances. To detach the issue of algorithm design from problems related to model misspecification and parameter estimation, we demonstrate the lack of robustness of the first order approximation and the feasibility of a specific second order approximation using simulated data.Bayesian inference, Importance sampling, Particle filter, State space model, Stochastic volatility.

Second Order Filter Distribution Approximations for Financial Time Series with Extreme Outlier

Particle Filters are now regularly used to obtain the filter distributions associated with state space financial time series. The method most commonly used nowadays is the auxiliary particle filter method in conjunction with a first order Taylor expansion of the log-likelihood. We argue in this paper that, for series such as stock return, which exhibit fairly frequent and extreme outliers, filters based on this first order approximation can easily break down. However, the auxiliary particle filter based on the much more rarely used second order approximation appears to perform well in these circumstances. We demonstrate our results with a typical stock market series.FParticle filters, Second order approximations, State space models, Stochastic volatility

Decision making with decision event graphs

We introduce a new modelling representation, the Decision Event Graph (DEG), for asymmetric multistage decision problems. The DEG explicitly encodes conditional independences and has additional significant advantages over other representations of asymmetric decision problems. The colouring of edges makes it possible to identify conditional independences on decision trees, and these coloured trees serve as a basis for the construction of the DEG. We provide an efficient backward-induction algorithm for finding optimal decision rules on DEGs, and work through an example showing the efficacy of these graphs. Simplifications of the topology of a DEG admit analogues to the sufficiency principle and barren node deletion steps used with influence diagrams

Problems in Bayesian statistics relating to discontinuous phenomena, catastrophe theory and forecasting

The aim of this thesis is to generalise Bayesian Forecasting processes to models where normality assumptions are, not appropriate. In particular I develop models that can change their minds and I utilise Catastrophe Theory in their description. Under squared-error loss types of criteria the estimates will be smoothed out, so for model description and prediction I need to use bounded loss functions. Unfortunately the induced types of estimators have not been investigated very fully and so two chapters of the thesis represent an attempt to develop theory up to a necessary level to be used on Times Series models of the above kind. An introduction to Catastrophe Theory is then given. Catastrophe Theory is basically a classification of C∞-potential functions and since the expected loss function is in fact itself a potential function, I can use the classification on them. Chapters 6 and 7 relate the topologies of the posterior distribution and loss function to the topologies of the posterior expected loss hence a Bayes classification of posterior distributions is possible. In Chapter 8, I relate these results to the forecasting of non-stationary time series obtaining models which are very much akin to the simple weighted moving average processes under which lies this firm mathematical foundation. From this I can generate pleasing models which adjust in a "Catastrophic" way to changes in the underlying process generating the data

Conduction mechanisms of epitaxial EuTiO3 thin films

To investigate leakage current density versus electric field characteristics, epitaxial EuTiO3 thin films were deposited on (001) SrTiO3 substrates by pulsed laser deposition and were post-annealed in a reducing atmosphere. This investigation found that conduction mechanisms are strongly related to temperature and voltage polarity. It was determined that from 50 to 150 K the dominant conduction mechanism was a space-charge-limited current under both negative and positive biases. From 200 to 300 K, the conduction mechanism shows Schottky emission and Fowler-Nordheim tunneling behaviors for the negative and positive biases, respectively. This work demonstrates that Eu3+ is one source of leakage current in EuTiO3 thin films.Comment: 17 pages,4 figures, conferenc

Causal discovery through MAP selection of stratified chain event graphs

We introduce a subclass of chain event graphs that we call stratified chain event graphs, and present a dynamic programming algorithm for the optimal selection of such chain event graphs that maximizes a decomposable score derived from a complete independent sample. We apply the algorithm to such a dataset, with a view to deducing the causal structure of the variables under the hypothesis that there are no unobserved confounders. We show that the algorithm is suitable for small problems. Similarities with and differences to a dynamic programming algorithm for MAP learning of Bayesian networks are highlighted, as are the relations to causal discovery using Bayesian networks