36,732 research outputs found
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
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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
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