Approximate Bayesian techniques for inference in stochastic dynamical systems

This thesis is concerned with approximate inference in dynamical systems, from a variational Bayesian perspective. When modelling real world dynamical systems, stochastic differential equations appear as a natural choice, mainly because of their ability to model the noise of the system by adding a variant of some stochastic process to the deterministic dynamics. Hence, inference in such processes has drawn much attention. Here two new extended frameworks are derived and presented that are based on basis function expansions and local polynomial approximations of a recently proposed variational Bayesian algorithm. It is shown that the new extensions converge to the original variational algorithm and can be used for state estimation (smoothing). However, the main focus is on estimating the (hyper-) parameters of these systems (i.e. drift parameters and diffusion coefficients). The new methods are numerically validated on a range of different systems which vary in dimensionality and non-linearity. These are the Ornstein-Uhlenbeck process, for which the exact likelihood can be computed analytically, the univariate and highly non-linear, stochastic double well and the multivariate chaotic stochastic Lorenz '63 (3-dimensional model). The algorithms are also applied to the 40 dimensional stochastic Lorenz '96 system. In this investigation these new approaches are compared with a variety of other well known methods such as the ensemble Kalman filter / smoother, a hybrid Monte Carlo sampler, the dual unscented Kalman filter (for jointly estimating the systems states and model parameters) and full weak-constraint 4D-Var. Empirical analysis of their asymptotic behaviour as a function of observation density or length of time window increases is provided.

Estimating parameters in stochastic systems:a variational Bayesian approach

This work is concerned with approximate inference in dynamical systems, from a variational Bayesian perspective. When modelling real world dynamical systems, stochastic differential equations appear as a natural choice, mainly because of their ability to model the noise of the system by adding a variation of some stochastic process to the deterministic dynamics. Hence, inference in such processes has drawn much attention. Here a new extended framework is derived that is based on a local polynomial approximation of a recently proposed variational Bayesian algorithm. The paper begins by showing that the new extension of this variational algorithm can be used for state estimation (smoothing) and converges to the original algorithm. However, the main focus is on estimating the (hyper-) parameters of these systems (i.e. drift parameters and diffusion coefficients). The new approach is validated on a range of different systems which vary in dimensionality and non-linearity. These are the Ornstein–Uhlenbeck process, the exact likelihood of which can be computed analytically, the univariate and highly non-linear, stochastic double well and the multivariate chaotic stochastic Lorenz ’63 (3D model). As a special case the algorithm is also applied to the 40 dimensional stochastic Lorenz ’96 system. In our investigation we compare this new approach with a variety of other well known methods, such as the hybrid Monte Carlo, dual unscented Kalman filter, full weak-constraint 4D-Var algorithm and analyse empirically their asymptotic behaviour as a function of observation density or length of time window increases. In particular we show that we are able to estimate parameters in both the drift (deterministic) and the diffusion (stochastic) part of the model evolution equations using our new methods.

A pragmatic Bayesian approach to wind field retrieval

The ERS-1 Satellite was launched in July 1991 by the European Space Agency into a polar orbit at about 800 km, carrying a C-band scatterometer. A scatterometer measures the amount of backscatter microwave radiation reflected by small ripples on the ocean surface induced by sea-surface winds, and so provides instantaneous snap-shots of wind flow over large areas of the ocean surface, known as wind fields. Inherent in the physics of the observation process is an ambiguity in wind direction; the scatterometer cannot distinguish if the wind is blowing toward or away from the sensor device. This ambiguity implies that there is a one-to-many mapping between scatterometer data and wind direction. Current operational methods for wind field retrieval are based on the retrieval of wind vectors from satellite scatterometer data, followed by a disambiguation and filtering process that is reliant on numerical weather prediction models. The wind vectors are retrieved by the local inversion of a forward model, mapping scatterometer observations to wind vectors, and minimising a cost function in scatterometer measurement space. This thesis applies a pragmatic Bayesian solution to the problem. The likelihood is a combination of conditional probability distributions for the local wind vectors given the scatterometer data. The prior distribution is a vector Gaussian process that provides the geophysical consistency for the wind field. The wind vectors are retrieved directly from the scatterometer data by using mixture density networks, a principled method to model multi-modal conditional probability density functions. The complexity of the mapping and the structure of the conditional probability density function are investigated. A hybrid mixture density network, that incorporates the knowledge that the conditional probability distribution of the observation process is predominantly bi-modal, is developed. The optimal model, which generalises across a swathe of scatterometer readings, is better on key performance measures than the current operational model. Wind field retrieval is approached from three perspectives. The first is a non-autonomous method that confirms the validity of the model by retrieving the correct wind field 99% of the time from a test set of 575 wind fields. The second technique takes the maximum a posteriori probability wind field retrieved from the posterior distribution as the prediction. For the third technique, Markov Chain Monte Carlo (MCMC) techniques were employed to estimate the mass associated with significant modes of the posterior distribution, and make predictions based on the mode with the greatest mass associated with it. General methods for sampling from multi-modal distributions were benchmarked against a specific MCMC transition kernel designed for this problem. It was shown that the general methods were unsuitable for this application due to computational expense. On a test set of 100 wind fields the MAP estimate correctly retrieved 72 wind fields, whilst the sampling method correctly retrieved 73 wind fields.

A study of the aerodynamic characteristics of captor hoods in local exhaust ventilation systems

The research objectives were:- 1.To review the literature to establish the factors which have traditionally been regarded as most crucial to the design of effectlve exhaust ventilation systems. 2. To design, construct, install and calibrate a wind tunnel. 3. To develop procedures for air velocity measurement followed by a comprehensive programme of aerodvnamic data collection and data analysis for a variety of conditions. The major research findings were:- a) The literature in the subject is inadequate. There is a particular need for a much greater understanding of the aerodynamics of the suction flow field. b) The discrepancies between the experimentally observed centre-line velocities and those predicted by conventional formulae are unacceptably large. c) There was little agreement between theoretically calculated and observed velocities in the suction zone of captor hoods. d) Improved empirical formulae for the prediction of centre-line velocity applicable to the classical geometrically shaped suction openings and the flanged condition could be (and were) derived. Further analysis of data revealed that: - i) Point velocity is directly proportional to the suction. flow rate and the ratio of the point velocity to the average face velocity is constant. ii) Both shape, and size of the suction opening are significant factors as the coordinates of their points govern the extent of the effect of the suction flow field. iii) The hypothetical ellipsoidal potential function and hyperbolic streamlines were found experimentally to be correct. iv) The effect of guide plates depends on the size, shape and the angle of fitting. The effect was to very approximately double the suction velocity but the exact effect is difficult to predict. v) The axially symmetric openings produce practically symmetric flow fields. Similarity of connection pieces between the suction opening and the main duct in each case is essential in order to induce a similar suction flow field. Additionally a pilot study was made in which an artificial extraneous air flow was created, measured and its interaction with the suction flow field measured and represented graphically.

The investigation of the sensitivity gradient of the visual field, as a function of stimulus dynamic range, in the normal and abnormal eye

The study utilized the advanced technology provided by automated perimeters to investigate the hypothesis that patients with retinitis pigmentosa behave atypically over the dynamic range and to concurrently determine the influence of extraneous factors on the format of the normal perimetric sensitivity profile. The perimetric processing of some patients with retinitis pigmentosa was considered to be abnormal in either the temporal and/or the spatial domain. The standard size III stimulus saturated the central regions and was thus ineffective in detecting early depressions in sensitivity in these areas. When stimulus size was scaled in inverse proportion to the square root of ganglion cell receptive field density (M-scaled), isosensitive profiles did not result, although cortical representation was theoretically equivalent across the visual field. It was conjectured that this was due to variations in the ganglion cell characteristics with increasing peripheral angle, most notably spatial summation. It was concluded that the development of perimetric routines incorporating stimulus sizes adjusted in proportion to the coverage factor of retinal ganglion cells would enhance the diagnostic capacity of perimetry. Good general and local correspondence was found between perimetric sensitivity and the available retinal cell counts. Intraocular light scatter arising both from simulations and media opacities depressed perimetric sensitivity. Attenuation was greater centrally for the smaller LED stimuli, whereas the reverse was true for the larger projected stimuli. Prior perimetric experience and pupil size also demonstrated eccentricity-dependent effect on sensitivity. Practice improved perimetric sensitivity for projected stimuli at eccentricities greater than or equal to 30o; particularly in the superior region. Increase in pupil size for LED stimuli enhanced sensitivity at eccentricities greater than 10o. Conversely, microfluctuation in the accommodative response during perimetric examination and the correction of peripheral refractive error had no significant influence on perimetric sensitivity.

Effects of rare-earth co-doping on the local structure of rare-earth phosphate glasses using high and low energy X-ray diffraction

Rare-earth co-doping in inorganic materials has a long-held tradition of facilitating highly desirable optoelectronic properties for their application to the laser industry. This study concentrates specifically on rare-earth phosphate glasses, (R2O3)x(R'2O3)y(P2O5)1-(x+y), where (R, R') denotes (Ce, Er) or (La, Nd) co-doping and the total rare-earth composition corresponds to a range between metaphosphate, RP3O9, and ultraphosphate, RP5O14. Thereupon, the effects of rare-earth co-doping on the local structure are assessed at the atomic level. Pair-distribution function analysis of high-energy X-ray diffraction data (Qmax = 28 Å-1) is employed to make this assessment. Results reveal a stark structural invariance to rare-earth co-doping which bears testament to the open-framework and rigid nature of these glasses. A range of desirable attributes of these glasses unfold from this finding; in particular, a structural simplicity that will enable facile molecular engineering of rare-earth phosphate glasses with 'dial-up' lasing properties. When considered together with other factors, this finding also demonstrates additional prospects for these co-doped rare-earth phosphate glasses in nuclear waste storage applications. This study also reveals, for the first time, the ability to distinguish between P-O and PO bonding in these rare-earth phosphate glasses from X-ray diffraction data in a fully quantitative manner. Complementary analysis of high-energy X-ray diffraction data on single rare-earth phosphate glasses of similar rare-earth composition to the co-doped materials is also presented in this context. In a technical sense, all high-energy X-ray diffraction data on these glasses are compared with analogous low-energy diffraction data; their salient differences reveal distinct advantages of high-energy X-ray diffraction data for the study of amorphous materials. © 2013 The Owner Societies.

Reporting and managing risk:a look at current practice at Tesco, RBS, local and central government

These case studies from CIMA highlight the need to embed risk management within more easily understood behaviours, consistent with the overall organisational culture. In each case, some form of internal audit team provides either an oversight function or acts as an expert link in that feedback loop. Frontline staff, managers and specialists should be completely aligned on risk, in part just to ensure that there is a consistency of approach. They should understand instinctively that good performance includes good risk management. Tesco has continued to thrive during the recession and remains a robust and efficient group of businesses despite the emergence of potential threats around consumer spending and the supply chain. RBS, by contrast, has suffered catastrophic and very public failures of risk management despite a large in-house function and stiff regulation of risk controls. Birmingham City Council, like all local authorities, is adapting to more commercial modes of operation and is facing diverse threats and opportunities emerging as a result of social change. And DCMS, like many other public sector organisations, has to handle an incredibly complex network of delivery partners within the context of a relatively recent overhaul of central government risk management processes. Key Findings: •Risk management is no longer solely a financial discipline, nor is it simply a concern for the internal control function. •Where organisations retain a discrete risk management cadre – often specialists at monitoring and evaluating a range of risks – their success is dependent on embedding risk awareness in the wider culture of the enterprise. •Risk management is most successful when it is explicitly linked to operational performance. •Clear leadership, specific goals, excellent influencing skills and open-mindedness to potential threats and opportunities are essential for effective risk management. •Bureaucratic processes and systems can hamper good risk management – either as a result of a ‘box-ticking mentality’ or because managers and staff believe they do not need to consider risk themselves.

Back to the local? Recalibrating the regional tier of governance in England

By contrast to the far-reaching devolution settlements elsewhere in the UK, political agreement on the governance of England outside London remains unsettled. There is cross- party consensus on the need to 'decentre down' authority to regions and localities, but limited agreement on how this should be achieved. This paper explores the welter of initiatives adopted by the recent Labour government that were ostensibly designed to make the meso-level of governance more coherent, accountable and responsive to meeting territorial priorities. Second, it explores the current Conservative-Liberal Democrat Coalition's programme of reform that involves the elimination of Labour's regional institutional architecture and is intended to restore powers to local government and communities and promote local authority co-operation around sub-regions. Labour's reforms were ineffective in achieving any substantial transfer of authority away from Whitehall and, given the Coalition's plans to cut public expenditure, the likelihood of any significant recalibration in central-local relations also appears improbable. © 2012 Copyright Taylor and Francis Group, LLC.

Local-Median Method of Forecasting for Regression Time Series under Outliers

2002 Mathematics Subject Classification: 62M20, 62-07, 62J05, 62P20.

Application of the D-Fullness Technique for Breakdown Point Study of the Trimmed Likelihood Estimator to a Generalized Logistic Model

2000 Mathematics Subject Classification: 62J12, 62F35

Growth, uniformity, local responsiveness, and system-wide adaptation in multiunit franchising

Using the resource-based view framework, we investigate the link between multiunit franchising (MUF) and performance on four key challenges in franchise chain management: growth, uniformity, local responsiveness, and system-wide adaptation. Our findings support the assertion that system growth is positively related to MUF rate within a system, in particular in relation to geographic expansion. Interestingly, while uniformity does not seem to be related to MUF rate, we find marginal support for an inverted u-shaped relationship between system-wide adaptation and MUF rate. Furthermore, the data suggest that local responsiveness and MUF rate are related in a u-shaped function.

An automatic tuning strategy for local fuzzy logic ramp metering algorithm using Particle Swarm Optimization (PSO)

Freeway systems are becoming more congested each day. One contribution to freeway traffic congestion comprises platoons of on-ramp traffic merging into freeway mainlines. As a relatively low-cost countermeasure to the problem, ramp meters are being deployed in both directions of an 11-mile section of I-95 in Miami-Dade County, Florida. The local Fuzzy Logic (FL) ramp metering algorithm implemented in Seattle, Washington, has been selected for deployment. The FL ramp metering algorithm is powered by the Fuzzy Logic Controller (FLC). The FLC depends on a series of parameters that can significantly alter the behavior of the controller, thus affecting the performance of ramp meters. However, the most suitable values for these parameters are often difficult to determine, as they vary with current traffic conditions. Thus, for optimum performance, the parameter values must be fine-tuned. This research presents a new method of fine tuning the FLC parameters using Particle Swarm Optimization (PSO). PSO attempts to optimize several important parameters of the FLC. The objective function of the optimization model incorporates the METANET macroscopic traffic flow model to minimize delay time, subject to the constraints of reasonable ranges of ramp metering rates and FLC parameters. To further improve the performance, a short-term traffic forecasting module using a discrete Kalman filter was incorporated to predict the downstream freeway mainline occupancy. This helps to detect the presence of downstream bottlenecks. The CORSIM microscopic simulation model was selected as the platform to evaluate the performance of the proposed PSO tuning strategy. The ramp-metering algorithm incorporating the tuning strategy was implemented using CORSIM's run-time extension (RTE) and was tested on the aforementioned I-95 corridor. The performance of the FLC with PSO tuning was compared with the performance of the existing FLC without PSO tuning. The results show that the FLC with PSO tuning outperforms the existing FL metering, fixed-time metering, and existing conditions without metering in terms of total travel time savings, average speed, and system-wide throughput.

Local luminous infrared galaxies: Spatially resolved mid-infrared observations with Spitzer/IRS

Luminous Infrared (IR) Galaxies (LIRGs, L_IR=10^11-10 L_⨀) are an important cosmological class of galaxies as they are the main contributors to the co-moving star formation rate density of the universe at z=1. In this paper we present a guaranteed time observation (GTO) Spitzer InfraRed Spectrograph (IRS) program aimed to obtain spectral mapping of a sample of 14 local d<76Mpc LIRGs. The data cubes map, at least, the central 20arcsec X 20arcsec to 30 arcsec X 30 arcsec regions of the galaxies, and use all four IRS modules covering the full 5-38 μ m spectral range. The final goal of this project is to characterize fully the mid-IR properties of local LIRGs as a first step to understanding their more distant counterparts. In this paper we present the first results of this GTO program. The IRS spectral mapping data allow us to build spectral maps of the bright mid-IR emission lines (e.g., [Ne II] 12.81 μ m, [Ne III]15.56 μ m, [S III] 18.71 μ m, H_2 at 17 μ m), continuum, the 6.2 and 11.3 μ m polycyclic aromatic hydrocarbon (PAH) features, and the 9.7 μ m silicate feature, as well as to extract 1D spectra for regions of interest in each galaxy. The IRS data are used to obtain spatially resolved measurements of the extinction using the 9.7 μ m silicate feature, and to trace star forming regions using the neon lines and the PAH features. We also investigate a number of active galactic nuclei (AGN) indicators, including the presence of high excitation emission lines and a strong dust continuum emission at around 6 9.7 μ m . We finally use the integrated Spitzer/IRS spectra as templates of local LIRGs. We discuss several possible uses for these templates, including the calibration of the star formation rate of IR-bright galaxies at high redshift. We also predict the intensities of the brightest mid-IR emission lines for LIRGs as a function of redshift, and compare them with the expected sensitivities of future space IR missions.

Risque de prix et décisions de production et d'exportation : le cas de l'agriculture au Québec

Cette thèse porte sur l’effet du risque de prix sur la décision des agriculteurs et les transformateurs québécois. Elle se divise en trois chapitres. Le premier chapitre revient sur la littérature. Le deuxième chapitre examine l’effet du risque de prix sur la production de trois produits, à savoir le maïs grain, la viande de porc et la viande d’agneau dans la province Québec. Le dernier chapitre est centré sur l’analyse de changement des préférences du transformateur québécois de porc pour ce qui est du choix de marché. Le premier chapitre vise à montrer l’importance de l’effet du risque du prix sur la quantité produite par les agriculteurs, tel que mis en évidence par la littérature. En effet, la littérature révèle l’importance du risque de prix à l’exportation sur le commerce international. Le deuxième chapitre est consacré à l’étude des facteurs du risque (les anticipations des prix et la volatilité des prix) dans la fonction de l’offre. Un modèle d’hétéroscédasticité conditionnelle autorégressive généralisée (GARCH) est utilisé afin de modéliser ces facteurs du risque. Les paramètres du modèle sont estimés par la méthode de l’Information Complète Maximum Vraisemblance (FIML). Les résultats empiriques montrent l’effet négatif de la volatilité du prix sur la production alors que la prévisibilité des prix a un effet positif sur la quantité produite. Comme attendu, nous constatons que l’application du programme d’assurance-stabilisation des revenus agricoles (ASRA) au Québec induit une plus importante sensibilité de l’offre par rapport au prix effectif (le prix incluant la compensation de l’ASRA) que par rapport au prix du marché. Par ailleurs, l’offre est moins sensible au prix des intrants qu’au prix de l’output. La diminution de l’aversion au risque de producteur est une autre conséquence de l’application de ce programme. En outre, l’estimation de la prime marginale relative au risque révèle que le producteur du maïs est le producteur le moins averse au risque (comparativement à celui de porc ou d’agneau). Le troisième chapitre consiste en l’analyse du changement de préférence du transformateur québécois du porc pour ce qui est du choix de marché. Nous supposons que le transformateur a la possibilité de fournir les produits sur deux marchés : étranger et local. Le modèle théorique explique l’offre relative comme étant une fonction à la fois d’anticipation relative et de volatilité relative des prix. Ainsi, ce modèle révèle que la sensibilité de l’offre relative par rapport à la volatilité relative de prix dépend de deux facteurs : d’une part, la part de l’exportation dans la production totale et d’autre part, l’élasticité de substitution entre les deux marchés. Un modèle à correction d’erreurs est utilisé lors d’estimation des paramètres du modèle. Les résultats montrent l’effet positif et significatif de l’anticipation relative du prix sur l’offre relative à court terme. Ces résultats montrent donc qu’une hausse de la volatilité du prix sur le marché étranger par rapport à celle sur le marché local entraine une baisse de l’offre relative sur le marché étranger à long terme. De plus, selon les résultats, les marchés étranger et local sont plus substituables à long terme qu’à court terme.

Restoring function after neuromuscular trauma: novel paradigms for enhancing volitional control of neural activity in untethered environments and vHAB, a gamified therapy platform

Thesis (Ph.D.)--University of Washington, 2016-08