Bayesian Analysis of Linear Inverse Problems with Applications in Economics and Finance

In my PhD thesis I propose a Bayesian nonparametric estimation method for structural econometric models where the functional parameter of interest describes the economic agent's behavior. The structural parameter is characterized as the solution of a functional equation, or by using more technical words, as the solution of an inverse problem that can be either ill-posed or well-posed. From a Bayesian point of view, the parameter of interest is a random function and the solution to the inference problem is the posterior distribution of this parameter. A regular version of the posterior distribution in functional spaces is characterized. However, the infinite dimension of the considered spaces causes a problem of non continuity of the solution and then a problem of inconsistency, from a frequentist point of view, of the posterior distribution (i.e. problem of ill-posedness). The contribution of this essay is to propose new methods to deal with this problem of ill-posedness. The first one consists in adopting a Tikhonov regularization scheme in the construction of the posterior distribution so that I end up with a new object that I call regularized posterior distribution and that I guess it is solution of the inverse problem. The second approach consists in specifying a prior distribution on the parameter of interest of the g-prior type. Then, I detect a class of models for which the prior distribution is able to correct for the ill-posedness also in infinite dimensional problems. I study asymptotic properties of these proposed solutions and I prove that, under some regularity condition satisfied by the true value of the parameter of interest, they are consistent in a "frequentist" sense. Once I have set the general theory, I apply my bayesian nonparametric methodology to different estimation problems. First, I apply this estimator to deconvolution and to hazard rate, density and regression estimation. Then, I consider the estimation of an Instrumental Regression that is useful in micro-econometrics when we have to deal with problems of endogeneity. Finally, I develop an application in finance: I get the bayesian estimator for the equilibrium asset pricing functional by using the Euler equation defined in the Lucas'(1978) tree-type models.

Detecting single-target changes in multiple object tracking: The case of peripheral vision.

In sports games, it is often necessary to perceive a large number of moving objects (e.g., the ball and players). In this context, the role of peripheral vision for processing motion information in the periphery is often discussed especially when motor responses are required. In an attempt to test the basal functionality of peripheral vision in those sports-games situations, a Multiple Object Tracking (MOT) task that requires to track a certain number of targets amidst distractors, was chosen. Participants’ primary task was to recall four targets (out of 10 rectangular stimuli) after six seconds of quasi-random motion. As a second task, a button had to be pressed if a target change occurred (Exp 1: stop vs. form change to a diamond for 0.5 s; Exp 2: stop vs. slowdown for 0.5 s). While eccentricities of changes (5-10° vs. 15-20°) were manipulated, decision accuracy (recall and button press correct), motor response time as well as saccadic reaction time were calculated as dependent variables. Results show that participants indeed used peripheral vision to detect changes, because either no or very late saccades to the changed target were executed in correct trials. Moreover, a saccade was more often executed when eccentricities were small. Response accuracies were higher and response times were lower in the stop conditions of both experiments while larger eccentricities led to higher response times in all conditions. Summing up, it could be shown that monitoring targets and detecting changes can be processed by peripheral vision only and that a monitoring strategy on the basis of peripheral vision may be the optimal one as saccades may be afflicted with certain costs. Further research is planned to address the question whether this functionality is also evident in sports tasks.

Detecting single-target changes in multiple object tracking: The case of peripheral vision

In sports games, it is often necessary to perceive a large number of moving objects (e.g., the ball and players). In this context, the role of peripheral vision for processing motion information in the periphery is often discussed especially when motor responses are required. In an attempt to test the capability of using peripheral vision in those sports-games situations, a Multiple-Object-Tracking task that requires to track a certain number of targets amidst distractors, was chosen to determine the sensitivity of detecting target changes with peripheral vision only. Participants’ primary task was to recall four targets (out of 10 rectangular stimuli) after six seconds of quasi-random motion. As a second task, a button had to be pressed if a target change occurred (Exp 1: stop vs. form change to a diamond for 0.5 s; Exp 2: stop vs. slowdown for 0.5 s). Eccentricities of changes (5-10° vs. 15-20°) were manipulated, decision accuracy (recall and button press correct), motor response time and saccadic reaction time (change onset to saccade onset) were calculated and eye-movements were recorded. Results show that participants indeed used peripheral vision to detect changes, because either no or very late saccades to the changed target were executed in correct trials. Moreover, a saccade was more often executed when eccentricities were small. Response accuracies were higher and response times were lower in the stop conditions of both experiments while larger eccentricities led to higher response times in all conditions. Summing up, it could be shown that monitoring targets and detecting changes can be processed by peripheral vision only and that a monitoring strategy on the basis of peripheral vision may be the optimal one as saccades may be afflicted with certain costs. Further research is planned to address the question whether this functionality is also evident in sports tasks.

Computer Assisted Diagnosis and Treatment Planning of Femoroacetabular Impingement (FAI)

Femoroacetabular impingement (FAI) is a dynamic conflict of the hip defined by a pathological, early abutment of the proximal femur onto the acetabulum or pelvis. In the past two decades, FAI has received increasing focus in both research and clinical practice as a cause of hip pain and prearthrotic deformity. Anatomical abnormalities such as an aspherical femoral head (cam-type FAI), a focal or general overgrowth of the acetabulum (pincer-type FAI), a high riding greater or lesser trochanter (extra-articular FAI), or abnormal torsion of the femur have been identified as underlying pathomorphologies. Open and arthroscopic treatment options are available to correct the deformity and to allow impingement-free range of motion. In routine practice, diagnosis and treatment planning of FAI is based on clinical examination and conventional imaging modalities such as standard radiography, magnetic resonance arthrography (MRA), and computed tomography (CT). Modern software tools allow three-dimensional analysis of the hip joint by extracting pelvic landmarks from two-dimensional antero-posterior pelvic radiographs. An object-oriented cross-platform program (Hip2Norm) has been developed and validated to standardize pelvic rotation and tilt on conventional AP pelvis radiographs. It has been shown that Hip2Norm is an accurate, consistent, reliable and reproducible tool for the correction of selected hip parameters on conventional radiographs. In contrast to conventional imaging modalities, which provide only static visualization, novel computer assisted tools have been developed to allow the dynamic analysis of FAI pathomechanics. In this context, a validated, CT-based software package (HipMotion) has been introduced. HipMotion is based on polygonal three-dimensional models of the patient’s pelvis and femur. The software includes simulation methods for range of motion, collision detection and accurate mapping of impingement areas. A preoperative treatment plan can be created by performing a virtual resection of any mapped impingement zones both on the femoral head-neck junction, as well as the acetabular rim using the same three-dimensional models. The following book chapter provides a summarized description of current computer-assisted tools for the diagnosis and treatment planning of FAI highlighting the possibility for both static and dynamic evaluation, reliability and reproducibility, and its applicability to routine clinical use.

Detecting single-target changes in multiple object tracking: The case of peripheral vision

In the current study it is investigated whether peripheral vision can be used to monitor multi-ple moving objects and to detect single-target changes. For this purpose, in Experiment 1, a modified MOT setup with a large projection and a constant-position centroid phase had to be checked first. Classical findings regarding the use of a virtual centroid to track multiple ob-jects and the dependency of tracking accuracy on target speed could be successfully replicat-ed. Thereafter, the main experimental variations regarding the manipulation of to-be-detected target changes could be introduced in Experiment 2. In addition to a button press used for the detection task, gaze behavior was assessed using an integrated eye-tracking system. The anal-ysis of saccadic reaction times in relation to the motor response shows that peripheral vision is naturally used to detect motion and form changes in MOT because the saccade to the target occurred after target-change offset. Furthermore, for changes of comparable task difficulties, motion changes are detected better by peripheral vision than form changes. Findings indicate that capabilities of the visual system (e.g., visual acuity) affect change detection rates and that covert-attention processes may be affected by vision-related aspects like spatial uncertainty. Moreover, it is argued that a centroid-MOT strategy might reduce the amount of saccade-related costs and that eye-tracking seems to be generally valuable to test predictions derived from theories on MOT. Finally, implications for testing covert attention in applied settings are proposed.

Evaluation of Binocular Vision Therapy Efficacy by 3D Video-Oculography Measurement of Binocular Alignment and Motility

Objective: To evaluate two cases of intermittent exotropia (IX(T)) treated by vision therapy the efficacy of the treatment by complementing the clinical examination with a 3-D video-oculography to register and to evidence the potential applicability of this technology for such purpose. Methods: We report the binocular alignment changes occurring after vision therapy in a woman of 36 years with an IX(T) of 25 prism diopters (Δ) at far and 18 Δ at near and a child of 10 years with 8 Δ of IX(T) in primary position associated to 6 Δ of left eye hypotropia. Both patients presented good visual acuity with correction in both eyes. Instability of ocular deviation was evident by VOG analysis, revealing also the presence of vertical and torsional components. Binocular vision therapy was prescribed and performed including different types of vergence, accommodation, and consciousness of diplopia training. Results: After therapy, excellent ranges of fusional vergence and a “to-the-nose” near point of convergence were obtained. The 3-D VOG examination (Sensoro Motoric Instruments, Teltow, Germany) confirmed the compensation of the deviation with a high level of stability of binocular alignment. Significant improvement could be observed after therapy in the vertical and torsional components that were found to become more stable. Patients were very satisfied with the outcome obtained by vision therapy. Conclusion: 3D-VOG is a useful technique for providing an objective register of the compensation of the ocular deviation and the stability of the binocular alignment achieved after vision therapy in cases of IX(T), providing a detailed analysis of vertical and torsional improvements.

The role of oscillatory brain activity in object processing and figure-ground segmentation in human vision

The perception of an object as a single entity within a visual scene requires that its features are bound together and segregated from the background and/or other objects. Here, we used magnetoencephalography (MEG) to assess the hypothesis that coherent percepts may arise from the synchronized high frequency (gamma) activity between neurons that code features of the same object. We also assessed the role of low frequency (alpha, beta) activity in object processing. The target stimulus (i.e. object) was a small patch of a concentric grating of 3c/°, viewed eccentrically. The background stimulus was either a blank field or a concentric grating of 3c/° periodicity, viewed centrally. With patterned backgrounds, the target stimulus emerged--through rotation about its own centre--as a circular subsection of the background. Data were acquired using a 275-channel whole-head MEG system and analyzed using Synthetic Aperture Magnetometry (SAM), which allows one to generate images of task-related cortical oscillatory power changes within specific frequency bands. Significant oscillatory activity across a broad range of frequencies was evident at the V1/V2 border, and subsequent analyses were based on a virtual electrode at this location. When the target was presented in isolation, we observed that: (i) contralateral stimulation yielded a sustained power increase in gamma activity; and (ii) both contra- and ipsilateral stimulation yielded near identical transient power changes in alpha (and beta) activity. When the target was presented against a patterned background, we observed that: (i) contralateral stimulation yielded an increase in high-gamma (>55 Hz) power together with a decrease in low-gamma (40-55 Hz) power; and (ii) both contra- and ipsilateral stimulation yielded a transient decrease in alpha (and beta) activity, though the reduction tended to be greatest for contralateral stimulation. The opposing power changes across different regions of the gamma spectrum with 'figure/ground' stimulation suggest a possible dual role for gamma rhythms in visual object coding, and provide general support of the binding-by-synchronization hypothesis. As the power changes in alpha and beta activity were largely independent of the spatial location of the target, however, we conclude that their role in object processing may relate principally to changes in visual attention.

The vision strategy of golf putting

Golfers, coaches and researchers alike, have all keyed in on golf putting as an important aspect of overall golf performance. Of the three principle putting tasks (green reading, alignment and the putting action phase), the putting action phase has attracted the most attention from coaches, players and researchers alike. This phase includes the alignment of the club with the ball, the swing, and ball contact. A significant amount of research in this area has focused on measuring golfer’s vision strategies with eye tracking equipment. Unfortunately this research suffers from a number of shortcomings, which limit its usefulness. The purpose of this thesis was to address some of these shortcomings. The primary objective of this thesis was to re-evaluate golfer’s putting vision strategies using binocular eye tracking equipment and to define a new, optimal putting vision strategy which was associated with both higher skill and success. In order to facilitate this research, bespoke computer software was developed and validated, and new gaze behaviour criteria were defined. Additionally, the effects of training (habitual) and competition conditions on the putting vision strategy were examined, as was the effect of ocular dominance. Finally, methods for improving golfer’s binocular vision strategies are discussed, and a clinical plan for the optometric management of the golfer’s vision is presented. The clinical management plan includes the correction of fundamental aspects of golfers’ vision, including monocular refractive errors and binocular vision defects, as well as enhancement of their putting vision strategy, with the overall aim of improving performance on the golf course. This research has been undertaken in order to gain a better understanding of the human visual system and how it relates to the sport performance of golfers specifically. Ultimately, the analysis techniques and methods developed are applicable to the assessment of visual performance in all sports.

Model Construction and Research using System Compositional Approach on Natural Hierarchical Neural Networks. Development of Computer Toolbox

System compositional approach to model construction and research of informational processes, which take place in biological hierarchical neural networks, is being discussed. A computer toolbox has been successfully developed for solution of tasks from this scientific sphere. A series of computational experiments investigating the work of this toolbox on olfactory bulb model has been carried out. The well-known psychophysical phenomena have been reproduced in experiments.

Sharing the vision: representing the matters of concern for design-led fledgling companies in Scotland

Design is being performed on an ever-increasing spectrum of complex practices arising in response to emerging markets and technologies, co-design, digital interaction, service design and cultures of innovation. This emerging notion of design has led to an expansive array of collaborative and facilitation skills to demonstrate and share how such methods can shape innovation. The meaning of these design things in practice can't be taken for granted as matters of fact, which raises a key challenge for design to represent its role through the contradictory nature of matters of concern. This paper explores an innovative, object-oriented approach within the field of design research, visually combining an actor-network theory framework with situational analysis, to report on the role of design for fledgling companies in Scotland, established and funded through the knowledge exchange hub Design in Action (DiA). Key findings and visual maps are presented from reflective discussions with actors from a selection of the businesses within DiA's portfolio. The suggestion is that any notions of strategic value, of engendering meaningful change, of sharing the vision of design, through design things, should be grounded in the reflexive interpretations of matters of concern that emerge.

Inverse analysis FOR two-dimensional structures using the boundary element method

Inverse analysis is currently an important subject of study in several fields of science and engineering. The identification of physical and geometric parameters using experimental measurements is required in many applications. In this work a boundary element formulation to identify boundary and interface values as well as material properties is proposed. In particular the proposed formulation is dedicated to identifying material parameters when a cohesive crack model is assumed for 2D problems. A computer code is developed and implemented using the BEM multi-region technique and regularisation methods to perform the inverse analysis. Several examples are shown to demonstrate the efficiency of the proposed model. (C) 2010 Elsevier Ltd. All rights reserved,

Leak detection by inverse transient analysis in an experimental PVC pipe system

Leakage reduction in water supply systems and distribution networks has been an increasingly important issue in the water industry since leaks and ruptures result in major physical and economic losses. Hydraulic transient solvers can be used in the system operational diagnosis, namely for leak detection purposes, due to their capability to describe the dynamic behaviour of the systems and to provide substantial amounts of data. In this research work, the association of hydraulic transient analysis with an optimisation model, through inverse transient analysis (ITA), has been used for leak detection and its location in an experimental facility containing PVC pipes. Observed transient pressure data have been used for testing ITA. A key factor for the success of the leak detection technique used is the accurate calibration of the transient solver, namely adequate boundary conditions and the description of energy dissipation effects since PVC pipes are characterised by a viscoelastic mechanical response. Results have shown that leaks were located with an accuracy between 4-15% of the total length of the pipeline, depending on the discretisation of the system model.

A simple and effective inverse projection scheme for void distribution control in topology optimization

The ability to control both the minimum size of holes and the minimum size of structural members are essential requirements in the topology optimization design process for manufacturing. This paper addresses both requirements by means of a unified approach involving mesh-independent projection techniques. An inverse projection is developed to control the minimum hole size while a standard direct projection scheme is used to control the minimum length of structural members. In addition, a heuristic scheme combining both contrasting requirements simultaneously is discussed. Two topology optimization implementations are contributed: one in which the projection (either inverse or direct) is used at each iteration; and the other in which a two-phase scheme is explored. In the first phase, the compliance minimization is carried out without any projection until convergence. In the second phase, the chosen projection scheme is applied iteratively until a solution is obtained while satisfying either the minimum member size or minimum hole size. Examples demonstrate the various features of the projection-based techniques presented.

Computer-aided Drug Design of Novel PLA(2) Inhibitor Candidates for Treatment of Snakebite

Phospholipases A(2) (PLA(2)) are enzymes commonly found in snake venoms from Viperidae and Elaphidae families, which are major components thereof. Many plants are used in traditional medicine its active agents against various effects induced by snakebite. This article presents the PLA(2) BthTX-I structure prediction based on homology modeling. In addition, we have performed virtual screening in a large database yielding a set of potential bioactive inhibitors. A flexible docking program was used to investigate the interactions between the receptor and the new ligands. We have performed molecular interaction fields (MIFs) calculations with the phospholipase model. Results confirm the important role of Lys49 for binding ligands and suggest three additional residues as well. We have proposed a theoretically nontoxic, drug-like, and potential novel BthTX-I inhibitor. These calculations have been used to guide the design of novel phospholipase inhibitors as potential lead compounds that may be optimized for future treatment of snakebite victims as well as other human diseases in which PLA(2) enzymes are involved.