A bayesian model for mixed responses and skew laten variable to measure HRQoL in children

The aim of the thesi is to formulate a suitable Item Response Theory (IRT) based model to measure HRQoL (as latent variable) using a mixed responses questionnaire and relaxing the hypothesis of normal distributed latent variable. The new model is a combination of two models already presented in literature, that is, a latent trait model for mixed responses and an IRT model for Skew Normal latent variable. It is developed in a Bayesian framework, a Markov chain Monte Carlo procedure is used to generate samples of the posterior distribution of the parameters of interest. The proposed model is test on a questionnaire composed by 5 discrete items and one continuous to measure HRQoL in children, the EQ-5D-Y questionnaire. A large sample of children collected in the schools was used. In comparison with a model for only discrete responses and a model for mixed responses and normal latent variable, the new model has better performances, in term of deviance information criterion (DIC), chain convergences times and precision of the estimates.

Local Earthquake Tomography by trans-dimensional Monte Carlo Sampling

In this study a new, fully non-linear, approach to Local Earthquake Tomography is presented. Local Earthquakes Tomography (LET) is a non-linear inversion problem that allows the joint determination of earthquakes parameters and velocity structure from arrival times of waves generated by local sources. Since the early developments of seismic tomography several inversion methods have been developed to solve this problem in a linearized way. In the framework of Monte Carlo sampling, we developed a new code based on the Reversible Jump Markov Chain Monte Carlo sampling method (Rj-McMc). It is a trans-dimensional approach in which the number of unknowns, and thus the model parameterization, is treated as one of the unknowns. I show that our new code allows overcoming major limitations of linearized tomography, opening a new perspective in seismic imaging. Synthetic tests demonstrate that our algorithm is able to produce a robust and reliable tomography without the need to make subjective a-priori assumptions about starting models and parameterization. Moreover it provides a more accurate estimate of uncertainties about the model parameters. Therefore, it is very suitable for investigating the velocity structure in regions that lack of accurate a-priori information. Synthetic tests also reveal that the lack of any regularization constraints allows extracting more information from the observed data and that the velocity structure can be detected also in regions where the density of rays is low and standard linearized codes fails. I also present high-resolution Vp and Vp/Vs models in two widespread investigated regions: the Parkfield segment of the San Andreas Fault (California, USA) and the area around the Alto Tiberina fault (Umbria-Marche, Italy). In both the cases, the models obtained with our code show a substantial improvement in the data fit, if compared with the models obtained from the same data set with the linearized inversion codes.

Multidimensional item response theory models with general and specific latent traits for ordinal data

The aim of the thesis is to propose a Bayesian estimation through Markov chain Monte Carlo of multidimensional item response theory models for graded responses with complex structures and correlated traits. In particular, this work focuses on the multiunidimensional and the additive underlying latent structures, considering that the first one is widely used and represents a classical approach in multidimensional item response analysis, while the second one is able to reflect the complexity of real interactions between items and respondents. A simulation study is conducted to evaluate the parameter recovery for the proposed models under different conditions (sample size, test and subtest length, number of response categories, and correlation structure). The results show that the parameter recovery is particularly sensitive to the sample size, due to the model complexity and the high number of parameters to be estimated. For a sufficiently large sample size the parameters of the multiunidimensional and additive graded response models are well reproduced. The results are also affected by the trade-off between the number of items constituting the test and the number of item categories. An application of the proposed models on response data collected to investigate Romagna and San Marino residents' perceptions and attitudes towards the tourism industry is also presented.

Statistical learning of random probability measures

The study of random probability measures is a lively research topic that has attracted interest from different fields in recent years. In this thesis, we consider random probability measures in the context of Bayesian nonparametrics, where the law of a random probability measure is used as prior distribution, and in the context of distributional data analysis, where the goal is to perform inference given avsample from the law of a random probability measure. The contributions contained in this thesis can be subdivided according to three different topics: (i) the use of almost surely discrete repulsive random measures (i.e., whose support points are well separated) for Bayesian model-based clustering, (ii) the proposal of new laws for collections of random probability measures for Bayesian density estimation of partially exchangeable data subdivided into different groups, and (iii) the study of principal component analysis and regression models for probability distributions seen as elements of the 2-Wasserstein space. Specifically, for point (i) above we propose an efficient Markov chain Monte Carlo algorithm for posterior inference, which sidesteps the need of split-merge reversible jump moves typically associated with poor performance, we propose a model for clustering high-dimensional data by introducing a novel class of anisotropic determinantal point processes, and study the distributional properties of the repulsive measures, shedding light on important theoretical results which enable more principled prior elicitation and more efficient posterior simulation algorithms. For point (ii) above, we consider several models suitable for clustering homogeneous populations, inducing spatial dependence across groups of data, extracting the characteristic traits common to all the data-groups, and propose a novel vector autoregressive model to study of growth curves of Singaporean kids. Finally, for point (iii), we propose a novel class of projected statistical methods for distributional data analysis for measures on the real line and on the unit-circle.

Constraints on neutrino mass fraction using Redshift Space Distortions

Redshift Space Distortions (RSD) are an apparent anisotropy in the distribution of galaxies due to their peculiar motion. These features are imprinted in the correlation function of galaxies, which describes how these structures distribute around each other. RSD can be represented by a distortions parameter $\beta$, which is strictly related to the growth of cosmic structures. For this reason, measurements of RSD can be exploited to give constraints on the cosmological parameters, such us for example the neutrino mass. Neutrinos are neutral subatomic particles that come with three flavours, the electron, the muon and the tau neutrino. Their mass differences can be measured in the oscillation experiments. Information on the absolute scale of neutrino mass can come from cosmology, since neutrinos leave a characteristic imprint on the large scale structure of the universe. The aim of this thesis is to provide constraints on the accuracy with which neutrino mass can be estimated when expoiting measurements of RSD. In particular we want to describe how the error on the neutrino mass estimate depends on three fundamental parameters of a galaxy redshift survey: the density of the catalogue, the bias of the sample considered and the volume observed. In doing this we make use of the BASICC Simulation from which we extract a series of dark matter halo catalogues, characterized by different value of bias, density and volume. This mock data are analysed via a Markov Chain Monte Carlo procedure, in order to estimate the neutrino mass fraction, using the software package CosmoMC, which has been conveniently modified. In this way we are able to extract a fitting formula describing our measurements, which can be used to forecast the precision reachable in future surveys like Euclid, using this kind of observations.

A Bayesian changepoint analysis on spatio-temporal point processes

Changepoint analysis is a well established area of statistical research, but in the context of spatio-temporal point processes it is as yet relatively unexplored. Some substantial differences with regard to standard changepoint analysis have to be taken into account: firstly, at every time point the datum is an irregular pattern of points; secondly, in real situations issues of spatial dependence between points and temporal dependence within time segments raise. Our motivating example consists of data concerning the monitoring and recovery of radioactive particles from Sandside beach, North of Scotland; there have been two major changes in the equipment used to detect the particles, representing known potential changepoints in the number of retrieved particles. In addition, offshore particle retrieval campaigns are believed may reduce the particle intensity onshore with an unknown temporal lag; in this latter case, the problem concerns multiple unknown changepoints. We therefore propose a Bayesian approach for detecting multiple changepoints in the intensity function of a spatio-temporal point process, allowing for spatial and temporal dependence within segments. We use Log-Gaussian Cox Processes, a very flexible class of models suitable for environmental applications that can be implemented using integrated nested Laplace approximation (INLA), a computationally efficient alternative to Monte Carlo Markov Chain methods for approximating the posterior distribution of the parameters. Once the posterior curve is obtained, we propose a few methods for detecting significant change points. We present a simulation study, which consists in generating spatio-temporal point pattern series under several scenarios; the performance of the methods is assessed in terms of type I and II errors, detected changepoint locations and accuracy of the segment intensity estimates. We finally apply the above methods to the motivating dataset and find good and sensible results about the presence and quality of changes in the process.

Model and control of tendon actuated robots

The use of tendons for the transmission of the forces and the movements in robotic devices has been investigated from several researchers all over the world. The interest in this kind of actuation modality is based on the possibility of optimizing the position of the actuators with respect to the moving part of the robot, in the reduced weight, high reliability, simplicity in the mechanic design and, finally, in the reduced cost of the resulting kinematic chain. After a brief discussion about the benefits that the use of tendons can introduce in the motion control of a robotic device, the design and control aspects of the UB Hand 3 anthropomorphic robotic hand are presented. In particular, the tendon-sheaths transmission system adopted in the UB Hand 3 is analyzed and the problem of force control and friction compensation is taken into account. The implementation of a tendon based antagonistic actuated robotic arm is then investigated. With this kind of actuation modality, and by using transmission elements with nonlinear force/compression characteristic, it is possible to achieve simultaneous stiffness and position control, improving in this way the safety of the device during the operation in unknown environments and in the case of interaction with other robots or with humans. The problem of modeling and control of this type of robotic devices is then considered and the stability analysis of proposed controller is reported. At the end, some tools for the realtime simulation of dynamic systems are presented. This realtime simulation environment has been developed with the aim of improving the reliability of the realtime control applications both for rapid prototyping of controllers and as teaching tools for the automatic control courses.

Mitochondrial dysfunction in a cell model of thyroid oncocytoma

The role of mitochondrial dysfunction in cancer has long been a subject of great interest. In this study, such dysfunction has been examined with regards to thyroid oncocytoma, a rare form of cancer, accounting for less than 5% of all thyroid cancers. A peculiar characteristic of thyroid oncocytic cells is the presence of an abnormally large number of mitochondria in the cytoplasm. Such mitochondrial hyperplasia has also been observed in cells derived from patients suffering from mitochondrial encephalomyopathies, where mutations in the mitochondrial DNA(mtDNA) encoding the respiratory complexes result in oxidative phosphorylation dysfunction. An increase in the number of mitochondria occurs in the latter in order to compensate for the respiratory deficiency. This fact spurred the investigation into the presence of analogous mutations in thyroid oncocytic cells. In this study, the only available cell model of thyroid oncocytoma was utilised, the XTC-1 cell line, established from an oncocytic thyroid metastasis to the breast. In order to assess the energetic efficiency of these cells, they were incubated in a medium lacking glucose and supplemented instead with galactose. When subjected to such conditions, glycolysis is effectively inhibited and the cells are forced to use the mitochondria for energy production. Cell viability experiments revealed that XTC-1 cells were unable to survive in galactose medium. This was in marked contrast to the TPC-1 control cell line, a thyroid tumour cell line which does not display the oncocytic phenotype. In agreement with these findings, subsequent experiments assessing the levels of cellular ATP over incubation time in galactose medium, showed a drastic and continual decrease in ATP levels only in the XTC-1 cell line. Furthermore, experiments on digitonin-permeabilised cells revealed that the respiratory dysfunction in the latter was due to a defect in complex I of the respiratory chain. Subsequent experiments using cybrids demonstrated that this defect could be attributed to the mitochondrially-encoded subunits of complex I as opposed to the nuclearencoded subunits. Confirmation came with mtDNA sequencing, which detected the presence of a novel mutation in the ND1 subunit of complex I. In addition, a mutation in the cytochrome b subunit of complex III of the respiratory chain was detected. The fact that XTC-1 cells are unable to survive when incubated in galactose medium is consistent with the fact that many cancers are largely dependent on glycolysis for energy production. Indeed, numerous studies have shown that glycolytic inhibitors are able to induce apoptosis in various cancer cell lines. Subsequent experiments were therefore performed in order to identify the mode of XTC-1 cell death when subjected to the metabolic stress imposed by the forced use of the mitochondria for energy production. Cell shrinkage and mitochondrial fragmentation were observed in the dying cells, which would indicate an apoptotic type of cell death. Analysis of additional parameters however revealed a lack of both DNA fragmentation and caspase activation, thus excluding a classical apoptotic type of cell death. Interestingly, cleavage of the actin component of the cytoskeleton was observed, implicating the action of proteases in this mode of cell demise. However, experiments employing protease inhibitors failed to identify the specific protease involved. It has been reported in the literature that overexpression of Bcl-2 is able to rescue cells presenting a respiratory deficiency. As the XTC-1 cell line is not only respiration-deficient but also exhibits a marked decrease in Bcl-2 expression, it is a perfect model with which to study the relationship between Bcl-2 and oxidative phosphorylation in respiratory-deficient cells. Contrary to the reported literature studies on various cell lines harbouring defects in the respiratory chain, Bcl-2 overexpression was not shown to increase cell survival or rescue the energetic dysfunction in XTC-1 cells. Interestingly however, it had a noticeable impact on cell adhesion and morphology. Whereas XTC-1 cells shrank and detached from the growth surface under conditions of metabolic stress, Bcl-2-overexpressing XTC-1 cells appeared much healthier and were up to 45% more adherent. The target of Bcl-2 in this setting appeared to be the actin cytoskeleton, as the cleavage observed in XTC-1 cells expressing only endogenous levels of Bcl-2, was inhibited in Bcl-2-overexpressing cells. Thus, although unable to rescue XTC-1 cells in terms of cell viability, Bcl-2 is somehow able to stabilise the cytoskeleton, resulting in modifications in cell morphology and adhesion. The mitochondrial respiratory deficiency observed in cancer cells is thought not only to cause an increased dependency on glycolysis but it is also thought to blunt cellular responses to anticancer agents. The effects of several therapeutic agents were thus assessed for their death-inducing ability in XTC-1 cells. Cell viability experiments clearly showed that the cells were more resistant to stimuli which generate reactive oxygen species (tert-butylhydroperoxide) and to mitochondrial calcium-mediated apoptotic stimuli (C6-ceramide), as opposed to stimuli inflicting DNA damage (cisplatin) and damage to protein kinases(staurosporine). Various studies in the literature have reported that the peroxisome proliferator-activated receptor-coactivator 1(PGC-1α), which plays a fundamental role in mitochondrial biogenesis, is also involved in protecting cells against apoptosis caused by the former two types of stimuli. In accordance with these observations, real-time PCR experiments showed that XTC-1 cells express higher mRNA levels of this coactivator than do the control cells, implicating its importance in drug resistance. In conclusion, this study has revealed that XTC-1 cells, like many cancer cell lines, are characterised by a reduced energetic efficiency due to mitochondrial dysfunction. Said dysfunction has been attributed to mutations in respiratory genes encoded by the mitochondrial genome. Although the mechanism of cell demise in conditions of metabolic stress is unclear, the potential of targeting thyroid oncocytic cancers using glycolytic inhibitors has been illustrated. In addition, the discovery of mtDNA mutations in XTC-1 cells has enabled the use of this cell line as a model with which to study the relationship between Bcl-2 overexpression and oxidative phosphorylation in cells harbouring mtDNA mutations and also to investigate the significance of such mutations in establishing resistance to apoptotic stimuli.

Respiratory chain complex I dysfunction in tumorigenesis

Diseases due to mutations in mitochondrial DNA probably represent the most common form of metabolic disorders, including cancer, as highlighted in the last years. Approximately 300 mtDNA alterations have been identified as the genetic cause of mitochondrial diseases and one-third of these alterations are located in the coding genes for OXPHOS proteins. Despite progress in identification of their molecular mechanisms, little has been done with regard to the therapy. Recently, a particular gene therapy approach, namely allotopic expression, has been proposed and optimized, although the results obtained are rather controversial. In fact, this approach consists in synthesis of a wild-type version of mutated OXPHOS protein in the cytosolic compartment and in its import into mitochondria, but the available evidence is based only on the partial phenotype rescue and not on the demonstration of effective incorporation of the functional protein into respiratory complexes. In the present study, we took advantage of a previously analyzed cell model bearing the m.3571insC mutation in MTND1 gene for the ND1 subunit of respiratory chain complex I. This frame-shift mutation induces in fact translation of a truncated ND1 protein then degraded, causing complex I disassembly, and for this reason not in competition with that allotopically expressed. We show here that allotopic ND1 protein is correctly imported into mitochondria and incorporated in complex I, promoting its proper assembly and rescue of its function. This result allowed us to further confirm what we have previously demonstrated about the role of complex I in tumorigenesis process. Injection of the allotopic clone in nude mice showed indeed that the rescue of complex I assembly and function increases tumor growth, inducing stabilization of HIF1α, the master regulator of tumoral progression, and consequently its downstream gene expression activation.

Correlations and Quantum Dynamics of 1D Fermionic Models: New Results for the Kitaev Chain with Long-Range Pairing

In the first part of the thesis, we propose an exactly-solvable one-dimensional model for fermions with long-range p-wave pairing decaying with distance as a power law. We studied the phase diagram by analyzing the critical lines, the decay of correlation functions and the scaling of the von Neumann entropy with the system size. We found two gapped regimes, where correlation functions decay (i) exponentially at short range and algebraically at long range, (ii) purely algebraically. In the latter the entanglement entropy is found to diverge logarithmically. Most interestingly, along the critical lines, long-range pairing breaks also the conformal symmetry. This can be detected via the dynamics of entanglement following a quench. In the second part of the thesis we studied the evolution in time of the entanglement entropy for the Ising model in a transverse field varying linearly in time with different velocities. We found different regimes: an adiabatic one (small velocities) when the system evolves according the instantaneous ground state; a sudden quench (large velocities) when the system is essentially frozen to its initial state; and an intermediate one, where the entropy starts growing linearly but then displays oscillations (also as a function of the velocity). Finally, we discussed the Kibble-Zurek mechanism for the transition between the paramagnetic and the ordered phase.

A Unified Model for XVA, including Interest Rates and Rating

We start in Chapter 2 to investigate linear matrix-valued SDEs and the Itô-stochastic Magnus expansion. The Itô-stochastic Magnus expansion provides an efficient numerical scheme to solve matrix-valued SDEs. We show convergence of the expansion up to a stopping time τ and provide an asymptotic estimate of the cumulative distribution function of τ. Moreover, we show how to apply it to solve SPDEs with one and two spatial dimensions by combining it with the method of lines with high accuracy. We will see that the Magnus expansion allows us to use GPU techniques leading to major performance improvements compared to a standard Euler-Maruyama scheme. In Chapter 3, we study a short-rate model in a Cox-Ingersoll-Ross (CIR) framework for negative interest rates. We define the short rate as the difference of two independent CIR processes and add a deterministic shift to guarantee a perfect fit to the market term structure. We show how to use the Gram-Charlier expansion to efficiently calibrate the model to the market swaption surface and price Bermudan swaptions with good accuracy. We are taking two different perspectives for rating transition modelling. In Section 4.4, we study inhomogeneous continuous-time Markov chains (ICTMC) as a candidate for a rating model with deterministic rating transitions. We extend this model by taking a Lie group perspective in Section 4.5, to allow for stochastic rating transitions. In both cases, we will compare the most popular choices for a change of measure technique and show how to efficiently calibrate both models to the available historical rating data and market default probabilities. At the very end, we apply the techniques shown in this thesis to minimize the collateral-inclusive Credit/ Debit Valuation Adjustments under the constraint of small collateral postings by using a collateral account dependent on rating trigger.