Non-parametric inference of the population of compact binaries from gravitational wave observations using binned Gaussian processes

The observation of gravitational waves from multiple compact binary coalescences by the LIGO-Virgo-KAGRA detector networks has enabled us to infer the underlying distribution of compact binaries across a wide range of masses, spins, and redshifts. In light of the new features found in the mass spectrum of binary black holes and the uncertainty regarding binary formation models, non-parametric population inference has become increasingly popular. In this work, we develop a data-driven clustering framework that can identify features in the component mass distribution of compact binaries simultaneously with those in the corresponding redshift distribution, from gravitational wave data in the presence of significant measurement uncertainties, while making very few assumptions on the functional form of these distributions. Our generalized model is capable of inferring correlations among various population properties such as the redshift evolution of the shape of the mass distribution itself, in contrast to most existing non-parametric inference schemes. We test our model on simulated data and demonstrate the accuracy with which it can re-construct the underlying distributions of component masses and redshifts. We also re-analyze public LIGO-Virgo-KAGRA data from events in GWTC-3 using our model and compare our results with those from some alternative parametric and non-parametric population inference approaches. Finally, we investigate the potential presence of correlations between mass and redshift in the population of binary black holes in GWTC-3 (those observed by the LIGO-Virgo-KAGRA detector network in their first 3 observing runs), without making any assumptions about the specific nature of these correlations.Comment: Upload accepted versio

Zipf's Law for Cities and the Double-Pareto-Lognormal Distribution

This dissertation concentrates on the size distribution of cities. From an empirical perspective, it is shown that Zipf's law for cities holds for the upper tail of the distribution and that the overall distribution is the Double-Pareto-Lognormal distribution. From a theoretical perspective, the dissertation builds a dynamic general equilibrium model of random urban growth with endogenous city formation, which explains the empirical finding of a Double-Pareto-Lognormal city size distribution

Pricing financial and insurance products in the multivariate setting

In finance and insurance there is often the need to construct multivariate distributions to take into account more than one source of risk, where such risks cannot be assumed to be independent. In the course of this thesis we are going to explore three models, namely the copula models, the trivariate reduction scheme and mixtures as candidate models for capturing the dependence between multiple sources of risk. This thesis contains results of three different projects. The first one is in financial mathematics, more precisely on the pricing of financial derivatives (multi-asset options) which depend on multiple underlying assets, where we construct the dependence between such assets using copula models and the trivariate reduction scheme. The second and the third projects are in actuarial mathematics, more specifically on the pricing of the premia that need to be paid by policyholders in the automobile insurance when more than one type of claim is considered. We do the pricing including all the information available about the characteristics of the policyholders and their cars (i.e. a priori ratemaking) and about the numbers of claims per type in which the policyholders have been involved (i.e. a posteriori ratemaking). In both projects we model the dependence between the multiple types of claims using mixture distributions/regression models: we consider the different types of claims to be modelled in terms of their own distribution/regression model but with a common heterogeneity factor which follows a mixing distribution/regression model that is responsible for the dependence between the multiple types of claims. In the second project we present a new model (i.e. the bivariate Negative Binomial-Inverse Gaussian regression model) and in the third one we present a new family of models (i.e. the bivariate mixed Poisson regression models with varying dispersion), both as suitable alternatives to the classically used bivariate mixed Poisson regression models

Power system vulnerability and performance: application from complexity scienze and complex network

Power system has been acknowledged as a complex system owing to its complexity resulting from interactions of different layers which include physical layer like generators, transformers, substations and cyber layer like communication units and human decision layer. Complex network theory has been widely used to analyze the power grids from basic topological properties to statistic robustness analysis and dynamic resilience property. However, there are still many problems need to be addressed. This thesis will pay more attention on the application and extension of complexity science and complex network theory in power system analysis from different aspects

Delimitation of Some Taxa of Ulnaria and Fragilaria (Bacillariophyceae) Based on Genetic, Morphological Data and Mating Compatibility

Fragilaria and Ulnaria are two closely related diatom genera for which the delimitation and circumscription of several species is unclear. We studied strains isolated from Lake Baikal and compared them with the species from freshwater reservoirs in Europe and Asia using phylogenetic and species delimitation methods, microscopy and interclonal crossing experiments. The results of the phylogenetic analyses of the fragments of rbcL and 18S rRNA genes revealed that baikalian F. radians clade was independent from the representatives of the genus from other localities. Among Ulnaria we found the following 18S rRNA phylogenetic tree groups at species level: U. acus, U. ulna and U. danica. Genetic distance between genera varied between 3.9-10.2% substitutions in rbcL gene and 3.2-11.5% in 18S rRNA. The boundary between intraspecies and interspecies polymorphism for studied species of Ulnaria and Fragilaria in these marker genes was around 0.8% substitutions. Morphometric characters of individual strains showed their variability and division into F. radians, U. acus and U. ulna together with U. danica. Strains of U. acus and U. danica from different localities of Europe and Asia were sexually compatible inside the species. Sexual reproduction has never been observed in monoclonal cultures, either between this species or with strains of the Fragilaria

Modelling of and empirical studies on portfolio choice, option pricing, and credit risk

This thesis develops and applies a statistical spanning test for mean-coherent regular risk portfolios. Similarly in spirt to Huberman and Kandel (1987), this test can be implemented by means of a simple semi-parametric instrumental variable regression, where instruments have a direct link with a stochastic discount factor. Applications to different asset classes are studied. The results are compared to the conventional mean-variance approach. The second part of the thesis concerns option pricing under stochastic volatility and credit risk modelling. It is shown that modelling dynamics of the implied prices of volatility risk can improve out-of-sample option pricing performance. Finally, an equity-based structural model of credit risk with a constant elasticity of volatility assumption is discussed. This model might be particularly suitable for analysis of high yield fixed income instruments, where correlation between credit spreads and equity returns is substantial.

The NANOGrav 15 yr Data Set: Search for Signals from New Physics

The 15 yr pulsar timing data set collected by the North American Nanohertz Observatory for Gravitational Waves (NANOGrav) shows positive evidence for the presence of a low-frequency gravitational-wave (GW) background. In this paper, we investigate potential cosmological interpretations of this signal, specifically cosmic inflation, scalar-induced GWs, first-order phase transitions, cosmic strings, and domain walls. We find that, with the exception of stable cosmic strings of field theory origin, all these models can reproduce the observed signal. When compared to the standard interpretation in terms of inspiraling supermassive black hole binaries (SMBHBs), many cosmological models seem to provide a better fit resulting in Bayes factors in the range from 10 to 100. However, these results strongly depend on modeling assumptions about the cosmic SMBHB population and, at this stage, should not be regarded as evidence for new physics. Furthermore, we identify excluded parameter regions where the predicted GW signal from cosmological sources significantly exceeds the NANOGrav signal. These parameter constraints are independent of the origin of the NANOGrav signal and illustrate how pulsar timing data provide a new way to constrain the parameter space of these models. Finally, we search for deterministic signals produced by models of ultralight dark matter (ULDM) and dark matter substructures in the Milky Way. We find no evidence for either of these signals and thus report updated constraints on these models. In the case of ULDM, these constraints outperform torsion balance and atomic clock constraints for ULDM coupled to electrons, muons, or gluons