arXiv subjects

Luciana Dalla Valle

Publications and source records attributed to Luciana Dalla Valle.

10 recordsLinked to original sources

arXiv2026

Bayesian model selection of vine copulas: a loss-based perspective

The growing popularity of vine copulas in multivariate statistical analysis is largely driven by their ability to capture complex dependence structures. However, this flexibility comes at a cost, as the number of possible vine models grows rapidly and becomes intractable even in moderately low-dimensional settings. These limitations affect the practical applicability of current Bayesian inference and model selection approaches, effectively restricting it to problems of relatively small-dimension due to their high computational cost. This paper addresses the still open challenge of efficient model selection and estimation in Bayesian vine methodology. We propose a novel framework for Bayesian vine copula model selection that combines loss-based model priors with the shotgun stochastic search strategy. The strength of the proposed approach is twofold: it promotes sparsity and enables fast and effective structure selection. Furthermore, our comprehensive framework jointly identifies the vine structure, selects the copula families, and estimates the model parameters. The power of the proposed approach is demonstrated via simulation studies and an application to a real dataset of EFT portfolio asset returns.

stat.ME↗

arXiv2023

A New Data Integration Framework for Covid-19 Social Media Information

The Covid-19 pandemic presents a serious threat to people health, resulting in over 250 million confirmed cases and over 5 million deaths globally. To reduce the burden on national health care systems and to mitigate the effects of the outbreak, accurate modelling and forecasting methods for short- and long-term health demand are needed to inform government interventions aiming at curbing the pandemic. Current research on Covid-19 is typically based on a single source of information, specifically on structured historical pandemic data. Other studies are exclusively focused on unstructured online retrieved insights, such as data available from social media. However, the combined use of structured and unstructured information is still uncharted. This paper aims at filling this gap, by leveraging historical and social media information with a novel data integration methodology. The proposed approach is based on vine copulas, which allow us to exploit the dependencies between different sources of information. We apply the methodology to combine structured datasets retrieved from official sources and a big unstructured dataset of information collected from social media. The results show that the combined use of official and online generated information contributes to yield a more accurate assessment of the evolution of the Covid-19 pandemic, compared to the sole use of official data.

cs.SI↗

arXiv2021

Social Media Integration of Flood Data: A Vine Copula-Based Approach

Floods are the most common and among the most severe natural disasters in many countries around the world. As global warming continues to exacerbate sea level rise and extreme weather, governmental authorities and environmental agencies are facing the pressing need of timely and accurate evaluations and predictions of flood risks. Current flood forecasts are generally based on historical measurements of environmental variables at monitoring stations. In recent years, in addition to traditional data sources, large amounts of information related to floods have been made available via social media. Members of the public are constantly and promptly posting information and updates on local environmental phenomena on social media platforms. Despite the growing interest of scholars towards the usage of online data during natural disasters, the majority of studies focus exclusively on social media as a stand-alone data source, while its joint use with other type of information is still unexplored. In this paper we propose to fill this gap by integrating traditional historical information on floods with data extracted by Twitter and Google Trends. Our methodology is based on vine copulas, that allow us to capture the dependence structure among the marginals, which are modelled via appropriate time series methods, in a very flexible way. We apply our methodology to data related to three different coastal locations on the South coast of the United Kingdom (UK). The results show that our approach, based on the integration of social media data, outperforms traditional methods in terms of evaluation and prediction of flood events.

stat.AP↗

arXiv2021

Bayesian Nonparametric Modelling of Conditional Multidimensional Dependence Structures

In recent years, conditional copulas, that allow dependence between variables to vary according to the values of one or more covariates, have attracted increasing attention. In high dimension, vine copulas offer greater flexibility compared to multivariate copulas, since they are constructed using bivariate copulas as building blocks. In this paper we present a novel inferential approach for multivariate distributions, which combines the flexibility of vine constructions with the advantages of Bayesian nonparametrics, not requiring the specification of parametric families for each pair copula. Expressing multivariate copulas using vines allows us to easily account for covariate specifications driving the dependence between response variables. More precisely, we specify the vine copula density as an infinite mixture of Gaussian copulas, defining a Dirichlet process (DP) prior on the mixing measure, and we perform posterior inference via Markov chain Monte Carlo (MCMC) sampling. Our approach is successful as for clustering as well as for density estimation. We carry out intensive simulation studies and apply the proposed approach to investigate the impact of natural disasters on financial development. Our results show that the methodology is able to capture the heterogeneity in the dataset and to reveal different behaviours of different country clusters in relation to natural disasters.

stat.ME↗

arXiv2021

Approximate Bayesian Conditional Copulas

Copula models are flexible tools to represent complex structures of dependence for multivariate random variables. According to Sklar's theorem (Sklar, 1959), any d-dimensional absolutely continuous density can be uniquely represented as the product of the marginal distributions and a copula function which captures the dependence structure among the vector components. In real data applications, the interest of the analyses often lies on specific functionals of the dependence, which quantify aspects of it in a few numerical values. A broad literature exists on such functionals, however extensions to include covariates are still limited. This is mainly due to the lack of unbiased estimators of the copula function, especially when one does not have enough information to select the copula model. Recent advances in computational methodologies and algorithms have allowed inference in the presence of complicated likelihood functions, especially in the Bayesian approach, whose methods, despite being computationally intensive, allow us to better evaluate the uncertainty of the estimates. In this work, we present several Bayesian methods to approximate the posterior distribution of functionals of the dependence, using nonparametric models which avoid the selection of the copula function. These methods are compared in simulation studies and in two realistic applications, from civil engineering and astrophysics.

stat.ME↗

arXiv2020

A Pólya-Gamma Sampler for a Generalized Logistic Regression

In this paper we introduce a novel Bayesian data augmentation approach for estimating the parameters of the generalised logistic regression model. We propose a Pólya-Gamma sampler algorithm that allows us to sample from the exact posterior distribution, rather than relying on approximations. A simulation study illustrates the flexibility and accuracy of the proposed approach to capture heavy and light tails in binary response data of different dimensions. The methodology is applied to two different real datasets, where we demonstrate that the Pólya-Gamma sampler provides more precise estimates than the empirical likelihood method, outperforming approximate approaches.

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arXiv2019

A Bayesian Non-linear State Space Copula Model to Predict Air Pollution in Beijing

Air pollution is a serious issue that currently affects many industrial cities in the world and can cause severe illness to the population. In particular, it has been proven that extreme high levels of airborne contaminants have dangerous short-term effects on human health, in terms of increased hospital admissions for cardiovascular and respiratory diseases and increased mortality risk. For these reasons, accurate estimation and prediction of airborne pollutant concentration is crucial. In this paper, we propose a flexible novel approach to model hourly measurements of fine particulate matter and meteorological data collected in Beijing in 2014. We show that the standard state space model, based on Gaussian assumptions, does not correctly capture the time dynamics of the observations. Therefore, we propose a non-linear non-Gaussian state space model where both the observation and the state equations are defined by copula specifications, and we perform Bayesian inference using the Hamiltonian Monte Carlo method. The proposed copula state space approach is very flexible, since it allows us to separately model the marginals and to accommodate a wide variety of dependence structures in the data dynamics. We show that the proposed approach allows us not only to predict particulate matter measurements, but also to investigate the effects of user specified climate scenarios.

stat.AP↗

arXiv2019

Bayesian Multivariate Nonlinear State Space Copula Models

In this paper we propose a flexible class of multivariate nonlinear non-Gaussian state space models, based on copulas. More precisely, we assume that the observation equation and the state equation are defined by copula families that are not necessarily equal. For each time point, the resulting model can be described by a C-vine copula truncated after the first tree, where the root node is represented by the latent state. Inference is performed within the Bayesian framework, using the Hamiltonian Monte Carlo method, where a further D-vine truncated after the first tree is used as prior distribution to capture the temporal dependence in the latent states. Simulation studies show that the proposed copula-based approach is extremely flexible, since it is able to describe a wide range of dependence structures and, at the same time, allows us to deal with missing data. The application to atmospheric pollutant measurement data shows that our approach is suitable for accurate modeling and prediction of data dynamics in the presence of missing values. Comparison to a Gaussian linear state space model and to Bayesian additive regression trees shows the superior performance of the proposed model with respect to predictive accuracy.

stat.ME↗

arXiv2017

Bayesian Nonparametric Conditional Copula Estimation of Twin Data

Several studies on heritability in twins aim at understanding the different contribution of environmental and genetic factors to specific traits. Considering the National Merit Twin Study, our purpose is to correctly analyse the influence of the socioeconomic status on the relationship between twins' cognitive abilities. Our methodology is based on conditional copulas, which allow us to model the effect of a covariate driving the strength of dependence between the main variables. We propose a flexible Bayesian nonparametric approach for the estimation of conditional copulas, which can model any conditional copula density. Our methodology extends the work of Wu et al (2015) by introducing dependence from a covariate in an infinite mixture model. Our results suggest that environmental factors are more influential in families with lower socio-economic position.

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arXiv2015

Default Probability Estimation via Pair Copula Constructions

In this paper we present a novel approach for firm default probability estimation. The methodology is based on multivariate contingent claim analysis and pair copula constructions. For each considered firm, balance sheet data are used to assess the asset value, and to compute its default probability. The asset pricing function is expressed via a pair copula construction, and it is approximated via Monte Carlo simulations. The methodology is illustrated through an application to the analysis of both operative and defaulted firms.

q-fin.RM↗