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Blood vessel networks, represented as 3D graphs, help predict disease biomarkers, simulate blood flow, and aid in synthetic image generation, relevant in both clinical and pre-clinical settings. However, generating realistic vessel graphs that correspond to an anatomy of interest is challenging. Previous methods aimed at generating vessel trees mostly in an autoregressive style and could not be applied to vessel graphs with cycles such as capillaries or specific anatomical structures such as the Circle of Willis. Addressing this gap, we introduce the first application of \textit{denoising diffusion models} in 3D vessel graph generation. Our contributions include a novel, two-stage generation method that sequentially denoises node coordinates and edges. We experiment with two real-world vessel datasets, consisting of microscopic capillaries and major cerebral vessels, and demonstrate the generalizability of our method for producing diverse, novel, and anatomically plausible vessel graphs., Comment: Accepted to MICCAI 2024

The Circle of Willis (CoW) is an important network of arteries connecting major circulations of the brain. Its vascular architecture is believed to affect the risk, severity, and clinical outcome of serious neuro-vascular diseases. However, characterizing the highly variable CoW anatomy is still a manual and time-consuming expert task. The CoW is usually imaged by two angiographic imaging modalities, magnetic resonance angiography (MRA) and computed tomography angiography (CTA), but there exist limited public datasets with annotations on CoW anatomy, especially for CTA. Therefore we organized the TopCoW Challenge in 2023 with the release of an annotated CoW dataset. The TopCoW dataset was the first public dataset with voxel-level annotations for thirteen possible CoW vessel components, enabled by virtual-reality (VR) technology. It was also the first large dataset with paired MRA and CTA from the same patients. TopCoW challenge formalized the CoW characterization problem as a multiclass anatomical segmentation task with an emphasis on topological metrics. We invited submissions worldwide for the CoW segmentation task, which attracted over 140 registered participants from four continents. The top performing teams managed to segment many CoW components to Dice scores around 90%, but with lower scores for communicating arteries and rare variants. There were also topological mistakes for predictions with high Dice scores. Additional topological analysis revealed further areas for improvement in detecting certain CoW components and matching CoW variant topology accurately. TopCoW represented a first attempt at benchmarking the CoW anatomical segmentation task for MRA and CTA, both morphologically and topologically., Comment: 24 pages, 11 figures, 9 tables. Summary Paper for the MICCAI TopCoW 2023 Challenge

We consider the problem of assessing whether, in an individual case, there is a causal relationship between an observed exposure and a response variable. When data are available on similar individuals we may be able to estimate prospective probabilities, but even under ideal conditions these are typically inadequate to identify the "probability of causation": instead we can only derive bounds for this. These bounds can be improved or amended when we have information on additional variables, such as mediators or covariates. When a covariate is unobserved or ignored, this will typically lead to biased inferences. We show by examples how serious such biases can be., Comment: 10 pages, 3 figures

The spread of the Sars-COV-2 pandemic in 2020 had a huge impact on the life course of all of us. This rapid spread has also caused an increase in the research production in topics related to COVID-19 with regard to different aspects. Italy has, unfortunately, been one of the first countries to be massively involved in the outbreak of the disease. In this paper we present an extensive scientometric analysis of the research production both at global (entire literature produced in the first 2 years after the beginning of the pandemic) and local level (COVID-19 literature produced by authors with an Italian affiliation). Our results showed that US and China are the most active countries in terms of number of publications and that the number of collaborations between institutions varies according to geographical distance. Moreover, we identified the medical-biological as the fields with the greatest growth in terms of literature production. Furthermore, we also better explored the relationship between the number of citations and variables obtained from the data set (e.g. number of authors per article). Using multiple correspondence analysis and quantile regression we shed light on the role of journal topics and impact factor, the type of article, the field of study and how these elements affect citations.

Niobium nitride (NbN) is a particularly promising material for quantum technology applications, as entails the degree of reproducibility necessary for large-scale of superconducting circuits. We demonstrate that resonators based on NbN thin films present a one-photon internal quality factor above 10$^5$ maintaining a high impedance (larger than 2k$\Omega$), with a footprint of approximately 50x100 $\mu$m$^2$ and a self-Kerr nonlinearity of few tenths of Hz. These quality factors, mostly limited by losses induced by the coupling to two-level systems, have been maintained for kinetic inductances ranging from tenths to hundreds of pH/square. We also demonstrate minimal variations in the performance of the resonators during multiple cooldowns over more than nine months. Our work proves the versatility of niobium nitride high-kinetic inductance resonators, opening perspectives towards the fabrication of compact, high-impedance and high-quality multimode circuits, with sizable interactions., Comment: 12 pages, 8 figures

The coefficient of variation is a useful indicator for comparing the spread of values between dataset with different units or widely different means. In this paper we address the problem of investigating the equality of the coefficients of variation from two independent populations. In order to do this we rely on the Bayesian Discrepancy Measure recently introduced in the literature. Computing this Bayesian measure of evidence is straightforward when the coefficient of variation is a function of a single parameter of the distribution. In contrast, it becomes difficult when it is a function of more parameters, often requiring the use of MCMC methods. We calculate the Bayesian Discrepancy Measure by considering a variety of distributions whose coefficients of variation depend on more than one parameter. We consider also applications to real data. As far as we know, some of the examined problems have not yet been covered in the literature.

A confidence distribution is a distribution for a parameter of interest based on a parametric statistical model. As such, it serves the same purpose for frequentist statisticians as a posterior distribution for Bayesians, since it allows to reach point estimates, to assess their precision, to set up tests along with measures of evidence, to derive confidence intervals, comparing the parameter of interest with other parameters from other studies, etc. A general recipe for deriving confidence distributions is based on classical pivotal quantities and their exact or approximate distributions. However, in the presence of model misspecifications or outlying values in the observed data, classical pivotal quantities, and thus confidence distributions, may be inaccurate. The aim of this paper is to discuss the derivation and application of robust confidence distributions. In particular, we discuss a general approach based on the Tsallis scoring rule in order to compute a robust confidence distribution. Examples and simulation results are discussed for some problems often encountered in practice, such as the two-sample heteroschedastic comparison, the receiver operating characteristic curves and regression models., Comment: submitted

The aim of this article is to make a contribution to the Bayesian procedure of testing precise hypotheses for parametric models. For this purpose, we define the Bayesian Discrepancy Measure that allows one to evaluate the suitability of a given hypothesis with respect to the available information (prior law and data). To summarise this information, the posterior median is employed, allowing a simple assessment of the discrepancy with a fixed hypothesis. The Bayesian Discrepancy Measure assesses the compatibility of a single hypothesis with the observed data, as opposed to the more common comparative approach where a hypothesis is rejected in favour of a competing hypothesis. The proposed measure of evidence has properties of consistency and invariance. After presenting the definition of the measure for a parameter of interest, both in the absence and in the presence of nuisance parameters, we illustrate some examples showing its conceptual and interpretative simplicity. Finally, we compare the BDT with the Full Bayesian Significance Test, a well-known Bayesian testing procedure for sharp hypotheses., Comment: 29 pages 9 figures

Research evaluations and comparison of the assessments of academic institutions (scientific areas, departments, universities etc.) are among the major issues in recent years in higher education systems. One method, followed by some national evaluation agencies, is to assess the research quality by the evaluation of a limited number of publications in a way that each publication is rated among $n$ classes. This method produces, for each institution, a distribution of the publications in the $n$ classes. In this paper we introduce a natural geometric way to compare these assessments by introducing an ad hoc distance from the performance of an institution to the best possible achievable assessment. Moreover, to avoid the methodological error of comparing non-homogeneous institutions, we introduce a {\em geometric score} based on such a distance. The latter represents the probability that an ideal institution, with the same configuration as the one under evaluation, performs worst. We apply our method, based on the geometric score, to rank, in two specific scientific areas, the Italian universities using the results of the evaluation exercise VQR 2011-2014.

We describe and contrast two distinct problem areas for statistical causality: studying the likely effects of an intervention ("effects of causes"), and studying whether there is a causal link between the observed exposure and outcome in an individual case ("causes of effects"). For each of these, we introduce and compare various formal frameworks that have been proposed for that purpose, including the decision-theoretic approach, structural equations, structural and stochastic causal models, and potential outcomes. It is argued that counterfactual concepts are unnecessary for studying effects of causes, but are needed for analysing causes of effects. They are however subject to a degree of arbitrariness, which can be reduced, though not in general eliminated, by taking account of additional structure in the problem., Comment: 28 pages. Invited paper for "Annual Review of Statistics and its Application"

We discuss an approach for fitting robust nonlinear regression models, which can be employed to model and predict the contagion dynamics of the Covid-19 in Italy. The focus is on the analysis of epidemic data using robust dose-response curves, but the functionality is applicable to arbitrary nonlinear regression models., Comment: 15 pages, 6 figures, submitted

We give a detailed explicit computation of weights of Kontsevich graphs which arise from connection and curvature terms within the globalization picture for the special case of symplectic manifolds. We will show how the weights for the curvature graphs can be explicitly expressed in terms of the hypergeometric function as well as by a much simpler formula combining it with the explicit expression for the weights of its underlined connection graphs. Moreover, we consider the case of a cotangent bundle, which will simplify the curvature expression significantly., Comment: 30 pages, 14 figures, to appear in Adv. Theor. Math. Phys

Suppose X and Y are binary exposure and outcome variables, and we have full knowledge of the distribution of Y, given application of X. From this we know the average causal effect of X on Y. We are now interested in assessing, for a case that was exposed and exhibited a positive outcome, whether it was the exposure that caused the outcome. The relevant "probability of causation", PC, typically is not identified by the distribution of Y given X, but bounds can be placed on it, and these bounds can be improved if we have further information about the causal process. Here we consider cases where we know the probabilistic structure for a sequence of complete mediators between X and Y. We derive a general formula for calculating bounds on PC for any pattern of data on the mediators (including the case with no data). We show that the largest and smallest upper and lower bounds that can result from any complete mediation process can be obtained in processes with at most two steps. We also consider homogeneous processes with many mediators. PC can sometimes be identified as 0 with negative data, but it cannot be identified at 1 even with positive data on an infinite set of mediators. The results have implications for learning about causation from knowledge of general processes and of data on cases., Comment: 23 pages, 2 figures

Likelihood-based estimation methods involve the normalising constant of the model distributions, expressed as a function of the parameter. However in many problems this function is not easily available, and then less efficient but more easily computed estimators may be attractive. In this work we study stationary time-series models, and construct and analyse "score-matching'' estimators, that do not involve the normalising constant. We consider two scenarios: a single series of increasing length, and an increasing number of independent series of fixed length. In the latter case there are two variants, one based on the full data, and another based on a sufficient statistic. We study the empirical performance of these estimators in three special cases, autoregressive (\AR), moving average (MA) and fractionally differenced white noise (\ARFIMA) models, and make comparisons with full and pairwise likelihood estimators. The results are somewhat model-dependent, with the new estimators doing well for $\MA$ and \ARFIMA\ models, but less so for $\AR$ models., Comment: 23 pages, 1 figure, 3 tables. arXiv admin note: text overlap with arXiv:1409.3690

In causal inference, and specifically in the \textit{Causes of Effects} problem, one is interested in how to use statistical evidence to understand causation in an individual case, and so how to assess the so-called {\em probability of causation} (PC). The answer relies on the potential responses, which can incorporate information about what would have happened to the outcome as we had observed a different value of the exposure. However, even given the best possible statistical evidence for the association between exposure and outcome, we can typically only provide bounds for the PC. Dawid et al. (2016) highlighted some fundamental conditions, namely, exogeneity, comparability, and sufficiency, required to obtain such bounds, based on experimental data. The aim of the present paper is to provide methods to find, in specific cases, the best subsample of the reference dataset to satisfy such requirements. To this end, we introduce a new variable, expressing the desire to be exposed or not, and we set the question up as a model selection problem. The best model will be selected using the marginal probability of the responses and a suitable prior proposal over the model space. An application in the educational field is presented., Comment: 16 pages, 3 figures, 2 tables

Many legal cases require decisions about causality, responsibility or blame, and these may be based on statistical data. However, causal inferences from such data are beset by subtle conceptual and practical difficulties, and in general it is, at best, possible to identify the "probability of causation" as lying between certain empirically informed limits. These limits can be refined and improved if we can obtain additional information, from statistical or scientific data, relating to the internal workings of the causal processes. In this paper we review and extend recent work in this area, where additional information may be available on covariate and/or mediating variables., Comment: 14 pages, 2 tables, 7 figures

An individual has been subjected to some exposure and has developed some outcome. Using data on similar individuals, we wish to evaluate, for this case, the probability that the outcome was in fact caused by the exposure. Even with the best possible experimental data on exposure and outcome, we typically can not identify this "probability of causation" exactly, but we can provide information in the form of bounds for it. Under appropriate assumptions, these bounds can be tightened if we can make other observations (e.g., on non-experimental cases), measure additional variables (e.g., covariates) or measure complete mediators. In this work we propose new bounds for the case that a third variable mediates partially the effect of the exposure on the outcome., Comment: 8 pages, 4 tables, 2 figures

We consider the problem of choosing between parametric models for a discrete observable, taking a Bayesian approach in which the within-model prior distributions are allowed to be improper. In order to avoid the ambiguity in the marginal likelihood function in such a case, we apply a homogeneous scoring rule. For the particular case of distinguishing between Poisson and Negative Binomial models, we conduct simulations that indicate that, applied prequentially, the method will consistently select the true model., Comment: 8 pages, 2 figures

We are deeply appreciative of the initiative of the editor, Marina Vanucci, in commissioning a discussion of our paper, and extremely grateful to all the discussants for their insightful and thought-provoking comments. We respond to the discussions in alphabetical order [arXiv:1409.5291]., Comment: Published at http://dx.doi.org/10.1214/15-BA942REJ in the Bayesian Analysis (http://projecteuclid.org/euclid.ba) by the International Society of Bayesian Analysis (http://bayesian.org/)

Given empirical evidence for the dependence of an outcome variable on an exposure variable, we can typically only provide bounds for the "probability of causation" in the case of an individual who has developed the outcome after being exposed. We show how these bounds can be adapted or improved if further information becomes available. In addition to reviewing existing work on this topic, we provide a new analysis for the case where a mediating variable can be observed. In particular we show how the probability of causation can be bounded when there is no direct effect and no confounding. Keywords: Causal inference, Mediation Analysis, Probability of Causation, Comment: 9 pages, 1 figure, 3 tables

Bayesian model selection with improper priors is not well-defined because of the dependence of the marginal likelihood on the arbitrary scaling constants of the within-model prior densities. We show how this problem can be evaded by replacing marginal log-likelihood by a homogeneous proper scoring rule, which is insensitive to the scaling constants. Suitably applied, this will typically enable consistent selection of the true model., Comment: Published at http://dx.doi.org/10.1214/15-BA942 in the Bayesian Analysis (http://projecteuclid.org/euclid.ba) by the International Society of Bayesian Analysis (http://bayesian.org/)

The aim of this paper is to compare numerically the performance of two estimators based on Hyv\"arinen's local homogeneous scoring rule with that of the full and the pairwise maximum likelihood estimators. In particular, two different model settings, for which both full and pairwise maximum likelihood estimators can be obtained, have been considered: the first order autoregressive model (AR(1)) and the moving average model (MA(1)). Simulation studies highlight very different behaviours for the Hyv\"arinen scoring rule estimators relative to the pairwise likelihood estimators in these two settings., Comment: 14 pages, 2 figures

Proper scoring rules are methods for encouraging honest assessment of probability distributions. Just like likelihood, a proper scoring rule can be applied to supply an unbiased estimating equation for any statistical model, and the theory of such equations can be applied to understand the properties of the associated estimator. In this paper we develop some basic scoring rule estimation theory, and explore robustness and interval estimation properties by means of theory and simulations., Comment: 27 pages, 3 figures

We give an overview of some uses of proper scoring rules in statistical inference, including frequentist estimation theory and Bayesian model selection with improper priors., Comment: 13 pages

While statisticians and quantitative social scientists typically study the "effects of causes" (EoC), Lawyers and the Courts are more concerned with understanding the "causes of effects" (CoE). EoC can be addressed using experimental design and statistical analysis, but it is less clear how to incorporate statistical or epidemiological evidence into CoE reasoning, as might be required for a case at Law. Some form of counterfactual reasoning, such as the "potential outcomes" approach championed by Rubin, appears unavoidable, but this typically yields "answers" that are sensitive to arbitrary and untestable assumptions. We must therefore recognise that a CoE question simply might not have a well-determined answer. It is nevertheless possible to use statistical data to set bounds within which any answer must lie. With less than perfect data these bounds will themselves be uncertain, leading to a compounding of different kinds of uncertainty. Still further care is required in the presence of possible confounding factors. In addition, even identifying the relevant "counterfactual contrast" may be a matter of Policy as much as of Science. Defining the question is as non-trivial a task as finding a route towards an answer. This paper develops some technical elaborations of these philosophical points, and illustrates them with an analysis of a case study in child protection. Keywords: benfluorex, causes of effects, counterfactual, child protection, effects of causes, Fre'chet bound, potential outcome, probability of causation, Comment: 27 pages, 1 table, 9 figures. This is a fairly substantial revision of version 1

The aim of this article is to introduce a new family of distributions, which generalizes the skew normal distribution (SN). This new family, called Beta skew-normal (BSN), arises naturally when we consider the distributions of order statistics of the SN. The BSN can also be obtained as a special case of the Beta generated distribution (Jones (2004)). In this work we pay attention to three other generalizations of the SN distribution: the Balakrishnan skew-normal (SNB) (Balakrishnan (2002), as a discussant of Arnold and Beaver (2002), Gupta and Gupta (2004), Sharafi and Behboodian (2008)), the generalized Balakrishnan skew-normal (GBSN) (Yadegari et al. (2008)) and a two parameter generalization of the Balakrishnan skew-normal (TBSN) (Bahrami et al. (2009)). The above three extensions are related to the Beta skew-normal distribution for particular values of the parameters. The paper is organized as follows: after describing briefly, in Section 2, the skew-normal distribution, its generalizations and listing their most important properties, in Section 3 we present some generalizations of the Beta distribution. In the last Section we define the Beta skew-normal distribution, we present its properties and some special cases. In particular the BSN contains the Beta half-normal distribution (Pescim et al. (2010)) as limiting case. Besides, we investigate its shape properties. We derive its moment generating function and we also compute numerically the first moment, the variance, the skewness and the kurtosis. We present two different methods which allow to simulate a BSN distribution. We explore its relationships with the other generalizations of the SN. We give some results concerning the SNB distribution. In particular we derive the exact distributions of the largest order statistic from SNB with parameters m and 1 and the shortest order statistic SNB with parameters m and -1., Comment: 21 pages, 3 figures and 1 table

In recent years, spatial and spatio-temporal modeling have become an important area of research in many fields (epidemiology, environmental studies, disease mapping). In this work we propose different spatial models to study hospital recruitment, including some potentially explicative variables. Interest is on the distribution per geographical unit of the ratio between the number of patients living in this geographical unit and the population in the same unit. Models considered are within the framework of Bayesian Latent Gaussian models. Our response variable is assumed to follow a binomial distribution, with logit link, whose parameters are the population in the geographical unit and the corresponding relative risk. The structured additive predictor accounts for effects of various covariates in an additive way, including smoothing functions of the covariates (for example spatial effect), linear effect of covariates. To approximate posterior marginals, which not available in closed form, we use integrated nested Laplace approximations (INLA), recently proposed for approximate Bayesian inference in latent Gaussian models. INLA has the advantage of giving very accurate approximations and being faster than McMC methods when the number of parameters does not exceed 6 (as it is in our case). Model comparisons are assessed using DIC criterion.