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Additional file 1: Table S1.List of the analyzed metabolites

Hierarchical nonparametric processes are popular tools for defining priors on collections of probability distributions, which induce dependence across multiple samples. In survival analysis problems, one is typically interested in modeling the hazard rates, rather than the probability distributions themselves, and the currently available methodologies are not applicable. Here, we fill this gap by introducing a novel, and analytically tractable, class of multivariate mixtures whose distribution acts as a prior for the vector of sample-specific baseline hazard rates. The dependence is induced through a hierarchical specification of the mixing random measures that ultimately corresponds to a composition of random discrete combinatorial structures. Our theoretical results allow to develop a full Bayesian analysis for this class of models, which can also account for right-censored survival data and covariates, and we also show posterior consistency. In particular, we emphasize that the posterior characterization we achieve is the key for devising both marginal and conditional algorithms for evaluating Bayesian inferences of interest. The effectiveness of our proposal is illustrated through some synthetic and real data examples.

The use of large datasets for targeted therapeutic interventions requires new ways to characterize the heterogeneity observed across subgroups of a specific population. In particular, models for partially exchangeable data are needed for inference on nested datasets, where the observations are assumed to be organized in different units and some sharing of information is required to learn distinctive features of the units. In this manuscript, we propose a nested common atoms model (CAM) that is particularly suited for the analysis of nested datasets where the distributions of the units are expected to differ only over a small fraction of the observations sampled from each unit. The proposed CAM allows a two-layered clustering at the distributional and observational level and is amenable to scalable posterior inference through the use of a computationally efficient nested slice sampler algorithm. We further discuss how to extend the proposed modeling framework to handle discrete measurements, and we conduct posterior inference on a real microbiome dataset from a diet swap study to investigate how the alterations in intestinal microbiota composition are associated with different eating habits. We further investigate the performance of our model in capturing true distributional structures in the population by means of a simulation study.

Consider an (observable) random sample of size n from an infinite population of individuals, each individual being endowed with a finite set of "features" from a collection of features (F-j)(j>1) with unknown probabilities (p(j))(j>1), i.e., p(j) is the probability that an individual displays feature F-j. Under this feature sampling framework, in recent years there has been a growing interest in estimating the sum of the probability masses p(j)'s of features observed with frequency r >= 0 in the sample, here denoted by M-n,M-r. This is the natural feature sampling counterpart of the classical problem of estimating small probabilities in the species sampling framework, where each individual is endowed with only one feature (or "species"). In this paper we study the problem of consistent estimation of the small mass M-n,M-r. We first show that there do not exist universally consistent estimators, in the multiplicative sense, of the missing mass M-n,M-0. Then, we introduce an estimator of M-n,M-r and identify sufficient conditions under which the estimator is consistent. In particular, we propose a nonparametric estimator (M) over cap (n,r) of M-n,M-r which has the same analytic form of the celebrated Good-Turing estimator for small probabilities, with the sole difference that the two estimators have different ranges (supports). Then, we show that (M) over cap (n,r) is strongly consistent, in the multiplicative sense, under the assumption that (p(j))(j >= 1) has regularly varying heavy tails.

The present‐day tectonic setting of the Eastern Mediterranean Sea results from a long deformation history, characterized by an alternation of extensional and contractional phases: from Mesozoic rifting to Late Cretaceous-present-day compression. This study focused on the tectonic reconstruction of the north-eastern side of the Mediterranean Sea, on a sector located between the Turkish coast and the northern Levantine Basin, using seismic reflection profiles. Previous studies dealt with the recent (Neogene) evolution because they did not have enough depth of investigation to recognize deeper reflections. We used vintage data such as MS and Strakhov surveys to analyze the deeper part of the area. We interpreted and depth-converted these seismic data, and we developed a sequential restoration to reconstruct the stratigraphic and structural evolution of the study area. In general, from north to south, we recognize the Cilicia Basin: a piggy-back basin bordered to the south by the offshore continuation of the Kyrenia Range. The Kyrenia Range is a positive flower structure generated during a transpressional phase because of the rotation of the Arabic plate. Southward, a secondary contractional system with an onlapping wedge is present in the area between the Kyrenia Range and another prominent ridge, i.e. the Larnaca Ridge. In the southern part, the same transpressional phase that generated the Kyrenia Range led to a positive inversion of an ancient extensional system, i.e. the Latakia Ridge. Beyond these positive flowers, the Levantine Basin is affected by extensional structures showing weak positive reactivation, including halokinetic features. In summary, we found that the inherited extensional structures strongly impacted the following contractional ones affecting both their geometry and their kinematics.

While the cost of sequencing genomes has decreased dramatically in recent years, this expense often remains non-trivial. Under a fixed budget, then, scientists face a natural trade-off between quantity and quality; they can spend resources to sequence a greater number of genomes (quantity) or spend resources to sequence genomes with increased accuracy (quality). Our goal is to find the optimal allocation of resources between quantity and quality. Optimizing resource allocation promises to reveal as many new variations in the genome as possible, and thus as many new scientific insights as possible. In this paper, we consider the common setting where scientists have already conducted a pilot study to reveal variants in a genome and are contemplating a follow-up study. We introduce a Bayesian nonparametric methodology to predict the number of new variants in the follow-up study based on the pilot study. When experimental conditions are kept constant between the pilot and follow-up, we demonstrate on real data from the gnomAD project that our prediction is more accurate than three recent proposals, and competitive with a more classic proposal. Unlike existing methods, though, our method allows practitioners to change experimental conditions between the pilot and the follow-up. We demonstrate how this distinction allows our method to be used for (i) more realistic predictions and (ii) optimal allocation of a fixed budget between quality and quantity.

Protection against disclosure is a legal and ethical obligation for agencies releasing microdata files for public use. Consider a microdata sample of size $n$ from a finite population of size $\bar{n}=n+\lambda n$, with $\lambda>0$, such that each record contains two disjoint types of information: identifying categorical information and sensitive information. Any decision about releasing data is supported by the estimation of measures of disclosure risk, which are functionals of the number of sample records with a unique combination of values of identifying variables. The most common measure is arguably the number $\tau_{1}$ of sample unique records that are population uniques. In this paper, we first study nonparametric estimation of $\tau_{1}$ under the Poisson abundance model for sample records. We introduce a class of linear estimators of $\tau_{1}$ that are simple, computationally efficient and scalable to massive datasets, and we give uniform theoretical guarantees for them. In particular, we show that they provably estimate $\tau_{1}$ all of the way up to the sampling fraction $(\lambda+1)^{-1}\propto (\log n)^{-1}$, with vanishing normalized mean-square error (NMSE) for large $n$. We then establish a lower bound for the minimax NMSE for the estimation of $\tau_{1}$, which allows us to show that: i) $(\lambda+1)^{-1}\propto (\log n)^{-1}$ is the smallest possible sampling fraction; ii) estimators' NMSE is near optimal, in the sense of matching the minimax lower bound, for large $n$. This is the main result of our paper, and it provides a precise answer to an open question about the feasibility of nonparametric estimation of $\tau_{1}$ under the Poisson abundance model and for a sampling fraction $(\lambda+1)^{-1}

In the 1920s, the English philosopher W.E. Johnson introduced a characterization of the symmetric Dirichlet prior distribution in terms of its predictive distribution. This is typically referred to as Johnson’s “sufficientness” postulate, and it has been the subject of many contributions in Bayesian statistics, leading to predictive characterization for infinite-dimensional generalizations of the Dirichlet distribution, i.e., species-sampling models. In this paper, we review “sufficientness” postulates for species-sampling models, and then investigate analogous predictive characterizations for the more general feature-sampling models. In particular, we present a “sufficientness” postulate for a class of feature-sampling models referred to as Scaled Processes (SPs), and then discuss analogous characterizations in the general setup of feature-sampling models.

Salt tectonics at salt-bearing margins is often interpreted as the combination of gravity spreading and gravity gliding, mainly driven by differential sedimentary loading and margin tilting, respectively. Nevertheless, in the Western Mediterranean Sea, the classical salt-tectonic models are incoherent with its morpho-structural setting: Messinian salt was deposited in a closed system formed several Ma before the deposition, horizontally throughout the entire deep basin, above a homogenous multi-kilometer pre-Messinian thickness. The subsidence is purely vertical in the deep basin, implying a regional constant initial salt thickness. The post-salt overburden is homogenous and the distal salt deformation occurred before the mid-lower slope normal-fault activation. Instead, the compilation of MCS and wide-angle seismic data highlighted a clear coincidence between crustal segmentation and salt morphology domains. The salt structures change morphology at the boundary between different crustal natures. Regional thermal anomalies and/or fluid escapes, associated with the exhumation phase, or mantle-heat segmentation, could therefore play a role in adding a further component to the already known salt-tectonics mechanisms. The compilation of crustal segmentation and salt morphologies in different salt-bearing margins, such as the Santos, Angolan, Gulf of Mexico and Morocco-Nova Scotia margins, seems to depict the same coincidence. In view of the evidences observed in the Western Mediterranean Sea, the influence of the temperature parameter on salt deformation should not be overlooked and warrants further investigation.

The mean density estimation of a random closed set in $$\mathbb {R}^d$$ , based on a single observation, is a crucial problem in several application areas. In the case of stationary random sets, a common practice to estimate the mean density is to take the n-dimensional volume fraction with observation window as large as possible. In the present paper, we provide large and moderate deviation results for these estimators when the random closed set $$\Theta _n$$ belongs to the quite general class of stationary Boolean models with Hausdorff dimension $$n

Etant donne un echantillon de taille n dans une population d’individus appartenant a differents types dont les proportions sont inconnues, comment estimer la probabilite de decouvrir un nouveau type au (n+1)-ieme tirage ? C’est un probleme classique en statistique, souvent appele le probleme de l’estimation de la masse manquante. Des resultats recents on montre : (i) l’impossibilite d’estimer la masse manquante sans imposer des hypotheses sur les proportions des types ; (ii) la convergence de l’estimateur de la masse manquante de Good–Turing sous l’hypothese que la queue des proportions des types decroit vers 0 comme une fonction reguliere de parametre α∈(0,1) ; (iii) la vitesse de convergence n−α/2 pour l’estimateur de Good–Turing pour la classe de probabilites a variation reguliere α∈(0,1). Dans cet article, nous proposons une preuve alternative, et remarquablement plus courte, de l’impossibilite de l’estimation de la masse manquante sans hypothese sur la distribution. Au dela de son interet propre, cette preuve alternative suggere une approche naturelle pour ameliorer et etendre les resultats de vitesse de convergence de l’estimateur de Good–Turing sous l’hypothese de proportions a variation reguliere α∈(0,1). En particulier, nous montrons que la vitesse de convergence n−α/2 est la meilleure que peut atteindre un estimateur, a une fonction a variation bornee pres. De plus, nous montrons qu’une borne inferieure a l’estimation du risque minimax est au moins d’echelle n−α/2, ce qui amene a la conjecture que l’estimateur de Good–Turing est l’estimateur minimax de vitesse optimale sous une hypothese de proportions a variation reguliere.

Post randomization methods are among the most popular disclosure limitation techniques for both categorical and continuous data. In the categorical case, given a stochastic matrix M and a specified variable, an individual belonging to category i is changed to category j with probability $$M_{i,j}$$ M i , j . Every approach to choose the randomization matrix M has to balance between two desiderata: (1) preserving as much statistical information from the raw data as possible; (2) guaranteeing the privacy of individuals in the dataset. This trade-off has generally been shown to be very challenging to solve. In this work, we use recent tools from the computer science literature and propose to choose M as the solution of a constrained maximization problems. Specifically, M is chosen as the solution of a constrained maximization problem, where we maximize the mutual information between raw and transformed data, given the constraint that the transformation satisfies the notion of differential privacy. For the general categorical model, it is shown how this maximization problem reduces to a convex linear programming and can be therefore solved with known optimization algorithms.

The Barents Sea Ice Sheet was part of an interconnected complex of ice sheets, collectively referred to as the Eurasian Ice Sheet, which covered north-westernmost Europe, Russia and the Barents Sea during the Last Glacial Maximum (around 21 ky BP). Due to common geological features, the Barents Sea component of this ice complex is seen as a paleo-analogue for the present-day West Antarctic Ice Sheet. Investigating key processes driving the last deglaciation of the Barents Sea Ice Sheet represents an important tool to interpret recent observations in Antarctica over the multi-millennial temporal scale of glaciological changes. We present results from a perturbed physics ensemble of ice sheet model simulations of the last deglaciation of the Barents Sea Ice Sheet, forced with transient atmospheric and oceanic conditions derived from AOGCM simulations. The ensemble of transient simulations is evaluated against the data-based DATED-1 reconstruction to construct minimum, maximum and average deglaciation scenarios. Despite a large model/data mismatch at the western and eastern ice sheet margins, the simulated and DATED-1 deglaciation scenarios agree well on the timing of the deglaciation of the central and northern Barents Sea. We find that the simulated deglaciation of the Barents Sea Ice Sheet is primarily driven by the oceanic forcing, with prescribed eustatic sea level rise amplifying the ice sheet sensitivity to sub-shelf melting over relatively short intervals. Our results highlight that the sub-shelf melting has a very strong control on the simulated grounding-line flux, showing that a slow, gradual ocean warming trend is capable of triggering sustained grounded ice discharge over multi-millennial timescales, even without taking into account marine ice sheet or ice cliff instability.

In the present paper, we address the problem of prediction within the setting of species sampling models. We consider d populations composed of different species with unknown proportions. Our goal is to predict specific features of additional and unobserved samples from the d populations by adopting a Bayesian nonparametric model. We focus on a broad class of hierarchical priors. These were introduced and investigated in [1], where also an algorithm for drawing predictions is devised, however, without any specific numerical illustration. The aim of this paper is twofold: on the one hand, we provide an illustration with an actual implementation of the algorithm of [1] and, on the other hand, we discuss its relevance with respect to complex prediction problems with species sampling data.

The Barents Sea Ice Sheet was a marine-based ice sheet, i.e., it rested on the Barents Sea floor during the Last Glacial Maximum (21 ky BP). The Bjørnøyrenna Ice Stream was the largest ice stream draining the Barents Sea Ice Sheet and is regarded as an analogue for contemporary ice streams in West Antarctica. Here, the retreat of the Bjørnøyrenna Ice Stream is simulated by means of two numerical ice sheet models and results assessed against geological data. We investigate the sensitivity of the ice stream to changes in ocean temperature and the impact of grounding-line physics on ice stream retreat. Our results suggest that the role played by sub-shelf melting depends on how the grounding-line physics is represented in the models. When an analytic constraint on the ice flux across the grounding line is applied, the retreat of Bjørnøyrenna Ice Stream is primarily driven by internal ice dynamics rather than by oceanic forcing. This suggests that implementations of grounding-line physics need to be carefully assessed when evaluating and predicting the response of contemporary marine-based ice sheets and individual ice streams to ongoing and future ocean warming.

Documenting patterns of spatio-temporal change in hyper-diverse communities remains a challenge for tropical ecology, yet is increasingly urgent as some long-term studies have shown major declines in bird communities even in relatively undisturbed sites. In 1982, Terborgh et al. quantified the structure and organization of the bird community in a 97-ha. plot in southeastern Peru. We revisited the same plot in 2018 and repeated the same intense combination of methodologies as the original study in order to evaluate community-wide changes. Contrary to the results from studies elsewhere, we found little change in bird distribution and abundance within the plot, although there were some declines related to loss of mixed-species flocks with a high level of species interdependence. This apparent stability suggests that large-scale forest reserves such as Manu National Park may provide the conditions necessary for establishing refugia from at least some of the effects of global change on birds.