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After being trained on a fully-labeled training set, where the observations are grouped into a certain number of known classes, novelty detection methods aim to classify the instances of an unlabeled test set while allowing for the presence of previously unseen classes. These models are valuable in many areas, ranging from social network and food adulteration analyses to biology, where an evolving population may be present. In this paper, we focus on a two-stage Bayesian semiparametric novelty detector, also known as Brand, recently introduced in the literature. Leveraging on a model-based mixture representation, Brand allows clustering the test observations into known training terms or a single novelty term. Furthermore, the novelty term is modeled with a Dirichlet Process mixture model to flexibly capture any departure from the known patterns. Brand was originally estimated using MCMC schemes, which are prohibitively costly when applied to high-dimensional data. To scale up Brand applicability to large datasets, we propose to resort to a variational Bayes approach, providing an efficient algorithm for posterior approximation. We demonstrate a significant gain in efficiency and excellent classification performance with thorough simulation studies. Finally, to showcase its applicability, we perform a novelty detection analysis using the openly-available Statlog dataset, a large collection of satellite imaging spectra, to search for novel soil types.

In this paper we focus on identifying differentially activated brain regions using a light sheet fluorescence microscopy—a recently developed technique for whole-brain imaging. Most existing statistical methods solve this problem by partitioning the brain regions into two classes: significantly and nonsignificantly activated. However, for the brain imaging problem at the center of our study, such binary grouping may provide overly simplistic discoveries by filtering out weak but important signals that are typically adulterated by the noise present in the data. To overcome this limitation, we introduce a new Bayesian approach that allows classifying the brain regions into several tiers with varying degrees of relevance. Our approach is based on a combination of shrinkage priors, widely used in regression and multiple hypothesis testing problems, and mixture models, commonly used in model-based clustering. In contrast to the existing regularizing prior distributions, which use either the spike-and-slab prior or continuous scale mixtures, our class of priors is based on a discrete mixture of continuous scale mixtures and devises a cluster shrinkage version of the horseshoe prior. As a result, our approach provides a more general setting for Bayesian sparse estimation, drastically reduces the number of shrinkage parameters needed, and creates a framework for sharing information across units of interest. We show that this approach leads to more biologically meaningful and interpretable results in our brain imaging problem, since it allows the discrimination between active and inactive regions, while at the same time ranking the discoveries into clusters representing tiers of similar importance.

This article illustrates intRinsic, an R package that implements novel state-of-the-art likelihood-based estimators of the intrinsic dimension of a dataset, an essential quantity for most dimensionality reduction techniques. In order to make these novel estimators easily accessible, the package contains a small number of high-level functions that rely on a broader set of efficient, low-level routines. Generally speaking, intRinsic encompasses models that fall into two categories: homogeneous and heterogeneous intrinsic dimension estimators. The first category contains the two nearest neighbors estimator, a method derived from the distributional properties of the ratios of the distances between each data point and its first two closest neighbors. The functions dedicated to this method carry out inference under both the frequentist and Bayesian frameworks. In the second category, we find the heterogeneous intrinsic dimension algorithm, a Bayesian mixture model for which an efficient Gibbs sampler is implemented. After presenting the theoretical background, we demonstrate the performance of the models on simulated datasets. This way, we can facilitate the exposition by immediately assessing the validity of the results. Then, we employ the package to study the intrinsic dimension of the Alon dataset, obtained from a famous microarray experiment. Finally, we show how the estimation of homogeneous and heterogeneous intrinsic dimensions allows us to gain valuable insights into the topological structure of a dataset.

The analysis of large-scale datasets, especially in biomedical contexts, frequently involves a principled screening of multiple hypotheses. The celebrated two-group model jointly models the distribution of the test statistics with mixtures of two competing densities, the null and the alternative distributions. We investigate the use of weighted densities and, in particular, non-local densities as working alternative distributions, to enforce separation from the null and thus refine the screening procedure. We show how these weighted alternatives improve various operating characteristics, such as the Bayesian false discovery rate, of the resulting tests for a fixed mixture proportion with respect to a local, unweighted likelihood approach. Parametric and nonparametric model specifications are proposed, along with efficient samplers for posterior inference. By means of a simulation study, we exhibit how our model compares with both well-established and state-of-the-art alternatives in terms of various operating characteristics. Finally, to illustrate the versatility of our method, we conduct three differential expression analyses with publicly-available datasets from genomic studies of heterogeneous nature.

Previous studies have shown that the use of labels such as “organic” or “local” may improve the perceived healthiness, attractiveness and taste evaluation of healthy food products and increase their likelihood of being purchased. The aim of this work was to examine whether labeling vegetable items could promote consumption of at least one vegetable dish among students in a university canteen. We analyzed the purchasing of vegetable dishes among 458 students during an eight-week intervention in a university canteen, where vegetable items alternatively received neutral, organic and local labels. We implemented a multilevel Bayesian analysis to incorporate prior knowledge extracted from data preceding the experiment and to account for potential confounders related to the design of the experiment. Our results suggest that the labels “organic,” “local” “organic & local” were not strongly associated with ordering at least one vegetable plate. Additional studies are warranted to further investigate the potential impact of vegetable plate labeling on customers’ purchasing choices.

Following the introduction of high-resolution player tracking technology, a new range of statistical analysis has emerged in sports, specifically in basketball. However, such high-dimensional data are often challenging for statistical inference and decision making. In this article we employ a state-of-the-art Bayesian mixture model that allows the estimation of heterogeneous intrinsic dimension (ID) within a dataset, and we propose some theoretical enhancements. Informally, the ID can be seen as an indicator of complexity and dependence of the data at hand, and it is usually assumed unique. Our method provides the capacity to reveal valuable insights about the hidden dynamics of sports interactions in space and time which helps to translate complex patterns into more coherent statistics. The application of this technique is illustrated using NBA basketball players’ tracking data, allowing effective classification and clustering. In movement data the analysis identified key stages of offensive actions, such as creating space for passing, preparation/shooting, and following through which are relevant for invasion sports. We found that the ID value spikes, reaching a peak between four and eight seconds in the offensive part of the court, after which it declines. In shot charts we obtained groups of shots that produce substantially higher and lower successes. Overall, game-winners tend to have a larger intrinsic dimension, indicative of greater unpredictability and unique shot placements. Similarly, we found higher ID values in plays when the score margin is smaller rather than larger. The exploitation of these results can bring clear strategic advantages in sports games.

Modern datasets are characterized by numerous features related by complex dependency structures. To deal with these data, dimensionality reduction techniques are essential. Many of these techniques rely on the concept of intrinsic dimension (id), a measure of the complexity of the dataset. However, the estimation of this quantity is not trivial: often, the id depends rather dramatically on the scale of the distances among data points. At short distances, the id can be grossly overestimated due to the presence of noise, becoming smaller and approximately scale-independent only at large distances. An immediate approach to examining the scale dependence consists in decimating the dataset, which unavoidably induces non-negligible statistical errors at large scale. This article introduces a novel statistical method, Gride, that allows estimating the id as an explicit function of the scale without performing any decimation. Our approach is based on rigorous distributional results that enable the quantification of uncertainty of the estimates. Moreover, our method is simple and computationally efficient since it relies only on the distances among data points. Through simulation studies, we show that Gride is asymptotically unbiased, provides comparable estimates to other state-of-the-art methods, and is more robust to short-scale noise than other likelihood-based approaches.

Mass spectrometry methods can record biomolecule abundance for a broad set of molec- ular masses given a sample of a specific biological tissue. In particular, the MALDI-MSI technique produces imaging data where, for each pixel, a mass spectrum is recorded. There is the urge to rely on suited statistical methods to model these data, fully addressing their morphological characteristics. Here, we investigate the use of Bayesian mixture models to segment these real biomedical images. We aim to detect groups of pixels that present sim- ilar patterns to extract interesting insights, such as anomalies that one cannot capture from the original pictures. This task is particularly challenging given the high dimensionality of the data and the spatial correlation among pixels. To account for the spatial nature of the dataset, we rely on Hidden Markov Random Fields.

Online shopping has become increasingly common in recent years and has influenced how we form our preferences and choose the items to buy. This influence also applies to the books we read: other readers’ online reviews are one of the most used tools to determine the next book we will buy. The increasing use of e-commerce websites has also led to a large availability of data to study how the users’ ratings interact with other variables. Here, we consider a dataset of Amazon’s best-selling books in the period 2009-2019. In particular, we study the similarities of the distributions of ratings and prices across different years. To fully capture the complexity of the observed data, we make use of flexible Bayesian nested mixture models to simultaneously avoid strict parametric assumptions and study the clustering structure of observations and years.

The notion of identifiability has a long history in the statistical literature, with econo- metrics providing the first theoretical contributions. On the one hand, within the frequentist paradigm, identifiability represents a critical issue to tackle, closely tied to the feasibility of the model estimation. On the other hand, identifiability issues in the Bayesian frame- work could be overcome by complementing the non-identifiable likelihood with additional prior beliefs summarized via an informative prior distribution. Unfortunately, since esti- mation is still feasible, unidentifiabily may remain unnoticed and silently hinder posterior consistency. This contribution provides a tool to inspect whether the model specification is weakly identified. Our procedure is based on estimating the intrinsic dimension of posterior samples. The methodology is illustrated with a simulated example.

The intrinsic dimension (id) of a dataset conveys essential information regarding the complexity of the underlying data-generating process. In particular, it describes the di- mensionality of the latent manifold on which the data-generating probability distribution has support. Complex datasets may be characterized by multiple manifolds having differ- ent ids. To properly estimate these heterogeneous ids, a recent modeling approach uses finite scale mixtures of Pareto distributions aided by a homogeneity-inducing term in the likelihood. In this contribution, we explore a different modeling perspective, estimating Pareto’s scale mixtures via spatial product partition models. We present the general idea and introduce Spider, our Bayesian nonparametric approach. Finally, we showcase some encouraging preliminary results.

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.

The simultaneous testing of multiple hypotheses is common to the analysis of high-dimensional data sets. The two-group model, first proposed by Efron, identifies significant comparisons by allocating observations to a mixture of an empirical null and an alternative distribution. In the Bayesian nonparametrics literature, many approaches have suggested using mixtures of Dirichlet Processes in the two-group model framework. Here, we investigate employing mixtures of two-parameter Poisson-Dirichlet Processes instead, and show how they provide a more flexible and effective tool for large-scale hypothesis testing. Our model further employs nonlocal prior densities to allow separation between the two mixture components. We obtain a closed-form expression for the exchangeable partition probability function of the two-group model, which leads to a straightforward Markov Chain Monte Carlo implementation. We compare the performance of our method for large-scale inference in a simulation study and illustrate its use on both a prostate cancer data set and a case-control microbiome study of the gastrointestinal tracts in children from underdeveloped countries who have been recently diagnosed with moderate-to-severe diarrhea.

A novelty detection model can be seen as a supervised classifier, trained on a fully- labeled training set, that allows for the presence of new classes in the test set not previously observed among the training units. When dealing with functional data, this requires learning the main patterns for the curves in the known classes, whilst being able to isolate signals that possess distinctive characteristics in the unlabeled set. In order to tackle this challenging problem, we propose a two-stage Bayesian semi-parametric novelty detector [2]. In the first stage, robust estimates are extracted from the training set via the Minimum Regularized Covariance Determinant (MRCD) estimator [1]. In the second stage, such information is employed to elicit informative priors within a Bayesian mixture of known groups plus a novelty term. To reflect the lack of knowledge on the latter component, we resort to a Dirichlet Process mixture model, thus overcoming the problematic a-priori specification of the expected number of novelties that may be present in the test set. The described methodology is applied to a spectroscopic dataset within a food authenticity study.

Partially exchangeable datasets are characterized by observations grouped into known, heterogeneous units. The recently developed Common Atoms Model (CAM) is a Bayesian nonparametric technique suited for analyzing this type of data. CAM induces a two-layered clustering structure: one across observations and another across units. In particular, the units are clustered according to their distributional similarities. In this article, we illustrate the versatility of CAM with an application to an openly available Spotify dataset. The dataset contains quantitative audio features for a large number of songs grouped by artists. After describing the data preprocessing steps, we employ CAM to group the Spotify artists according to the distributions of the energy of their songs.

Following the introduction of high-resolution player tracking technology, a new range of statistical analysis has emerged in sports, specifically in basketball. However, such high-dimensional data are often challenging for statistical inference and decision making. In this article we employ a state-of-the-art Bayesian mixture model that allows the estimation of heterogeneous intrinsic dimension (ID) within a dataset, and we propose some theoretical enhancements. Informally, the ID can be seen as an indicator of complexity and dependence of the data at hand, and it is usually assumed unique. Our method provides the capacity to reveal valuable insights about the hidden dynamics of sports interactions in space and time which helps to translate complex patterns into more coherent statistics. The application of this technique is illustrated using NBA basketball players’ tracking data, allowing effective classification and clustering. In movement data the analysis identified key stages of offensive actions, such as creating space for passing, preparation/shooting, and following through which are relevant for invasion sports. We found that the ID value spikes, reaching a peak between four and eight seconds in the offensive part of the court, after which it declines. In shot charts we obtained groups of shots that produce substantially higher and lower successes. Overall, game-winners tend to have a larger intrinsic dimension, indicative of greater unpredictability and unique shot placements. Similarly, we found higher ID values in plays when the score margin is smaller rather than larger. The exploitation of these results can bring clear strategic advantages in sports games.

Previous studies have shown that the use of labels such as “organic” or “local” may improve the perceived healthiness, attractiveness and taste evaluation of healthy food products and increase their likelihood of being purchased. The aim of this work was to examine whether labeling vegetable items could promote consumption of at least one vegetable dish among students in a university canteen. We analyzed the purchasing of vegetable dishes among 458 students during an eight-week intervention in a university canteen, where vegetable items alternatively received neutral, organic and local labels. We implemented a multilevel Bayesian analysis to incorporate prior knowledge extracted from data preceding the experiment and to account for potential confounders related to the design of the experiment. Our results suggest that the labels “organic,” “local” “organic & local” were not strongly associated with ordering at least one vegetable plate. Additional studies are warranted to further investigate the potential impact of vegetable plate labeling on customers’ purchasing choices.

One of the founding paradigms of machine learning is that a small number of variables is often sufficient to describe high-dimensional data. The minimum number of variables required is called the intrinsic dimension (ID) of the data. Contrary to common intuition, there are cases where the ID varies within the same data set. This fact has been highlighted in technical discussions, but seldom exploited to analyze large data sets and obtain insight into their structure. Here we develop a robust approach to discriminate regions with different local IDs and segment the points accordingly. Our approach is computationally efficient and can be proficiently used even on large data sets. We find that many real-world data sets contain regions with widely heterogeneous dimensions. These regions host points differing in core properties: folded versus unfolded configurations in a protein molecular dynamics trajectory, active versus non-active regions in brain imaging data, and firms with different financial risk in company balance sheets. A simple topological feature, the local ID, is thus sufficient to achieve an unsupervised segmentation of high-dimensional data, complementary to the one given by clustering algorithms.

The simultaneous testing of multiple hypotheses is common to the analysis of high-dimensional data sets. The two-group model, first proposed by Efron, identifies significant comparisons by allocating observations to a mixture of an empirical null and an alternative distribution. In the Bayesian nonparametrics literature, many approaches have suggested using mixtures of Dirichlet Processes in the two-group model framework. Here, we investigate employing mixtures of two-parameter Poisson-Dirichlet Processes instead, and show how they provide a more flexible and effective tool for large-scale hypothesis testing. Our model further employs nonlocal prior densities to allow separation between the two mixture components. We obtain a closed-form expression for the exchangeable partition probability function of the two-group model, which leads to a straightforward Markov Chain Monte Carlo implementation. We compare the performance of our method for large-scale inference in a simulation study and illustrate its use on both a prostate cancer data set and a case-control microbiome study of the gastrointestinal tracts in children from underdeveloped countries who have been recently diagnosed with moderate-to-severe diarrhea.

Given a sample of unlabeled observations, the goal of a novelty detection method is to identify which units substantially deviate from the observed labeled patterns. Therefore, in a model-based framework, it is firstly of paramount importance to learn the components that correspond to the manifest groups in the training set. Secondly, one needs to take into account the lack of knowledge regarding the statistical novelties. Thirdly, contaminated elements in the known classes could greatly jeopardize the identification of new groups. Motivated by these challenges, we propose a two-stage Bayesian non-parametric novelty detector. At stage one, robust estimates are extracted from the training set and, subsequently, such information is employed to elicit informative priors within a flexible semiparametric mixture. This general paradigm can be easily adapted to complex modeling frameworks: we provide here an application to functional data from a food authenticity study.

In a standard classification framework, a discriminating rule is usually built from a trustworthy set of labeled units. In this context, test observations will be automatically classified as to have arisen from one of the known groups encountered in the training set, without the possibility of detecting previously unseen classes. To overcome this limitation, an adaptive semi-parametric Bayesian classifier is introduced for modeling the test units, where robust knowledge is extracted from the training set and incorporated within the priors’ model specification. A successful application of the proposed approach in a real-world problem is addressed.

I modelli mistura bayesiani sono onnipresenti in statistica per la loro semplicità e flessibilità e possono essere facilmente impiegati in un'ampia varietà di contesti. In questa tesi, miriamo a fornire alcuni contributi agli attuali metodi bayesiani di analisi dei dati, spesso motivati ​​da domande di ricerca provenienti da applicazioni biologiche. In particolare, ci concentriamo sullo sviluppo di nuovi modelli mistura bayesiani, tipicamente in un ambiente non parametrico, per migliorare ed estendere aree di ricerca che coinvolgono dati caratterizzati da grande dimensioni: la modellazione di dati nested, test di ipotesi simultaneo e la riduzione della dimensionalità. \\ Pertanto, il nostro obiettivo è duplice: sviluppare metodi statistici robusti motivati da un solido background teorico e proporre algoritmi efficienti, scalabili e trattabili per le loro applicazioni. \\ La tesi è organizzata come segue. Nel capitolo 1 esamineremo brevemente il background metodologico e discuteremo i concetti necessari che appartengono alle diverse aree a cui contribuiremo con questa tesi. \\ Nel capitolo 2 proponiamo un modello di atomi comuni (CAM) per nested data, che supera le limitazioni del processo del nested Dirichlet Process, come discusso in \ citep {Camerlenghi2018}. Deriviamo le sue proprietà teoriche e sviluppiamo uno slice sampler per dati nested al fine di ottenere un algoritmo efficiente per la simulazione della posterior. Abbiamo poi incorporato il modello in un framework di Rounded mixture of Gaussian Kernels, così da applicare il nostro metodo a una abundance table derivante da uno studio di microbioma. \\ Nel capitolo \ref {BNPT} sviluppiamo una versione BNP del two-group model, modellando sia $ f_0 $ che $ f_1 $ con Pitman-Yor mixtures models. Proponiamo di fissare i due parametri $ \sigma_0 $ e $ \sigma_1 $ in modo che $ \sigma_0> \sigma_1 $, in base alla logica secondo cui il PY che modella la distribuzione nulla dovrebbe essere più vicino alla sua mi, Bayesian mixture models are ubiquitous in statistics due to their simplicity and flexibility and can be easily employed in a wide variety of contexts. In this dissertation, we aim at providing a few contributions to current Bayesian data analysis methods, often motivated by research questions from biological applications. In particular, we focus on the development of novel Bayesian mixture models, typically in a nonparametric setting, to improve and extend active research areas that involve large-scale data: the modeling of nested data, multiple hypothesis testing, and dimensionality reduction.\\ Therefore, our goal is twofold: to develop robust statistical methods motivated by a solid theoretical background, and to propose efficient, scalable and tractable algorithms for their applications.\\ The thesis is organized as follows. In Chapter \ref{intro} we shortly review the methodological background and discuss the necessary concepts that belong to the different areas that we will contribute to with this dissertation. \\ In Chapter \ref{CAM} we propose a Common Atoms model (CAM) for nested datasets, which overcomes the limitations of the nested Dirichlet Process, as discussed in \citep{Camerlenghi2018}. We derive its theoretical properties and develop a slice sampler for nested data to obtain an efficient algorithm for posterior simulation. We then embed the model in a Rounded Mixture of Gaussian kernels framework to apply our method to an abundance table from a microbiome study.\\ In Chapter \ref{BNPT} we develop a BNP version of the two-group model \citep{Efron2004}, modeling both the null density $f_0$ and the alternative density $f_1$ with Pitman-Yor process mixture models. We propose to fix the two discount parameters $\sigma_0$ and $\sigma_1$ so that $\sigma_0>\sigma_1$, according to the rationale that the null PY should be closer to its base measure (appropriately chosen to be a standard Gaussian base measure), while the alternative PY should have fewer constr

One of the founding paradigms of machine learning is that a small number of variables is often sufficient to describe high-dimensional data. The minimum number of variables required is called the intrinsic dimension (ID) of the data. Contrary to common intuition, there are cases where the ID varies within the same data set. This fact has been highlighted in technical discussions, but seldom exploited to analyze large data sets and obtain insight into their structure. Here we develop a robust approach to discriminate regions with different local IDs and segment the points accordingly. Our approach is computationally efficient and can be proficiently used even on large data sets. We find that many real-world data sets contain regions with widely heterogeneous dimensions. These regions host points differing in core properties: folded versus unfolded configurations in a protein molecular dynamics trajectory, active versus non-active regions in brain imaging data, and firms with different financial risk in company balance sheets. A simple topological feature, the local ID, is thus sufficient to achieve an unsupervised segmentation of high-dimensional data, complementary to the one given by clustering algorithms.

Survey methodologists confront complicated choices regarding survey design since they want to ensure high participation rates and quality data in a relatively short period of time. Indeed, declining participation rates and inadequate data quality are serious problems in the field of surveys, particularly if they are ad-ministered via the Internet. This paper shows whether a shortened questionnaire and SMS/e-mail reminders maximize response rates and data quality. Our email survey is targeted at students registered in degree courses at the University of Milan Bicocca. It is an experiment, assessing the effects of different combinations of reminders and var-ious questionnaire lengths on participation, accuracy of filling out the questionnaire and overall response time.

Objectives The main purpose of this study was to describe the relationship between patellar maximal craniocaudal thickness and femoral trochlear groove depth in normal dogs and to valuate the intra-observer or inter-observer variability of maximal trochlear depth and maximal patellar craniocaudal thickness using computed tomography. Methods Trochlear groove depth and patellar maximal craniocaudal thickness of 40 limbs (20 dogs) were measured by three independent veterinarians using three-dimensional multiplanar reconstruction computed tomography images. The patellar maximal craniocaudal thickness/trochlear depth ratio was determined. Results The mean ratio of these stifles was 0.46 (range 0.24-0.70), meaning that the mean maximal depth of the trochlea was 46% of the mean maximal-patellar thickness. Clinical Significance A wide range of maximal-patellar-craniocaudal-thickness/maximal trochlear-depth ratio was found suggesting that breed studies should be performed to determine a breed-specific patellar-thickness/trochlear-depth ratio. To make decisions on when and where to perform a sulcoplasty during patellar luxation surgery, patella/trochlea thickness relationship should be measured for each breed with patellar tracking from stifle hyperflexion to stifle hyperextension.

Objectives The main purpose of this study was to describe the relationship between patellar maximal craniocaudal thickness and femoral trochlear groove depth in normal dogs and to valuate the intra-observer or inter-observer variability of maximal trochlear depth and maximal patellar craniocaudal thickness using computed tomography. Methods Trochlear groove depth and patellar maximal craniocaudal thickness of 40 limbs (20 dogs) were measured by three independent veterinarians using three-dimensional multiplanar reconstruction computed tomography images. The patellar maximal craniocaudal thickness/trochlear depth ratio was determined. Results The mean ratio of these stifles was 0.46 (range 0.24-0.70), meaning that the mean maximal depth of the trochlea was 46% of the mean maximal-patellar thickness. Clinical Significance A wide range of maximal-patellar-craniocaudal-thickness/maximal trochlear-depth ratio was found suggesting that breed studies should be performed to determine a breed-specific patellar-thickness/trochlear-depth ratio. To make decisions on when and where to perform a sulcoplasty during patellar luxation surgery, patella/trochlea thickness relationship should be measured for each breed with patellar tracking from stifle hyperflexion to stifle hyperextension.

In recent years, state of the art brain imaging techniques like Functional Magnetic Resonance Imaging (fMRI), have raised new challenges to the statistical community, which is asked to provide new frameworks for modeling and data analysis. Here, motivated by resting state fMRI data, which can be seen as a collection of spatially dependent functional observations among brain regions, we propose a parsimonious but flexible representation of their dependence structure leveraging a Bayesian time-dependent latent factor model. Adopting an assumption of separability of the covariance structure in space and time, we are able to substantially reduce the computational cost and, at the same time, provide interpretable results. Theoretical properties of the model along with identifiability conditions are discussed. For model fitting, we propose a mcmc algorithm to enable posterior inference. We illustrate our work through an application to a dataset coming from the enkirs project, discussing the estimated covariance structure and also performing model selection along with network analysis. Our modeling is preliminary but offers ideas for developing fully Bayesian fMRI models, incorporating a plausible space and time dependence structure.

In recent years, state of the art brain imaging techniques like Functional Magnetic Resonance Imaging (fMRI), have raised new challenges to the statistical community, which is asked to provide new frameworks for modeling and data analysis. Here, motivated by resting state fMRI data, which can be seen as a collection of spatially dependent functional observations among brain regions, we propose a parsimonious but flexible representation of their dependence structure leveraging a Bayesian time-dependent latent factor model. Adopting an assumption of separability of the covariance structure in space and time, we are able to substantially reduce the computational cost and, at the same time, provide interpretable results. Theoretical properties of the model along with identifiability conditions are discussed. For model fitting, we propose a mcmc algorithm to enable posterior inference. We illustrate our work through an application to a dataset coming from the enkirs project, discussing the estimated covariance structure and also performing model selection along with network analysis. Our modeling is preliminary but offers ideas for developing fully Bayesian fMRI models, incorporating a plausible space and time dependence structure.

In questo articolo, si utilizzano i dati dell’Anagrafe Studenti predisposta dal MIUR per analizzare le tendenze nelle iscrizioni e nel numero di laureati dei corsi di laurea in Sociologia, in Italia. L’analisi mostra che, tra il 2003/04 e il 2011/12, nei corsi di laurea triennali, si è avuta una consistente contrazione delle matricole, molto più marcata di quella registrata dall’università italiana nel suo complesso. Se si considera la composizione dei nuovi ingressi, si nota che la Sociologia attrae una quota considerevolmente elevata di donne, di soggetti meno giovani e di studenti meno brillanti (limitato numero di liceali, voti di maturità mediamente più bassi) e che questa tendenza è peggiorata nel tempo. D’altro canto, si è verificato un aumento nelle immatricolazioni e nel numero di laureati per i corsi di laurea magistrali. Ciò sembra connesso all’introduzione di nuovi corsi e ad accordi speciali tra alcune università ed autorità/enti locali, piuttosto che all’aumentata efficacia delle carriere degli studenti. L’analisi è accompagnata da un esame dell’eterogeneità dei modelli che caratterizzano i corsi di laurea in Sociologia.