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This study addresses the challenge of classifying cell shapes from noisy contours, such as those obtained through cell instance segmentation of histological images. We assess the performance of various features for shape classification, including Elliptical Fourier Descriptors, curvature features, and lower dimensional representations. Using an annotated synthetic dataset of noisy contours, we identify the most suitable shape descriptors and apply them to a set of real images for qualitative analysis. Our aim is to provide a comprehensive evaluation of descriptors for classifying cell shapes, which can support cell type identification and tissue characterization-critical tasks in both biological research and histopathological assessments.

Conformal inference is a method that provides prediction sets for machine learning models, operating independently of the underlying distributional assumptions and relying solely on the exchangeability of training and test data. Despite its wide applicability and popularity, its application in graph-structured problems remains underexplored. This paper addresses this gap by developing an approach that leverages the rich information encoded in the graph structure of predicted classes to enhance the interpretability of conformal sets. Using a motivating example from genomics, specifically imaging-based spatial transcriptomics data and single-cell RNA sequencing data, we demonstrate how incorporating graph-structured constraints can improve the interpretation of cell type predictions. This approach aims to generate more coherent conformal sets that align with the inherent relationships among classes, facilitating clearer and more intuitive interpretations of model predictions. Additionally, we provide a technique to address non-exchangeability, particularly when the distribution of the response variable changes between training and test datasets. We implemented our method in the open-source R package scConform, available at https://github.com/ccb-hms/scConform.

Delineating and classifying individual cells in microscopy tissue images is a complex task, yet it is a pivotal endeavor in various medical and biological investigations. We propose a new deep learning framework (CISCA) for automatic cell instance segmentation and classification in histological slices to support detailed morphological and structural analysis or straightforward cell counting in digital pathology workflows and brain cytoarchitecture studies. At the core of CISCA lies a network architecture featuring a lightweight U-Net with three heads in the decoder. The first head classifies pixels into boundaries between neighboring cells, cell bodies, and background, while the second head regresses four distance maps along four directions. The network outputs from the first and second heads are integrated through a tailored post-processing step, which ultimately yields the segmentation of individual cells. A third head enables simultaneous classification of cells into relevant classes, if required. We showcase the effectiveness of our method using four datasets, including CoNIC, PanNuke, and MoNuSeg, which are publicly available H\&E datasets. Additionally, we introduce CytoDArk0, a novel dataset consisting of Nissl-stained images of the cortex, cerebellum, and hippocampus from mammals belonging to the orders Cetartiodactyla and Primates. We evaluate CISCA in comparison to other state-of-the-art methods, demonstrating CISCA's robustness and accuracy in segmenting and classifying cells across diverse tissue types, magnifications, and staining techniques.

In many applied sciences a popular analysis strategy for high-dimensional data is to fit many multivariate generalized linear models in parallel. This paper presents a novel approach to address the resulting multiple testing problem by combining a recently developed sign-flip test with permutation-based multiple-testing procedures. Our method builds upon the univariate standardized flip-scores test which offers robustness against misspecified variances in generalized linear models, a crucial feature in high-dimensional settings where comprehensive model validation is particularly challenging. We extend this approach to the multivariate setting, enabling adaptation to unknown response correlation structures. This approach yields relevant power improvements over conventional multiple testing methods when correlation is present.

Despite the versatility of generalized linear mixed models in handling complex experimental designs, they often suffer from misspecification and convergence problems. This makes inference on the values of coefficients problematic. To address these challenges, we propose a robust extension of the score-based statistical test using sign-flipping transformations. Our approach efficiently handles within-variance structure and heteroscedasticity, ensuring accurate regression coefficient testing. The approach is illustrated by analyzing the reduction of health issues over time for newly adopted children. The model is characterized by a binomial response with unbalanced frequencies and several categorical and continuous predictors. The proposed approach efficiently deals with critical problems related to longitudinal nonlinear models, surpassing common statistical approaches such as generalized estimating equations and generalized linear mixed models.

Aberrant respondents are common but yet extremely detrimental to the quality of social surveys or questionnaires. Recently, factor mixture models have been employed to identify individuals providing deceptive or careless responses. We propose a comprehensive factor mixture model for continuous outcomes that combines confirmatory and exploratory factor models to classify both the non-aberrant and aberrant respondents. The flexibility of the proposed {classification model} allows for the identification of two of the most common aberrant response styles, namely faking and careless responding. We validated our approach by means of two simulations and two case studies. The results indicate the effectiveness of the proposed model in dealing with aberrant responses in social and behavioural surveys., Comment: 25 pages, 5 figures, 7 tables. Supplementary materials are available at https://github.com/niccolocao/CFAmixEFA

Deep learning has proven to be more effective than other methods in medical image analysis, including the seemingly simple but challenging task of segmenting individual cells, an essential step for many biological studies. Comparative neuroanatomy studies are an example where the instance segmentation of neuronal cells is crucial for cytoarchitecture characterization. This paper presents an end-to-end framework to automatically segment single neuronal cells in Nissl-stained histological images of the brain, thus aiming to enable solid morphological and structural analyses for the investigation of changes in the brain cytoarchitecture. A U-Net-like architecture with an EfficientNet as the encoder and two decoding branches is exploited to regress four color gradient maps and classify pixels into contours between touching cells, cell bodies, or background. The decoding branches are connected through attention gates to share relevant features, and their outputs are combined to return the instance segmentation of the cells. The method was tested on images of the cerebral cortex and cerebellum, outperforming other recent deep-learning-based approaches for the instance segmentation of cells.

The statistical shape analysis called Procrustes analysis minimizes the distance between matrices by similarity transformations. The method returns a set of optimal orthogonal matrices, which project each matrix into a common space. This manuscript presents two types of distances derived from Procrustes analysis for exploring between-matrices similarity. The first one focuses on the residuals from the Procrustes analysis, i.e., the residual-based distance metric. In contrast, the second one exploits the fitted orthogonal matrices, i.e., the rotational-based distance metric. Thanks to these distances, similarity-based techniques such as the multidimensional scaling method can be applied to visualize and explore patterns and similarities among observations. The proposed distances result in being helpful in functional magnetic resonance imaging (fMRI) data analysis. The brain activation measured over space and time can be represented by a matrix. The proposed distances applied to a sample of subjects -- i.e., matrices -- revealed groups of individuals sharing patterns of neural brain activation.

In comparative neuroanatomy, the characterization of brain cytoarchitecture is critical to a better understanding of brain structure and function, as it helps to distill information on the development, evolution, and distinctive features of different populations. The automatic segmentation of individual brain cells is a primary prerequisite and yet remains challenging. A new method (MR-NOM) was developed for the instance segmentation of cells in Nissl-stained histological images of the brain. MR-NOM exploits a multi-scale approach to deliberately over-segment the cells into superpixels and subsequently merge them via a classifier based on shape, structure, and intensity features. The method was tested on images of the cerebral cortex, proving successful in dealing with cells of varying characteristics that partially touch or overlap, showing better performance than two state-of-the-art methods.

When analyzing data researchers make some decisions that are either arbitrary, based on subjective beliefs about the data generating process, or for which equally justifiable alternative choices could have been made. This wide range of data-analytic choices can be abused, and has been one of the underlying causes of the replication crisis in several fields. Recently, the introduction of multiverse analysis provides researchers with a method to evaluate the stability of the results across reasonable choices that could be made when analyzing data. Multiverse analysis is confined to a descriptive role, lacking a proper and comprehensive inferential procedure. Recently, specification curve analysis adds an inferential procedure to multiverse analysis, but this approach is limited to simple cases related to the linear model, and only allows researchers to infer whether at least one specification rejects the null hypothesis, but not which specifications should be selected. In this paper we present a Post-selection Inference approach to Multiverse Analysis (PIMA) which is a flexible and general inferential approach that accounts for all possible models, i.e., the multiverse of reasonable analyses. The approach allows for a wide range of data specifications (i.e. pre-processing) and any generalized linear model; it allows testing the null hypothesis of a given predictor not being associated with the outcome, by merging information from all reasonable models of multiverse analysis, and provides strong control of the family-wise error rate such that it allows researchers to claim that the null-hypothesis can be rejected for each specification that shows a significant effect. The inferential proposal is based on a conditional resampling procedure. To be continued..., Comment: 37 pages, 2 figures

Generalized linear models usually assume a common dispersion parameter, an assumption that is seldom true in practice. Consequently, standard parametric methods may suffer appreciable loss of type I error control. As an alternative, we present a semi-parametric group-invariance method based on sign flipping of score contributions. Our method requires only the correct specification of the mean model, but is robust against any misspecification of the variance. We present tests for single as well as multiple regression coefficients. The test is asymptotically valid but shows excellent performance in small samples. We illustrate the method using RNA sequencing count data, for which it is difficult to model the overdispersion correctly. The method is available in the R library flipscores.

Functional alignment between subjects is an important assumption of functional magnetic resonance imaging (fMRI) group-level analysis. However, it is often violated in practice, even after alignment to a standard anatomical template. Hyperalignment, based on sequential Procrustes orthogonal transformations, has been proposed as a method of aligning shared functional information into a common high-dimensional space and thereby improving inter-subject analysis. Though successful, current hyperalignment algorithms have a number of shortcomings, including difficulties interpreting the transformations, a lack of uniqueness of the procedure, and difficulties performing whole-brain analysis. To resolve these issues, we propose the ProMises (Procrustes von Mises-Fisher) model. We reformulate functional alignment as a statistical model and impose a prior distribution on the orthogonal parameters (the von Mises-Fisher distribution). This allows for the embedding of anatomical information into the estimation procedure by penalizing the contribution of spatially distant voxels when creating the shared functional high-dimensional space. Importantly, the transformations, aligned images, and related results are all unique. In addition, the proposed method allows for efficient whole-brain functional alignment. In simulations and application to data from four fMRI studies we find that ProMises improves inter-subject classification in terms of between-subject accuracy and interpretability compared to standard hyperalignment algorithms., Comment: 28 pages, 9 figures

We propose a novel resampling-based method to construct an asymptotically exact test for any subset of hypotheses on coefficients in high-dimensional linear regression. It can be embedded into any multiple testing procedure to make confidence statements on relevant predictor variables. The method constructs permutation test statistics for any individual hypothesis by means of repeated splits of the data and a variable selection technique; then it defines a test for any subset by suitably aggregating its variables' test statistics. The resulting procedure is extremely flexible, as it allows different selection techniques and several combining functions. We present it in two ways: an exact method and an approximate one, that requires less memory usage and shorter computation time, and can be scaled up to higher dimensions. We illustrate the performance of the method with simulations and the analysis of real gene expression data., Comment: 31 pages (16 pages main, 15 pages appendix), 12 figures

Between the years 2015 and 2019, members of the Horizon 2020-funded Innovative Training Network named "AMVA4NewPhysics" studied the customization and application of advanced multivariate analysis methods and statistical learning tools to high-energy physics problems, as well as developed entirely new ones. Many of those methods were successfully used to improve the sensitivity of data analyses performed by the ATLAS and CMS experiments at the CERN Large Hadron Collider; several others, still in the testing phase, promise to further improve the precision of measurements of fundamental physics parameters and the reach of searches for new phenomena. In this paper, the most relevant new tools, among those studied and developed, are presented along with the evaluation of their performances., Comment: 101 pages, 21 figures, submitted to Elsevier. [v2]: Updated to published version (in 'Reviews in Physics')

Sum-based global tests are highly popular in multiple hypothesis testing. In this paper we propose a general closed testing procedure for sum tests, which provides lower confidence bounds for the proportion of true discoveries (TDP), simultaneously over all subsets of hypotheses. These simultaneous inferences come for free, i.e., without any adjustment of the alpha-level, whenever a global test is used. Our method allows for an exploratory approach, as simultaneity ensures control of the TDP even when the subset of interest is selected post hoc. It adapts to the unknown joint distribution of the data through permutation testing. Any sum test may be employed, depending on the desired power properties. We present an iterative shortcut for the closed testing procedure, based on the branch and bound algorithm, which converges to the full closed testing results, often after few iterations; even if it is stopped early, it controls the TDP. We compare the properties of different choices for the sum test through simulations, then we illustrate the feasibility of the method for high dimensional data on brain imaging and genomics data., Comment: Main: 27 pages, 3 figures. Appendices: 19 pages, 7 figures

We propose a permutation-based method for testing a large collection of hypotheses simultaneously. Our method provides lower bounds for the number of true discoveries in any selected subset of hypotheses. These bounds are simultaneously valid with high confidence. The methodology is particularly useful in functional Magnetic Resonance Imaging cluster analysis, where it provides a confidence statement on the percentage of truly activated voxels within clusters of voxels, avoiding the well-known spatial specificity paradox. We offer a user-friendly tool to estimate the percentage of true discoveries for each cluster while controlling the family-wise error rate for multiple testing and taking into account that the cluster was chosen in a data-driven way. The method adapts to the spatial correlation structure that characterizes functional Magnetic Resonance Imaging data, gaining power over parametric approaches.

The Procrustes-based perturbation model (Goodall, 1991) allows minimization of the Frobenius distance between matrices by similarity transformation. However, it suffers from non-identifiability, critical interpretation of the transformed matrices, and inapplicability in high-dimensional data. We provide an extension of the perturbation model focused on the high-dimensional data framework, called the ProMises (Procrustes von Mises-Fisher) model. The ill-posed and interpretability problems are solved by imposing a proper prior distribution for the orthogonal matrix parameter (i.e., the von Mises-Fisher distribution) which is a conjugate prior, resulting in a fast estimation process. Furthermore, we present the Efficient ProMises model for the high-dimensional framework, useful in neuroimaging, where the problem has much more than three dimensions. We found a great improvement in functional magnetic resonance imaging (fMRI) connectivity analysis because the ProMises model permits incorporation of topological brain information in the alignment's estimation process., Comment: 22 pages, 7 figures

Permutation testing in linear models, where the number of nuisance coefficients is smaller than the sample size, is a well-studied topic. The common approach of such tests is to permute residuals after regressing on the nuisance covariates. Permutation-based tests are valuable in particular because they can be highly robust to violations of the standard linear model, such as non-normality and heteroscedasticity. Moreover, in some cases they can be combined with existing, powerful permutation-based multiple testing methods. Here, we propose permutation tests for models where the number of nuisance coefficients exceeds the sample size. The performance of the novel tests is investigated with simulations. In a wide range of simulation scenarios our proposed permutation methods provided appropriate type I error rate control, unlike some competing tests, while having good power., Comment: Accepted for publication in Journal of Statistical Computation and Simulation

The massive diffusion of social media fosters disintermediation and changes the way users are informed, the way they process reality, and the way they engage in public debate. The cognitive layer of users and the related social dynamics define the nature and the dimension of informational threats. Users show the tendency to interact with information adhering to their preferred narrative and to ignore dissenting information. Confirmation bias seems to account for users decisions about consuming and spreading content; and, at the same time, aggregation of favored information within those communities reinforces group polarization. In this work, the authors address the problem of (mis)information operations with a holistic and integrated approach. Cognitive weakness induced by this new information environment are considered. Moreover, (mis)information operations, with particular reference to the Italian context, are considered; and the fact that the phenomenon is more complex than expected is highlighted. The paper concludes by providing an integrated research roadmap accounting for the possible future technological developments., Comment: The paper first appeared in Volume 18, Issue 3 of the Journal of Information Warfare

In the past two decades, psychological science has experienced an unprecedented replicability crisis which uncovered several issues. Among others, statistical inference is too often viewed as an isolated procedure limited to the analysis of data that have already been collected. We build on and further develop an idea proposed by Gelman and Carlin (2014) termed "prospective and retrospective design analysis". Rather than focusing only on the statistical significance of a result and on the classical control of type I and type II errors, a comprehensive design analysis involves reasoning about what can be considered a plausible effect size. Furthermore, it introduces two relevant inferential risks: the exaggeration ratio or Type M error (i.e., the predictable average overestimation of an effect that emerges as statistically significant), and the sign error or Type S error (i.e., the risk that a statistically significant effect is estimated in the wrong direction). Another important aspect of design analysis is that it can be usefully carried out both in the planning phase of a study and for the evaluation of studies that have already been conducted, thus increasing researchers' awareness during all phases of a research project. We use a familiar example in psychology where the researcher is interested in analyzing the differences between two independent groups. We examine the case in which the plausible effect size is formalized as a single value, and propose a method in which uncertainty concerning the magnitude of the effect is formalized via probability distributions. Through several examples, we show that even though a design analysis requires big effort, it has the potential to contribute to planning more robust and replicable studies. Finally, future developments in the Bayesian framework are discussed., Comment: 35 pages, 4 figures, manuscript currently under review

Generalized linear models are often misspecified due to overdispersion, heteroscedasticity and ignored nuisance variables. Existing quasi-likelihood methods for testing in misspecified models often do not provide satisfactory type-I error rate control. We provide a novel semi-parametric test, based on sign-flipping individual score contributions. The tested parameter is allowed to be multi-dimensional and even high-dimensional. Our test is often robust against the mentioned forms of misspecification and provides better type-I error control than its competitors. When nuisance parameters are estimated, our basic test becomes conservative. We show how to take nuisance estimation into account to obtain an asymptotically exact test. Our proposed test is asymptotically equivalent to its parametric counterpart., Comment: To appear in Journal of the Royal Statistical Society: Series B (Methodology). Early view version (2020)

In this article we provide initial findings regarding the problem of solving likelihood equations by means of a maximum entropy approach. Unlike standard procedures that require equating at zero the score function of the maximum-likelihood problem, we propose an alternative strategy where the score is instead used as external informative constraint to the maximization of the convex Shannon's entropy function. The problem involves the re-parameterization of the score parameters as expected values of discrete probability distributions where probabilities need to be estimated. This leads to a simpler situation where parameters are searched in smaller (hyper) simplex space. We assessed our proposal by means of empirical case studies and a simulation study, this latter involving the most critical case of logistic regression under data separation. The results suggested that the maximum entropy re-formulation of the score problem solves the likelihood equation problem. Similarly, when maximum-likelihood estimation is difficult, as for the case of logistic regression under separation, the maximum entropy proposal achieved results (numerically) comparable to those obtained by the Firth's Bias-corrected approach. Overall, these first findings reveal that a maximum entropy solution can be considered as an alternative technique to solve the likelihood equation., Comment: 14 pages, 2 figure, research article