Papers

The increasing ability to securely access electronic health records (EHR) has created unprecedented opportunities to monitor the health trajectories of large heterogeneous patient populations throughout their lifetime. Repeated measurements of time-varying covariates (such as biomarkers measured via routine blood tests) can inform dynamic risk prediction of time-to-event outcomes, updating risk estimates as new information becomes available. Existing dynamic risk prediction approaches often assume homogeneous longitudinal trajectories across individuals. This assumption is not met when there is heterogeneity driven by latent subgroup structure (e.g. due to unobserved confounders), as is often the case with real-world biomedical data. At present, accounting for such heterogeneity is only available in joint latent class models for longitudinal and time-to-event data, but they are computationally intensive, often prohibitively so for large-scale data, such as those present in EHR settings. To address these challenges, we propose a novel landmarking approach that integrates latent class mixed models (LCMMs) to capture latent heterogeneity in longitudinal trajectories. Our method is implemented in a modular R package, landmaRk, which is available on CRAN and allows users to flexibly specify the components of a landmarking analysis, beyond our proposed approach. Through simulation studies, we demonstrate improvements in prediction performance in the presence of latent heterogeneity compared to traditional landmarking strategies, while remaining computationally efficient for large datasets. We also provide a proof-of-concept illustration using real data.

College students commonly report insufficient sleep and poor sleep quality, with ~30% meeting insomnia criteria, posing significant threats to their physical growth, cognitive development, and overall well-being, as well as imposing a substantial economic burden on society [1]. The hyperarousal model of insomnia [2] emphasizes that hyperarousal across cognitive, emotional, and physiological domains mutually reinforces one another. Neuroimaging studies have further identified prefrontal hypoactivity as a key neural substrate underlying these dysfunctional cognitions and elevated arousal, reflecting a failure of top-down modulatory control over both limbic reactivity [3] and brainstem arousal nuclei [4]. Moreover, transcranial photobiomodulation (tPBM) therapy targeting the prefrontal cortex has demonstrated therapeutic efficacy across neuropsychiatric disorders with insomnia comorbidities [5,6], providing preliminary support for its application in insomnia. However, the neuro mechanisms underlying tPBM's therapeutic effects on insomnia remain to be elucidated.

High-dimensional economic datasets often display strong co-movement driven by a small number of latent factors, which are typically modeled using approximate factor models. When the number of variables is large relative to the sample size, the eigenvalues and eigenvectors of the sample covariance matrix are severely distorted, which in turn makes principal component based estimators of the factor structure unstable. To address the high-dimensional problem, we propose a Bayesian model for approximate factor structures. We show that the posterior convergence rate is of the same order as benchmark results for high-dimensional spiked covariance models. Simulation studies show that the proposed method more accurately recovers the factor structure in approximate factor models than existing methods. Real data analyses on macro–financial datasets illustrate that the proposed method provides interpretable estimates of latent factor structure and performs competitively in forecasting exercises.

Interventions can be varied continuously in many causal models. Differentiating a specified smooth intervention protocol produces vector fields on a statistical model, and their Lie brackets describe the noncommutativity of the corresponding local perturbations. We formulate this differential geometry of interventions on smooth statistical models and call the resulting framework infinitesimal causality (IC). Given a constant-rank distribution spanned by visible intervention fields, we define the normal Lie-bracket residual and show that its vanishing is exactly the involutivity condition in the classical Frobenius theorem. We establish the coordinate invariance of the zero-residual property and characterize its dependence on the intervention protocol, visible span, and metric. Fully observed and latent-variable examples delineate the additional structural assumptions needed to interpret bracket residuals causally. We also distinguish tangent vectors on a statistical parameter manifold from derivatives of stochastic kernels. In the finite-state linearization of a Markov category, normalization and copy compatibility yield well-typed first-order defects. Normalization is automatic for differentiable paths of stochastic kernels, whereas copy compatibility characterizes a more restrictive deterministic or comonoid-preserving perturbation. Together, the geometric and kernel-level constructions make IC a precise foundation for Lie-bracket-based causal diagnostics and identify the assumptions required to pass from local intervention geometry to causal conclusions.

We develop Partial Wavelet Canonical Coherence for measuring the direct canonical association between two multivariate nonstationary time series after adjustment for possibly high-dimensional confounders. To the best of our knowledge, this is the first method that establishes a frequency-domain formulation of the partial canonical correlation analysis for time series. Through a wavelet approach, the proposed method yields a scale-specific, time-varying measure of association capable to work with potential data nonstationarities. We formulate the target quantity under the multivariate locally stationary wavelet framework, develop principled estimation through local wavelet spectral matrices, and incorporate principal-component reduction for stable adjustment in high-dimensions. Simulations show that the method removes spurious marginal association induced by confounding and accurately recovers direct association, including in higher-dimensional settings. Analysis of U.S. exchange-traded funds reveals substantial time-varying and scale-dependent direct canonical association after adjustment for external market effects.

Invariant coordinate selection (ICS) is a dimensionality reduction technique based on the joint diagonalization of two scatter matrices. While principal component analysis relies solely on variance, ICS seeks directions of maximal or minimal generalized kurtosis, making it a powerful alternative for clustering and anomaly detection. Despite its theoretical and practical relevance, no dedicated Python implementation of ICS is currently available, limiting its integration into modern machine-learning workflows. We introduce ICSpyLab, the first Python package implementing ICS. It provides a broad collection of scatter matrices, multiple algorithms for computing invariant components, and several component-selection criteria. Designed for both practitioners and researchers, ICSpyLab follows a standard estimator interface, facilitating its use within machine-learning pipelines while remaining flexible for methodological extensions. The documentation includes detailed explanations and reproducible examples. ICSpyLab is released under the MIT license and is openly available at: https://github.com/cbecquart/ICSpyLab.

Ferguson's 1973 introduction of the Dirichlet process marked a breakthrough in Bayesian nonparametric statistics. For the first time, a prior on the space of probability measures fulfilled two key desiderata: large support and analytical tractability. In this paper, we review three complementary constructions of the Dirichlet process, whose roots can be traced back to Ferguson: through finite-dimensional distributions, via normalization of a gamma process, and through predictive distributions. Each perspective not only deepens the understanding of the Dirichlet process but also provides a template for generalizations, from normalized random measures with independent increments to Gibbs–type priors and beyond. Over the past fifty years, the Dirichlet process has become the cornerstone of Bayesian nonparametric methodology and applications, while simultaneously inspiring the expansion of the landscape of nonparametric priors. Since de Finetti laid out the Bayesian nonparametric framework in the 1930s, the key obstacle had been the absence of a tractable nonparametric prior. Ferguson's contribution overcame this challenge, providing a solution to a decades-long open problem. In recognition of this decisive advance, it seems appropriate to refer to the Dirichlet process as the Ferguson–Dirichlet process.

Learning causal models from fragmented biomedical data is challenging because clinical, molecular, and imaging variables are often incomplete or not jointly observed. We propose RetiSEM, a domain-constrained structural equation modelling (SEM) framework for causal graph recovery and mediation analysis under limited multimodal resources. This proposed work organises variables into biologically informed blocks, applies forbidden-edge constraints, and decomposes pathway-level effects into TE, NDE, and NIE components. We evaluate RetiSEM across ten synthetic benchmark scenarios that vary in dimensionality, nonlinearity, causal depth, and pathway structure, together with a fragmented real-world setting that combines NHANES clinical variables with externally derived retinal representations. This approach achieves lower structural error and higher causal accuracy than unconstrained baselines across the synthetic benchmarks. In the real-data analysis, retinal variables behave mainly as downstream biomarker-like indicators, with smaller but detectable indirect effects. These findings support our strategy as an interpretable framework for testing structured causal hypotheses in limited-resource biomedical AI. The code and resources for this work are publicly available at: https://github.com/Inamullah-Colab/ReitSEM.

We study the problem of estimating the arrival times of vertices in a uniform random recursive tree from its unlabeled structure. We adopt a pointwise perspective and analyze the distribution of the relative estimation error, and derive tail bounds that are uniform in both the vertex and the tree size. For the ranking induced by Jordan centrality, the probability that the estimate exceeds the true arrival time by a factor $S$ decays on the order of $1/S$, while the probability of underestimating the arrival time by a factor $1/S$ decays exponentially in $S$. We introduce a refined centrality measure whose overestimation tail decays on the order of $(\log S)/S^{2}$, at the cost of a heavier lower tail of order $1/S^{2}$. These results reveal a tradeoff between upper- and lower-tail performance in arrival-time estimation that is invisible to the previously studied risk functional. Nevertheless, the refined centrality measure attains the optimal order of the risk for all its parameter values.

Nonlinear mixed-effects models are widely used to analyze longitudinal data, but existing open-source software often supports only a limited subset of the model structures, inference methods, machine-learning components, automatic differentiation techniques, and random-effects distributions required in modern applications. We introduce NoLimits.jl, an open-source Julia package for flexible and composable nonlinear mixed-effects modeling. Its macro-based modeling language enables observation and latent-state models to be constructed from diverse building blocks, including ordinary differential equations, Markov models, and neural networks. NoLimits.jl supports flexible, covariate-dependent observation and random-effects distributions and provides a unified interface to frequentist inference through Laplace approximation, stochastic expectation maximization, and Bayesian Markov chain Monte Carlo methods. We demonstrate the package on three case studies showcasing its workflows, integration of differentiable machine-learning components, and data-driven estimation of random-effects distributions using normalizing flows. Together, these capabilities substantially expand the range of nonlinear mixed-effects models that can be specified, estimated, and compared within a single open-source framework.

Data augmentation is a simple and model-agnostic approach for exploiting known invariances in learning problems. Given a group acting on the input space, one augments the training set with transformed copies of each sample. Because it exploits symmetries without modifying the underlying learning algorithm, data augmentation can be applied broadly across learning methods. However, this universality comes at a computational cost: when the group is large, full group-sized augmentation quickly becomes computationally infeasible. This raises a fundamental question: Can partial data augmentation achieve the same statistical benefits as full augmentation in terms of generalization and sample complexity? We develop a general framework for investigating this question using Fourier analysis and the representation theory of finite groups. We show that, for a broad class of classical learning problems, partial data augmentation based on a randomly sampled subset of group elements achieves the same minimax rates as full augmentation, up to an approximation error that vanishes as the subset size increases. Our results provide a theoretical explanation for why partial augmentation can retain the statistical benefits of full augmentation despite enforcing symmetry only approximately, and shed light on a recently raised question in learning with symmetries: whether statistically optimal learning under general group invariances can be achieved using computationally scalable methods. Moreover, we prove a complementary impossibility result: enforcing exact invariance via data augmentation requires averaging over the entire group, and cannot be achieved by any strict subset when the hypothesis space is sufficiently expressive. Together, these results provide a unified perspective on full and partial data augmentation, as well as exact and approximate symmetry enforcement.

Auditory models are central tools for studying spatial hearing, yet their validation typically relies on heuristic performance metrics rather than principled statistical methods. We present two contributions building on a Bayesian sound localisation model that jointly infers sound direction from noisy perceptual features and individual head-related transfer functions (HRTFs). First, we derive an explicit likelihood function and validate it through parameter recovery on simulated data and fitting to behavioural responses from 33 participants, demonstrating that the framework reliably identifies individual sensorimotor and spectral parameters. Second, we use this framework to compare four HRTF template interpolation methods, showing that full-sphere spatial coverage and high-frequency spectral fidelity are the primary determinants of template quality, while the specific interpolation algorithm is secondary. Together, these results show that standard model-based statistical methods can address both fundamental questions in spatial hearing and applied problems such as perceptual HRTF evaluation. An open-source Python implementation is released alongside this work.

Covariate selection in Generalized Linear Models (GLMs) is a fundamental problem in statistics, as including irrelevant predictors might lead to overfitting and poor interpretability, while omitting relevant ones might result in biased estimates. Most Bayesian approaches to variable selection – including spike-and-slab priors and continuous shrinkage priors – have key limitations, e.g., (i) are based on non fully conjugate formulations, (ii) are restricted to a linear model, or (iii) lack posterior consistency guarantees for the variable selection procedure and model parameters. In this work, we propose a fully Bayesian hierarchical and conjugate framework for covariate selection in GLMs, applicable to any distribution in the exponential family, based on modeling a binary inclusion indicator that directly encodes covariate inclusion in the linear predictor. In our approach, variable selection and parameter estimation are performed simultaneously, incorporating both sources of uncertainty in posterior inference. Consequently, our methodology provides a valid post-model Bayesian selection procedure. We present theoretical guarantees of the proposed fully conjugate Bayesian variable selection for GLMs, establishing posterior consistency of both the inclusion indicators and the active regression coefficients. We derive an efficient Gibbs Sampling algorithm with a corresponding R package implementation. We validate the proposed method on synthetic and real-world datasets, demonstrating competitive predictive and inferential performance.

The growing reliance on machine learning for decisions across sectors underscores the importance of model transparency and interpretability. Existing post hoc explainability methods and inherently interpretable approaches shed light on model behavior, yet they primarily reveal how models exploit correlations to maximize performance in prediction tasks. However, many decisions require causal insights and the possibility of using models for what-if scenario evaluation. To address this, we propose the integration of causal machine learning with inherently interpretable models for cross-sectional data. We evaluate these methods in terms of predictive accuracy and interpretability. Our findings show that the proposed approach achieves competitive performance in prediction and what-if analysis while offering transparency on the system structure, causal relationships among variables, and the functional forms that connect them. This work contributes to research on causality, machine learning interpretability, and data-driven decision support by offering informed, transparent, and causally grounded decisions.

Classical kernel estimators of second order are interpreted in terms of random Weierstrass-type operators, particularly random Steklov operators. This leads us to obtain explicit nonasymptotic confidence bands and intervals for distribution functions $F$ and their derivatives $F^{(k)}$. Under the only assumption that $F^{(k)}$ is uniformly continuous, confidence bands for $F^{(k)}$ are established by using the Dvoretzky-Kiefer-Wolfowitz inequality. To give confidence intervals, we allow $F^{(k)}$ to have isolated discontinuities of the first kind, so that we really estimate the midpoint function $(F^{(k)})_{\star}(x)$. The proofs are based either on concentration inequalities for subordinated stochastic processes or accurate estimates of the MSE of the corresponding estimators. The length of the confidence bands and intervals depends on the degree of smoothness of $F^{(k)}$ measured in terms of the second modulus of continuity. Both lengths are of order $n^{-1 / 2}$ if $F$ is locally a polynomial of degree $k+1$ at most.

The aim of this work is to propose a statistical model for spatio-temporal data on meshed surfaces based on the Stochastic Partial Differential Equation (SPDE) modeling approach. Specifically, we focus on a class of advection-diffusion SPDEs defined on smooth compact orientable closed Riemannian manifolds of dimension 2, and their discretization via a Galerkin approach. We demonstrate how this method enables the development of scalable algorithms for the simulation and prediction of Gaussian random fields that are solutions to the discretized SPDE. Additionally, we present recent developments in the inference of such models. The method is applied to a simulated spatio-temporal dataset exhibiting advective and diffusive behavior on the sphere, as well as to a real case study on aerosol optical depth in the atmosphere across the globe's surface.

AI-assisted interviews promise to reduce respondent burden in surveys by allowing respondents to describe experiences naturally while an AI system noisily maps those accounts into structured survey variables. That mapping is a measurement process that is fallible, versioned, adaptive, and potentially behaves differently across subgroups. This paper proposes Adaptive Matrix Validation (AMV), a design in which each respondent completes an AI-assisted interview, which is then mapped into tabular data by the AI. Respondents are also asked a small, randomized set of structured questions, which are used for statistical adjustment. The estimator first calibrates the mapped values using validation answers from other respondents, then corrects the remaining error with the validation answers observed for the target respondent. The paper develops estimators for item means, subgroup estimates, and regression coefficients when outcomes, predictors, or both are mapped from interviews. It also gives planning formulas the number of validation questions required and the sample size. A design-calibration simulation, an American Time Use Survey emulation, and a CHAMPS verbal-autopsy narrative study show when sparse validation can improve precision and when it cannot

Visual assessment of residual plots is a common approach for diagnosing linear models, but it relies on manual evaluation, which does not scale well and can lead to inconsistent decisions across analysts. The lineup protocol, which embeds the observed plot among null plots, can reduce subjectivity but requires even more human effort. In today's data-driven world, such tasks are well suited for automation. We present a new R package that uses a computer vision model to automate the evaluation of residual plots. An accompanying Shiny application is provided for ease of use. Given a sample of residuals, the model predicts a visual signal strength (VSS) and offers supporting information to help analysts assess model fit.

We propose a sensitivity analysis method for missing not at random (MNAR) data in the context of linear multilevel (mixed-effects) models. The outcome and dropout risk are both modelled using multilevel models and a bias adjustment due to MNAR data is derived. This bias can be estimated from observed data conditional on specified values of sensitivity parameter(s). Under the assumption that these parameters lie within a plausible range, the method partially identify the parameters of interest, yielding bounds for estimation and inference under assumptions weaker than missing at random. The proposed analysis is investigated in a simulation study and illustrated with an analysis of the association between loneliness and physical activity with memory trajectories, adjusting for demographic, socioeconomic, and health covariates.

Random variables are the bread and butter of statistics, and visualisations are one of the most versatile tools in the field, so it is a wonder why we do not have a methodology for visualising random variables. This gap is particularly evident for exploratory data analysis (EDA). We address this gap by designing a mathematical framework for visualisation, which argues that we should consider visualisations to be continuous functions. In the case of random variable inputs, this means the visualisations should obey the continuous mapping theorem (CMT). By breaking the visual function down into its components, we are able to identify which parts of the mapping are ill-defined for random variable inputs and redefine them in a way that guarantees both the flexibility required for EDA and the statistical sensibility of CMT. This formalisation represents a complete integration of uncertainty into the grammar of graphics, which we show by implementing the theory in the R package, "ggdibbler". The ggdibbler software is a "ggplot2" extension that allows users to replace the data of any plotting function with a random variable, with the guarantee that the visualisation will have the same convergence properties as its underlying data.

Reliable structural health monitoring (SHM) of offshore wind turbine (OWT) support structures requires fast state estimation from sparse measurements. Repeated high fidelity finite element or aeroelastic analyses are difficult to use directly in online monitoring loops, while purely data-driven surrogates can require large training sets. This paper presents Digi Turbine, a synthetic reliability-aware Physics Informed Neural Network (PINN) benchmark for OWT monopile support structure monitoring. The workflow embeds a simplified Euler Bernoulli beam equation with Winkler soil foundation in the training objective, couples it with Bayesian-prior-informed inverse identification, and adds First Order Reliability Method (FORM) screening. All validation uses synthetic configurations with analytical or finite-difference ground truth motivated by the NREL 5MW reference turbine context.

We study probabilistic forecasting of the 2026 FIFA World Cup, the first edition with 48 teams and an added Round of 32. The main idea is to describe team strength not only by the current Elo rating, but by a short history of recent Elo differences. We then reduce this history to a few informative directions using categorical sufficient dimension reduction (SDR). The reduced scores are used in a Poisson double-regression model for home and away goals, which gives full outcome probabilities. We compare eleven models, including logistic regression, standard Poisson regression, ARIMA, and neural-network forecasts of the Elo series, gradient boosting, an ensemble model, and four categorical SDR variants based on sliced inverse regression (SIR) and sliced average variance estimation (SAVE). The models are evaluated out of sample on the 2018 and 2022 World Cups using the ranked probability score (RPS). The results show that SDR-based poisson models improve the traditional approaches, suggesting that recent Elo history contains useful predictive information that is not captured by the current Elo difference alone.

Automated diabetic retinopathy (DR) grading from colour fundus photographs can achieve strong predictive performance, but clinical interpretation requires more than an image-level label. It requires understanding how lesion evidence is distributed around retinal vessels and how this evidence relates to quantitative vascular biomarkers. We present a dual-edge spatial-Jacobian image graph for interpretable DR grading. Each fundus image is represented as a graph node with four aligned evidence streams: AutoMorph vessel information ($X_1$), DR-XAI-style lesion evidence maps ($X_2$), a 128-dimensional lesion-based contrastive image embedding ($X_3$), and AutoMorph morphometric biomarkers ($X_4$). The spatial edge branch ($X_{12}$) encodes vessel-lesion geometry, while the Jacobian branch ($X_{34}$) models embedding-biomarker sensitivity. Lightweight two-token attention fuses both edge families into a final image graph. On 2,910 matched non-augmented APTOS images, the full graph achieves 0.8076 accuracy, 0.8312 quadratic weighted kappa, 0.5915 macro-F1, and 0.9330 adjacent-grade accuracy; referable DR reaches 0.9055 accuracy and 0.9711 AUROC. The framework is positioned as an explainable representation-learning tool for lesion-biomarker hypothesis generation, rather than as a deployment-ready clinical classifier. The code is available at https://github.com/Inamullah-Colab/dual-edge-dr-graph-xai.

In practical experiments, block variables often arise from multiple sources of heterogeneity. To address the confounding problem, this paper proposes a blocked aliased component-number pattern (B$^2$-ACNP) to analyze the confounding properties of s-level designs with multi-block variables. We calculate the values of (B$^2$-ACNP) via a blocked wordlength distribution matrix. The classification patterns of existing criteria can be expressed as functions of specific elements within the B$^2$-ACNP, thereby stablishing connections within a unified framework. Further, we provide confounding algorithms and visualization methods of the B$^2$-ACNP. Finally, case analysis clarifies the significant role of the B$^2$-ACNP. The Python code is available in the Appendix.

We propose a non-stationary model constructed using a mixture of spatio-temporal covariance models with advection effects; namely, models that have larger covariance values along an orientation vector in the spatio-temporal index set, that simulate wind direction and cloud movement. We show that a mixture of such models can allow for wind direction change in data during (estimated) time intervals, unlike traditional models that use rigid advection effects. We construct a MCMC procedure for Bayesian estimation, and illustrate the method with the analysis of a severe rainfall event from the southeastern region of Brazil.

The mean cumulative function (MCF) summarizes how events accumulate over time for a recurrent or multi-component endpoint. The MCF, and its integral over a given time horizon, the area under the MCF (AUMCF), provide interpretable summaries of recurrent-event burden in the presence of right-censoring and terminal events. Existing approaches for these estimands have focused primarily on nonparametric treatment comparisons, covariate-adjusted augmentation, and linearized test statistics. Herein, we propose a pseudo-value-based regression approach for estimating covariate effects on the MCF and AUMCF at a fixed truncation time. The proposed method uses influence-function-based pseudo-values as regression outcomes, allowing estimation with standard generalized estimating equation machinery and, under an identity link, ordinary least squares. Through simulation studies, we evaluate estimation accuracy, confidence interval coverage, type I error control, and power across a range of recurrent-event settings. We demonstrate the utility of the proposed covariate adjustment procedure through an application to the ORATORIO clinical trial, evaluating the safety and efficacy of ocrelizumab for the treatment of primary progressive multiple sclerosis. Overall, pseudo-value-based regression provides a simple and interpretable framework for modeling covariate effects on cumulative recurrent-event burden over time.

Authoritative positioning, navigation, and timing (PNT) resilience frameworks (the DHS Resilient PNT Conformance Framework, RPCF, and peers) define what resilience means but supply only self-attestation: a checklist or a maturity Level, with no engine and no measurement. We build the missing measurement layer as an open, deterministic scoring engine over a PNT simulator, emitting per-dimension sub-scores traceable to a scenario and an oracle, and ask whether a single composite score or maturity Level is a stable basis for a decision. Across seven architectures spanning cross-dimension tradeoffs, a Dirichlet simplex over the seven RPCF categories, and a five-threat ensemble, the answer splits in two. The composite winner is stable under active denial and under near-equal weightings (about 1 percent flip rate), so a single number is safe precisely where one design dominates; but re-weighting alone flips it in up to 22 percent of draws under nominal conditions, where designs contend, a known composite-indicator sensitivity. The sharper, weighting-invariant failure is categorical: a weakest-link maturity Level (our minimum-over-categories operationalization of the RPCF ladder, not the framework's rule) depends on the threat assumed, not the architecture, changing for one architecture in seven. Because the composite rewards declared techniques, a constructed single-band receiver declaring all seven outscores a more resilient system: self-attestation can be gamed by declaration. And apparent fourfold GNSS redundancy reduces, by the definition of a shared common-mode failure domain, to an effective diversity of one. Conclusions hold under +/-20 percent perturbation of every driver within the reduction. We report per-dimension sub-scores with provenance and a rank range, not a phantom single number. A self-assessment aligned to RPCF v2.0, not a certification.

Spectral community detection estimates latent labels from the leading eigenspace of a network adjacency matrix, but releasing the resulting labels can disclose sensitive relational information. We consider this problem under differential privacy for both ordinary and bipartite networks. For ordinary networks, the protected unit is a single edge, leading to edge differential privacy (edge-DP). For bipartite networks, the inferential target is the community structure of the left-side nodes, while the protected unit is an entire right-side incidence profile, leading to column-node-DP. We propose NetPTR, a private spectral clustering procedure that releases a noisy empirical spectral embedding after a stability test. The algorithm requires perturbation bounds for empirical eigenspaces under neighboring-network changes, which yield computable stability certificates and local sensitivity bounds. For ordinary networks, we establish edge-DP and the error bound under the degree-corrected stochastic blockmodel, which separates the non-private spectral clustering error from the additional privacy-induced error. It therefore guarantees weak consistency in sparse networks and exact recovery in moderate sparse networks. A matching lower bound shows that the required privacy budget is sharp up to logarithmic factors. We further develop a column-node-DP algorithm for bipartite networks and prove consistency under a bipartite degree-corrected block model. Simulations and real-data examples illustrate the resulting privacy–accuracy tradeoff.

In many real-world scenarios, especially those involving privacy constraints or data summarization, data are available only in aggregated forms, such as histograms or frequency tables. This work introduces a novel Bayesian method for inferring the underlying population distribution by fitting a mixture model to binned data. While we focus on mixtures of normal distributions, the framework is flexible and can be extended to other distributional families. We place a prior distribution on the number of mixture components, accommodating both finite and countably infinite mixtures, and perform inference using reversible jump MCMC. The proposed approach demonstrates strong performance on large-scale data, showcasing the potential of nonparametric Bayesian modeling in practical applications. Furthermore, we extend the method to model multiple histograms simultaneously and cluster them using the Dirichlet process. This enables information sharing across populations and provides a principled posterior probability to assess homogeneity between groups. Some theoretical results supporting the performance of our proposed methodology are also discussed.

Despite the implicit appearance of logit-normal random variables in many inferential problems, the logit-normal distribution is poorly studied. Most frustratingly, no default method exists for finding logit-normal moments, which are often assumed analytically unknown. In this paper, we introduce a method for estimating logit-normal moments of any positive integer order, based on approximating the logistic function. We will show our method is highly accurate up to the $8^\text{th}$ moment, avoids the numerical instability observed with Mordell integral based approximations of the first moment, and is faster than numerical integration in R. Focusing on two inferential applications, we will show our approximation methods are sufficiently accurate to enable faster implementation of Expectation Propagation for logistic regression, but is not general enough to directly evaluate the logistic normal integral that appears in some logistic mixed models.