Papers

Researchers across different fields, including but not limited to ecology, biology, and healthcare, often face the challenge of sparse data. Such sparsity can lead to uncertainties, estimation difficulties, and potential biases in modeling. Here we introduce a novel data augmentation method that combines multiple sparse time series datasets when they share similar statistical properties, thereby improving parameter estimation and model selection reliability. We demonstrate the effectiveness of this approach through validation studies comparing Hawkes and Poisson processes, followed by application to subjective pain dynamics in patients with sickle cell disease (SCD), a condition affecting millions worldwide, particularly those of African, Mediterranean, Middle Eastern, and Indian descent.

Examination of T-cell receptor (TCR) clonality has become a way of understanding immunologic response to cancer and its interventions in recent years. An aspect of these analyses is determining which receptors expand or contract statistically significantly as a function of an exogenous perturbation such as therapeutic intervention. We characterize the commonly used Fisher's exact test approach for such analyses and propose an alternative formulation that does not necessitate pairwise, within-patient comparisons. We develop this flexible Bayesian longitudinal mixture model that accommodates variable length patient followup and handles missingness where present, not omitting data in estimation because of structural practicalities. Once clones are partitioned by the model into dynamic (expanding or contracting) and static categories, one can associate their counts or other characteristics with disease state, interventions, baseline biomarkers, and patient prognosis. We apply these developments to a cohort of prostate cancer patients who underwent randomized metastasis-directed therapy or not. Our analyses reveal a significant increase in clonal expansions among MDT patients and their association with later progressions both independent and within strata of MDT. Analysis of receptor motifs and VJ gene enrichment combinations using a high-dimensional penalized log-linear model we develop also suggests distinct biological characteristics of expanding clones, with and without inducement by MDT.

In modern biomedical and econometric studies, longitudinal processes are often characterized by complex time-varying associations and abrupt regime shifts that are shared across correlated outcomes. Standard functional data analysis (FDA) methods, which prioritize smoothness, often fail to capture these dynamic structural features, particularly in high-dimensional settings. This article introduces Adaptive Joint Learning (AJL), a hierarchical regularization framework designed to integrate functional variable selection with structural changepoint detection in multivariate time-varying coefficient models. Unlike standard simultaneous estimation approaches, we propose a theoretically grounded two-stage screening-and-refinement procedure. This framework first synergizes adaptive group-wise penalization with sure screening principles to robustly identify active predictors, followed by a refined fused regularization step that effectively borrows strength across multiple outcomes to detect local regime shifts. We provide a rigorous theoretical analysis of the estimator in the ultra-high-dimensional regime (p >> n). Crucially, we establish the sure screening consistency of the first stage, which serves as the foundation for proving that the refined estimator achieves the oracle property-performing as well as if the true active set and changepoint locations were known a priori. A key theoretical contribution is the explicit handling of approximation bias via undersmoothing conditions to ensure valid asymptotic inference. The proposed method is validated through comprehensive simulations and an application to Sleep-EDF data, revealing novel dynamic patterns in physiological states.

This paper establishes convergence rates for learning elliptic pseudo-differential operators, a fundamental operator class in partial differential equations and mathematical physics. In a wavelet-Galerkin framework, we formulate learning over this class as a structured infinite-dimensional regression problem with multiscale sparsity. Building on this structure, we propose a sparse, data- and computation-efficient estimator, which leverages a novel matrix compression scheme tailored to the learning task and a nested-support strategy to balance approximation and estimation errors. In addition to obtaining convergence rates for the estimator, we show that the learned operator induces an efficient and stable Galerkin solver whose numerical error matches its statistical accuracy. Our results therefore contribute to bringing together operator learning, data-driven solvers, and wavelet methods in scientific computing.

Language diffusion models aim to improve sampling speed and coherence over autoregressive LLMs. We introduce Neural Flow Diffusion Models for language generation, an extension of NFDM that enables the straightforward application of continuous diffusion models to discrete state spaces. NFDM learns a multivariate forward process from the data, ensuring that the forward process and generative trajectory are a good fit for language modeling. Our model substantially reduces the likelihood gap with autoregressive models of the same size, while achieving sample quality comparable to that of previous latent diffusion models.

Supporting Go/No-Go decisions prior to launch requires assessing real-time telemetry data against redline limits established during the design qualification phase. Family data from ground testing or previous flights is commonly used to detect initiating failure modes and their timing; however, this approach relies heavily on engineering judgment and is more error-prone for new launch vehicles. To address these limitations, we utilize Long-Term Short-Term Memory (LSTM) networks for supervised classification of time-series anomalies. Although, initial training labels derived from simulated anomaly data may be suboptimal due to variations in anomaly strength, anomaly settling times, and other factors. In this work, we propose a novel statistical detector based on the Mahalanobis distance and forward-backward detection fractions to adjust the supervised training labels. We demonstrate our method on digital twin simulations of a ground-stage propulsion system with 20.8 minutes of operation per trial and O(10^8) training timesteps. The statistical data relabeling improved precision and recall of the LSTM classifier by 7% and 22% respectively.

Machine learning (ML) is a tool to exploit remote sensing data for the monitoring and implementation of the United Nations' Sustainable Development Goals (SDGs). In this paper, we report on a meta-analysis to evaluate the performance of ML applied to remote sensing data to monitor SDGs. Specifically, we aim to 1) estimate the average performance; 2) determine the degree of heterogeneity between and within studies; and 3) assess how study features influence model performance. Using PRISMA guidelines, a search was performed across multiple academic databases to identify potentially relevant studies. A random sample of 200 was screened by three reviewers, resulting in 86 trials within 20 studies with 14 study features. Overall accuracy was the most reported performance metric. It was analyzed using double arcsine transformation and a three-level random effects model. The average overall accuracy of the best model was 0.90 [0.86, 0.92]. There was considerable heterogeneity in model performance, 64% of which was between studies. The only significant feature was the prevalence of the majority class, which explained 61% of the between-study heterogeneity. None of the other thirteen features added value to the model. The most important contributions of this paper are the following two insights. 1) Overall accuracy is the most popular performance metric, yet arguably the least insightful. Its sensitivity to class imbalance makes it necessary to normalize it, which is far from common practice. 2) The field needs to standardize the reporting. Reporting of the confusion matrix for independent test sets is the most important ingredient for between-study comparisons of ML classifiers. These findings underscore the need for robust and comparable evaluation metrics in machine learning applications to ensure reliable and actionable insights for effective SDG monitoring and policy formulation.

A Multinomial Logit (MNL) model is composed of a finite universe of items $[n]=\{1,..., n\}$, each assigned a positive weight. A query specifies an admissible subset – called a slate – and the model chooses one item from that slate with probability proportional to its weight. This query model is also known as the Plackett-Luce model or conditional sampling oracle in the literature. Although MNLs have been studied extensively, a basic computational question remains open: given query access to slates, how efficiently can we learn weights so that, for every slate, the induced choice distribution is within total variation distance $\varepsilon$ of the ground truth? This question is central to MNL learning and has direct implications for modern recommender system interfaces. We provide two algorithms for this task, one with adaptive queries and one with non-adaptive queries. Each algorithm outputs an MNL $M'$ that induces, for each slate $S$, a distribution $M'_S$ on $S$ that is within $\varepsilon$ total variation distance of the true distribution. Our adaptive algorithm makes $O\left(\frac{n}{\varepsilon^{3}}\log n\right)$ queries, while our non-adaptive algorithm makes $O\left(\frac{n^{2}}{\varepsilon^{3}}\log n \log\frac{n}{\varepsilon}\right)$ queries. Both algorithms query only slates of size two and run in time proportional to their query complexity. We complement these upper bounds with lower bounds of $\Omega\left(\frac{n}{\varepsilon^{2}}\log n\right)$ for adaptive queries and $\Omega\left(\frac{n^{2}}{\varepsilon^{2}}\log n\right)$ for non-adaptive queries, thus proving that our adaptive algorithm is optimal in its dependence on the support size $n$, while the non-adaptive one is tight within a $\log n$ factor.

As artificial intelligence increasingly drives critical decisions, the ability to genuinely explain how neural networks make predictions is essential for trust. Yet, most current explanation methods offer post-hoc rationalizations rather than guaranteeing a true reflection of the model's reasoning. We introduce the notion of explanatory alignment, a requirement that explanations directly construct predictions rather than rationalize them. To achieve this in complex data domains, we present Pointwise-interpretable Networks (PiNets), a pseudo-linear architecture that forms linear models instance-wise. Evaluated on image classification and segmentation tasks, PiNets demonstrate that their explanations are deeply faithful across four criteria: meaningfulness, alignment, robustness, and sufficiency (MARS). Our contributions pave the way for promising avenues: by reconciling the predictive power of deep learning with the interpretability of linear models, PiNets provide a principled foundation for trustworthy AI and data-driven scientific discovery.

The emergence of generative AI (GAI) has sparked diverse opinions regarding its appropriate use across various domains, including education. This pilot study investigates university students' perceptions of GAI in higher education classrooms, aiming to lay the groundwork for understanding these attitudes. With a participation rate of approximately 4.4%, the study highlights the challenges of engaging students in GAI-related research and underscores the need for larger sample sizes in future studies. By gaining insights into student perspectives, instructors can better prepare to integrate discussions of GAI into their classrooms, fostering informed and critical engagement with this transformative technology.

We propose a discrete transport equation on graphs which connects distributions on both vertices and edges. We then derive a discrete analogue of the Benamou-Brenier formulation for Wasserstein-$1$ distance on a graph and as a result classify all $W_1$ geodesics on graphs.

Time-to-event endpoints are central to evaluating treatment efficacy across disease areas. In clinical trials with time-to-event endpoints, the information available for interim and final analyses is often determined by the number of observed events rather than by the number of enrolled patients. Interim monitoring therefore requires assessing how many additional events are expected to accrue by scheduled future analysis dates. Quantifying uncertainty around these counts is essential for assessing whether planned information levels are likely to be reached, anticipating delays or event overrunning, and supporting operational decisions while the trial is ongoing. This is especially relevant where event accrual is low as in pediatric hemato-oncology trials. Although methods for predicting time to endpoint maturation are well established, interval prediction for event counts at fixed calendar times remains less developed. We propose a patient-level framework for constructing such intervals at interim analyses of time-to-event trials. Conditionally on the interim data, the future count follows a Poisson–binomial law with patient-specific event probabilities; we estimate this law using a conditional parametric bootstrap. Under standard regularity conditions, the bootstrap is consistent and yields asymptotically calibrated prediction intervals. The framework accommodates staggered entry, patient-level covariates, administrative censoring, loss to follow-up, and possible dependence between entry dates and loss to follow-up, before conditioning on the realised interim data. We study its operating characteristics in simulation studies and illustrate the method using a real-world phase III trial in childhood acute lymphoblastic leukaemia.

Class imbalance significantly degrades classification performance, yet its effects are rarely analyzed from a unified theoretical perspective. We propose a principled framework based on three fundamental scales: the imbalance coefficient $\eta$, the sample–dimension ratio $\kappa$, and the intrinsic separability $\Delta$. Starting from the Gaussian Bayes classifier, we derive closed-form Bayes errors and show how imbalance shifts the discriminant boundary, yielding a deterioration slope that predicts four regimes: Normal, Mild, Extreme, and Catastrophic. Using a balanced high-dimensional genomic dataset, we vary only $\eta$ while keeping $\kappa$ and $\Delta$ fixed. Across parametric and non-parametric models, empirical degradation closely follows theoretical predictions: minority Recall collapses once $\log(\eta)$ exceeds $\Delta\sqrt{\kappa}$, Precision increases asymmetrically, and F1-score and PR-AUC decline in line with the predicted regimes. These results show that the triplet $(\eta,\kappa,\Delta)$ provides a model-agnostic, geometrically grounded explanation of imbalance-induced deterioration.

This paper proposes distributed estimation procedures for three scalar-on-function regression models: the functional linear model (FLM), the functional non-parametric model (FNPM), and the functional partial linear model (FPLM). The framework addresses two key challenges in functional data analysis, namely the high computational cost of large samples and limitations on sharing raw data across institutions. Monte Carlo simulations show that the distributed estimators substantially reduce computation time while preserving high estimation and prediction accuracy for all three models. When block sizes become too small, the FPLM exhibits overfitting, leading to narrower prediction intervals and reduced empirical coverage probability. An example of an empirical study using the tecator dataset further supports these findings.

Online hate spreads rapidly, yet little is known about whether preventive and scalable strategies can curb it. We conducted the largest randomized controlled trial of hate speech prevention to date: a 20-week messaging campaign on X in Nigeria targeting ethnic hate. 73,136 users who had previously engaged with hate speech were randomly assigned to receive prosocial video messages from Nigerian celebrities. The campaign reduced hate content by 2.5% to 5.5% during treatment, with about 75% of the reduction persisting over the following four months. Reaching a larger share of a user's audience reduced amplification of that user's hate posts among both treated and untreated users, cutting hate reposts by over 50% for the most exposed accounts. Scalable messaging can limit online hate without removing content.

We study a ridge estimator for the high-dimensional two-way fixed effect regression model with a sparse bipartite network. We develop concentration inequalities showing that when the ridge parameters increase as the log of the network size, the bias, and the variance-covariance matrix of the vector of estimated fixed effects converge to deterministic equivalents that depend only on the expected network. We provide simulations and an application using administrative data on wages for worker-firm matches.

Nested case-control (NCC) studies are a widely adopted design in epidemiology to investigate exposure-disease relationships. This paper examines weighted analyses in NCC studies, focusing on two prominent weighting methods: Kaplan-Meier (KM) weights and Generalized Additive Model (GAM) weights. We consider three target estimands: log-hazard ratios, conditional survival, and associations between exposures. While KM- and GAM-weights are generally robust, we identify specific scenarios where they can lead to biased estimates. We demonstrate that KM-weights can lead to biased estimates when a proportion of the originating cohort is effectively ineligible for NCC selection, particularly with small case proportions or numerous matching factors. Instead, GAM-weights can yield biased results if interactions between matching factors influence disease risk and are not adequately incorporated into weight calculation. Using Directed Acyclic Graphs (DAGs), we develop a framework to systematically determine which variables should be included in weight calculations. We show that the optimal set of variables depends on the target estimand and the causal relationships between matching factors, exposures, and disease risk. We illustrate our findings with both synthetic and real data from the European Prospective Investigation into Cancer and nutrition (EPIC) study. Additionally, we extend the application of GAM-weights to "untypical" NCC studies, where only a subset of cases are included. Our work provides crucial insights for conducting accurate and robust weighted analyses in NCC studies.

The \pkg{pintervals} package aims to provide a unified framework for constructing prediction intervals and calibrating predictions in a model-agnostic setting using set-aside calibration data. It comprises routines to construct conformal as well as parametric and bootstrapped prediction intervals from any model that outputs point predictions. Several R packages and functions already exist for constructing prediction intervals, but they often focus on specific modeling frameworks or types of predictions, or require manual customization for different models or applications. By providing a consistent interface for a variety of prediction interval construction approaches (all model-agnostic), \pkg{pintervals} allows researchers to apply and compare them across different modeling frameworks and applications.

Robust estimation of the covariance matrix and detection of outliers remain major challenges in statistical data analysis, particularly when the proportion of contaminated observations increases with the size of the dataset. Outliers can severely bias parameter estimates and induce a masking effect, whereby some outliers conceal the presence of other outliers, further complicating their detection. Although many approaches have been proposed for covariance estimation and outlier detection, to our knowledge, none of these methods have been implemented in an online setting. In this paper, we focus on online covariance matrix estimation and outlier detection. Specifically, we propose a new method for simultaneously and online estimating the geometric median and variance, which allows us to calculate the Mahalanobis distance for each incoming data point before deciding whether it should be considered an outlier. To mitigate the masking effect, robust estimation techniques for the mean and variance are required. Our approach uses the geometric median for robust estimation of the location and the median covariance matrix for robust estimation of the dispersion parameters. The new online methods proposed for parameter estimation and outlier detection allow real-time identification of outliers as data are observed sequentially. The performance of our methods is demonstrated on simulated datasets.

Index tracking, also known as passive investing, has gained significant traction in financial markets due to its cost-effective and efficient approach to replicating the performance of a specific market index. This review paper provides a comprehensive overview of the various modeling approaches and strategies developed for index tracking, highlighting the strengths and limitations of each approach. We categorize the index tracking models into three broad frameworks: optimization-based models, statistical-based models and machine learning based data-driven approach. A comprehensive empirical study conducted on the S&P 500 dataset demonstrates that the tracking error volatility model under the optimization-based framework delivers the most precise index tracking, the convex co-integration model, under the statistical-based framework achieves the strongest return-risk balance, and the deep neural network with fixed noise model within the data-driven framework provides a competitive performance with notably low turnover and high computational efficiency. By combining a critical review of the existing literature with comparative empirical analysis, this paper aims to provide insights into the evolving landscape of index tracking and its practical implications for investors and fund managers.

This paper addresses the nonparametric estimation of a spatially varying, heteroskedastic variance function on the unit sphere within a regression framework. While adaptive regression estimation is well-established on manifolds, characterizing localized noise structures presents unique theoretical obstacles due to bias propagation from the unknown mean function. To circumvent this, we propose a fully data-driven, multiresolution estimator based on localized spherical frames, namely, needlets, combined with a hard-thresholding protocol and a sample-splitting scheme. The approach exploits the excellent spatial and frequency localization properties of needlets to adaptively capture the local features of the variance function. We prove that the proposed estimator achieves the minimax-optimal rate of convergence over spherical Besov spaces under standard loss functions, exhibiting spatial adaptivity without requiring prior knowledge of the regularity of the variance function. This adaptivity highlights the efficacy of the method in analyzing spherical data characterized by complex heteroskedastic errors, with potential applications in fields such as cosmology, environmental modeling, and geophysics

We study when geometric simplicity of decision boundaries, used here as a notion of interpretability, can conflict with accurate approximation of axis-aligned decision trees by shallow neural networks. Decision trees induce rule-based, axis-aligned decision regions (finite unions of boxes), whereas shallow ReLU networks are typically trained as score models whose predictions are obtained by thresholding. We analyze the infinite-width, bounded-norm, single-hidden-layer ReLU class through the Radon total variation ($\mathrm{R}\mathrm{TV}$) seminorm, which controls the geometric complexity of level sets. We first show that the hard tree indicator $1_A$ has infinite $\mathrm{R}\mathrm{TV}$. Moreover, two natural split-wise continuous surrogates–piecewise-linear ramp smoothing and sigmoidal (logistic) smoothing–also have infinite $\mathrm{R}\mathrm{TV}$ in dimensions $d>1$, while Gaussian convolution yields finite $\mathrm{R}\mathrm{TV}$ but with an explicit exponential dependence on $d$. We then separate two goals that are often conflated: classification after thresholding (recovering the decision set) versus score learning (learning a calibrated score close to $1_A$). For classification, we construct a smooth barrier score $S_A$ with finite $\mathrm{R}\mathrm{TV}$ whose fixed threshold $\tau=1$ exactly recovers the box. Under a mild tube-mass condition near $\partial A$, we prove an $L_1(P)$ calibration bound that decays polynomially in a sharpness parameter, along with an explicit $\mathrm{R}\mathrm{TV}$ upper bound in terms of face measures. Experiments on synthetic unions of rectangles illustrate the resulting accuracy–complexity tradeoff and how threshold selection shifts where training lands along it.

We study the mutual singularity of countable Gaussian mixture models (GMMs), with particular emphasis on infinite-dimensional settings. We first establish that a countable mixture of Gaussian probability measures is itself a well-defined probability measure. We then prove a general measure-theoretic result showing that if every component of one countable mixture is mutually singular with every component of another, then the two mixtures are mutually singular. Combining this result with the Feldman–Hájek characterization of equivalence and singularity for Gaussian measures yields a sufficient condition for the mutual singularity of countable Gaussian mixtures. We also discuss the mixed case, in which the presence of equivalent components prevents mutual singularity and leads naturally to a decomposition into singular and absolutely continuous parts. To illustrate these theoretical results, we present a series of numerical experiments involving high-dimensional Gaussian mixture models. The experiments demonstrate the emergence of increasing separability with dimension under different mechanisms, including mean shifts, covariance differences, and independently generated random mixtures. A complementary experiment with a shared Gaussian component shows that complete asymptotic separation fails when the pairwise singularity condition is violated. Together, the theoretical and numerical results provide a measure-theoretic framework for understanding asymptotic separability in high-dimensional Gaussian mixture models.

The asymptotic distribution of the likelihood-ratio statistic for testing parameters on the boundary is well known to be a chi-squared mixture. The mixture weights have been shown to correspond to the intrinsic volumes of an associated tangent cone, unifying a wide range of previously isolated special cases. While the weights are fully understood for an arbitrary number of parameters of interest on the boundary, much less is known when nuisance parameters are also constrained to the boundary, a situation that frequently arises in applications. We provide the first general characterization of the asymptotic distribution of the likelihood-ratio test statistic when both the number of parameters of interest and the number of nuisance parameters on the boundary are arbitrary. We analyze how the cone geometry changes when moving from a problem with K parameters of interest on the boundary to one with K-m parameters of interest and m nuisances. In the orthogonal case we show that the resulting change in the chi-bar weights admits a closed-form difference pattern that redistributes probability mass across adjacent degrees of freedom, and that this pattern remains the dominant component of the weight shift under arbitrary covariance structures when the nuisance vector is one-dimensional. For a generic number of nuisance parameters, we introduce a new rank-based aggregation of intrinsic volumes that yields an accurate approximation of the mixture weights. Comprehensive simulations support the theory and demonstrate the accuracy of the proposed approximation.

We propose a novel estimation framework for quadratic functionals of precision matrices in high-dimensional settings, particularly in regimes where the feature dimension $p$ exceeds the sample size $n$. Traditional moment-based estimators with bias correction remain consistent when $p<n$ (i.e., $p/n \to c <1$). However, they break down entirely once $p>n$, highlighting a fundamental distinction between the two regimes due to rank deficiency and high-dimensional complexity. Our approach resolves these issues by combining a spectral-moment representation with constrained optimization, resulting in consistent estimation under mild moment conditions. The proposed framework provides a unified approach for inference on a broad class of high-dimensional statistical measures. We illustrate its utility through two representative examples: the optimal Sharpe ratio in portfolio optimization and the multiple correlation coefficient in regression analysis. Simulation studies demonstrate that the proposed estimator effectively overcomes the fundamental $p>n$ barrier where conventional methods fail.

While multimodal mobility systems have the potential to bring many benefits to travelers, drivers, the environment, and traffic congestion, such systems typically involve multiple non-cooperative decision-makers who may selfishly optimize their own objectives without considering the overall system benefits. This paper aims to investigate market-based interactions of travelers and ride-sourcing drivers in the context of multimodal mobility systems. We propose a unified mathematical modeling framework to capture the decentralized travelers and drivers' decision-making process and balance the network's demand and supply by equilibrium pricing. Such a model allows analyses of the impact of decentralized decision-making on multimodal mobility efficiencies. The proposed formulation can be further convexified to efficiently compute the equilibrium ride-sourcing prices. We conduct numerical experiments on different settings of transportation networks to gain policy insights. We find that travelers prefer ride-sourcing and multimodal transportation more than the driving option when they are more sensitive to prices. We also find that travelers may need to be subsidized to use multimodal transportation when there is fewer transit hubs in the network or, ride-sourcing drivers become too sensitive to the prices. However, we find that more transit hubs in the network increases the total empty VMT of ride-sourcing drivers by increasing the total relocation time. The proposed model can be used by policymakers and platform operators to design pricing and subsidy schemes that align individual decision-making with system-level efficiency and evaluate the trade-offs between accessibility and environmental impacts in multimodal transportation networks.

We analyze neural scaling laws in a solvable model of last-layer fine-tuning where targets have intrinsic, instance-heterogeneous difficulty. In our Latent Instance Difficulty (LID) model, each input's target variance is governed by a latent “precision” drawn from a heavy-tailed distribution. While generalization loss recovers standard scaling laws, our main contribution connects this to inference. The pass@$k$ failure rate exhibits a power-law decay, $k^{-\beta_\text{eff}}$, but the observed exponent $\beta_\text{eff}$ is training-dependent. It grows with sample size $N$ before saturating at an intrinsic limit $\beta$ set by the difficulty distribution's tail. This coupling reveals that learning shrinks the “hard tail” of the error distribution: improvements in the model's generalization error steepen the pass@$k$ curve until irreducible target variance dominates. The LID model yields testable, closed-form predictions for this behavior, including a compute-allocation rule that favors training before saturation and inference attempts after. We validate these predictions in simulations and in two real-data proxies: CIFAR-10H (human-label variance) and a maths teacher-student distillation task.

We propose an extension of Markov-switching generalized additive models for location, scale, and shape (MS-GAMLSS) that allows covariates to influence not only the parameters of the state-dependent distributions but also the state transition probabilities. Traditional MS-GAMLSS, which combine distributional regression with hidden Markov models, typically assume time-homogeneous (i.e., constant) transition probabilities, thereby preventing regime shifts from responding to covariate-driven changes. Our approach overcomes this limitation by modeling the transition probabilities as smooth functions of covariates, enabling a flexible, data-driven characterization of covariate-dependent regime dynamics. Estimation is carried out within a penalized likelihood framework, where automatic smoothness selection controls model complexity and guards against overfitting. We evaluate the proposed methodology through simulations and applications to daily Lufthansa stock prices and Spanish energy prices. Our results show that incorporating macroeconomic indicators into the transition probabilities yields additional insights into market dynamics. Data and R code to reproduce the results are available online.

We develop a Bayesian nonparametric framework for inference in spatio-temporal Hawkes processes, extending existing theoretical results beyond the purely temporal setting. Our framework encompasses modelling both the background and triggering components of the Hawkes process through Gaussian Processes priors. Under appropriate smoothness and regularity assumptions on the true parameter and the nonparametric prior family, we derive explicit posterior contraction rates for the conditional intensity function and the model's parameter, in the asymptotic regime of repeatedly observed and independent sequences. Our analysis generalizes known contraction results for purely temporal Hawkes processes to the spatio-temporal setting, which allows to jointly model self-excitation across time and space in event data. These results provide, to our knowledge, the first theoretical guarantees for Bayesian nonparametric methods in spatio-temporal point data.

In medical diagnostics, leveraging multiple biomarkers can significantly improve classification accuracy compared to using a single biomarker. While existing methods based on exponential tilting or density ratio models have shown promise, their assumptions may be overly restrictive in practice. In this paper, we adopt a flexible semiparametric model that relates the density ratio of diseased to healthy subjects through an unknown monotone transformation of a linear combination of biomarkers. To enhance estimation efficiency, we propose a smoothed likelihood framework that exploits the smoothness in the underlying densities and transformation function. Building on the maximum smoothed likelihood methodology, we construct estimators for the model parameters and the associated probability density functions. We develop an effective computational algorithm for implementation, derive asymptotic properties of the proposed estimators, and establish procedures for estimating the receiver operating characteristic (ROC) curve and the area under the curve (AUC). Through simulation studies and a real-data application, we demonstrate that the proposed method yields more accurate and efficient estimates than existing approaches.