Papers

In this work, we develop a hypothesis testing framework to determine whether pairwise comparison data is generated by an underlying generalized Thurstone model $\mathcal{T}_F$ for a given choice function $F$. While prior work has predominantly focused on parameter estimation and uncertainty quantification for such models, we address the fundamental problem of minimax hypothesis testing for $\mathcal{T}_F$ models. We formulate this testing problem by introducing a notion of separation distance between general pairwise comparison models and the class of $\mathcal{T}_F$ models. We then derive upper and lower bounds on the critical threshold for testing that depend on the topology of the observation graph. For the special case of complete observation graphs, this threshold scales as $\Theta((nk)^{-1/2})$, where $n$ is the number of agents and $k$ is the number of comparisons per pair. Furthermore, we propose a hypothesis test based on our separation distance, construct confidence intervals, establish time-uniform bounds on the probabilities of type I and II errors using reverse martingale techniques, and derive minimax lower bounds using information-theoretic methods. Finally, we validate our results through experiments on synthetic and real-world datasets.

Single-arm studies in the early development phases of new treatments are not uncommon in the context of rare diseases or in paediatrics. If an assessment of efficacy is to be made at the end of such a study, the observed endpoints can be compared with reference values that can be derived from historical data. For a time-to-event endpoint, a statistical comparison with a reference curve can be made using the one-sample log-rank test. In order to ensure the interpretability of the results of this test, the role of the reference curve is crucial. This quantity is often estimated from a historical control group using a parametric procedure. Hence, it should be noted that it is subject to estimation uncertainty. However, this aspect is not taken into account in the one-sample log-rank test statistic. We analyse this estimation uncertainty for the common situation that the reference curve is estimated parametrically using the maximum likelihood method, and indicate how the variance estimation of the one-sample log-rank test can be adapted in order to take this variability into account. The resulting test procedures are illustrated using a data example and analysed in more detail using simulations, particularly in comparison with established two-sample methods.

Many modern datasets consist of multiple related matrices measured on a common set of units, with the goal of recovering a shared low-dimensional subspace. The Angle-based Joint and Individual Variation Explained (AJIVE) framework addresses this problem through equal-weight aggregation, which can be suboptimal when views exhibit statistical heterogeneity in signal-to-noise ratios and dimensions, as well as structural heterogeneity from individual components. For equal-weight AJIVE, we show that the previously identified “non-diminishing” error barrier is geometry dependent: under near-orthogonal deterministic loading orientations, the second-order term is reduced, whereas under sign-symmetric random loadings, it is centered and averages out, yielding a $K^{-1/2}$-type rate without iterative refinement. Under a majority sign-alignment condition in rank-one setting, a bias at the squared single-view perturbation scale can persist. For general weights, we establish error bounds that disentangle the two layers of heterogeneity, and propose HeteroJIVE, the weighted AJIVE estimator using an explicit weight that is optimal whenever its identifiability gap is constant. We also provide a data-driven plug-in implementation of HeteroJIVE, together with an optional geometry-adaptive extension of this data-driven procedure. Simulations and analyses of multi-omics and image data illustrate the practical benefits of HeteroJIVE.

Probabilistic seismic inverse modeling often requires the prediction of both spatially correlated geological heterogeneities (e.g., facies) and continuous parameters (e.g., rock and elastic properties). Generative adversarial networks (GANs) provide an efficient training-image-based simulation framework capable of reproducing complex geological models with high accuracy and comparably low generative cost. However, their application in stochastic geophysical inversion for multivariate property prediction is limited, as representing multiple coupled properties requires large and unstable networks with high memory and training demands. A more recent variant of GANs with spatially adaptive denormalization (SPADE-GAN) enables the direct conditioning of facies spatial distributions on local probability maps. Leveraging on such features, an iterative geostatistical inversion algorithm is proposed, SPADE-GANInv, integrating a pre-trained SPADE-GAN with geostatistical simulation, for the prediction of facies and multiple correlated continuous properties from seismic data. The SPADE-GAN is trained to reproduce realistic facies geometries, while sequential stochastic co-simulation predicts the spatial variability of the facies-dependent continuous properties. At each iteration, a set of subsurface realizations is generated and used to compute synthetic seismic data. The realizations providing the highest similarity coefficient to the observed data are used to update the subsurface probability models in the next iteration. The method is demonstrated on both 2-D synthetic scenarios and field data, targeting the prediction of facies, porosity, and acoustic impedance from full-stack seismic data. Results show that the algorithm enables accurate multivariate prediction, mitigates the impact of biased prior data, and accommodates additional local conditioning such as well logs.

In decentralized federated learning (DFL), the presence of abnormal clients, often caused by noisy or poisoned data, can significantly disrupt the learning process and degrade the overall robustness of the model. Previous methods on this issue often require a sufficiently large number of normal neighboring clients or prior knowledge of reliable clients, which reduces the practical applicability of DFL. To address these limitations, we develop here a novel adaptive DFL (aDFL) approach for robust estimation. The key idea is to adaptively adjust the learning rates of clients. By assigning smaller rates to suspicious clients and larger rates to normal clients, aDFL mitigates the negative impact of abnormal clients on the global model in a fully adaptive way. Our theory does not put any stringent conditions on neighboring nodes and requires no prior knowledge. A rigorous convergence analysis is provided to guarantee the oracle property of aDFL. Extensive numerical experiments demonstrate the superior performance of the aDFL method.

Hypothesis test plays a key role in uncertain statistics based on uncertain measure. This paper extends the parametric hypothesis of a single uncertain population to multiple cases, thereby addressing a broader range of scenarios. First, an uncertain family-wise error rate is defined to control the overall error in simultaneous testing. Subsequently, a hypothesis test of two uncertain populations is proposed, and the rejection region for the null hypothesis at a significance level is derived, laying the foundation for further analysis. Building on this, a homogeneity test for multiple populations is developed to assess whether the unknown population parameters differ significantly. When there is no significant difference in these parameters among finite populations or within a subset, a common test is used to determine whether they equal a fixed constant. Finally, homogeneity and common tests for normal uncertain populations with means and standard deviations are conducted under three cases: only means, only standard deviations, or both are unknown. Numerical simulations demonstrate the feasibility and accuracy of the proposed methods, and a real example is provided to illustrate their effectiveness.

Contrastive learning is among the most popular and powerful approaches for self-supervised representation learning, where the goal is to map semantically similar samples close together while separating dissimilar ones in the latent space. Existing theoretical methods assume that downstream task classes are drawn from the same latent class distribution used during the pretraining phase. However, in real-world settings, downstream tasks may not only exhibit distributional shifts within the same label space but also introduce new or broader label spaces, leading to domain generalization challenges. In this work, we introduce novel generalization bounds that explicitly account for both types of mismatch: domain shift and domain generalization. Specifically, we analyze scenarios where downstream tasks either (i) draw classes from the same latent class space but with shifted distributions, or (ii) involve new label spaces beyond those seen during pretraining. Our analysis reveals how the performance of contrastively learned representations depends on the statistical discrepancy between pretraining and downstream distributions. This extended perspective allows us to derive provable guarantees on the performance of learned representations on average classification tasks involving class distributions outside the pretraining latent class set.

Model-based filtering is often carried out while subject to an imperfect model, as learning partially-observable stochastic systems remains a challenge. Recent work on Bayesian inference found that tempering the likelihood or full posterior of an imperfect model can improve predictive accuracy, as measured by expected negative log likelihood. In this paper, we develop the tempered Bayes filter, improving estimation performance through both of the aforementioned, and one newly introduced, modalities. The result admits a recursive implementation with a computational complexity no higher than that of the original Bayes filter. Our analysis reveals that – besides the well-known fact in the field of Bayesian inference that likelihood tempering affects the balance between prior and likelihood – full-posterior tempering tunes the level of entropy in the final belief distribution. We further find that a region of the tempering space can be understood as interpolating between the Bayes- and MAP filters, recovering these as special cases. Analytical results further establish conditions under which a tempered Bayes filter achieves improved predictive performance. Specializing the results to the linear Gaussian case, we obtain the tempered Kalman filter. In this context, we interpret how the parameters affect the Kalman state estimate and covariance propagation. Empirical results confirm that our method consistently improves predictive accuracy over the Bayes filter baseline.

Located in northern Chile (23.7{\deg}S, 70.4{\deg}W), Antofagasta has an exceptionally arid and stable climate characterized by minimal precipitation and consistent weather patterns. Nevertheless, despite these climate conditions being meaningful for several research and practical applications, our understanding of weather dynamics remains limited. The available meteorological data from 1969 to 2016 is analogical, which presents a significant challenge to analyze because these records are riddled with missing values, some measurements were taken at irregular measuring intervals, making it an interesting puzzle to grasp the Antofagasta's climate scenario. To overcome this issue, we present a comprehensive statistical analysis of atmospheric temperature, pressure, and humidity time series. Our analytical approach involves the q-triplet calculation method, serving as a powerful tool to identify distinctive behavior within systems under non-equilibrium states. Our results suggest that, in general, the q-triplet values satisfy the condition $q_\text{sens}<1<q_\text{stat}<q_\text{rel}$, a pattern that has been observed in previous studies.

We propose an observation-driven modeling framework that allows model parameters to vary over time through an implicit score-driven (ISD) update. The ISD update maximizes the logarithmic observation density with respect to the parameter vector while penalizing the weighted L2 norm relative to a one-step-ahead predicted parameter. This yields an implicit stochastic-gradient update. We show that the popular class of explicit score-driven (ESD) models arises when the observation log density is linearly approximated around the prediction. By preserving the full density, the ISD update extends the favorable local properties of the ESD update to a global setting. For log-concave observation densities, whether correctly specified or not, the ISD filter is stable for all learning rates, and its updates are contractive in mean squared error toward the (pseudo-)true parameter at every time step. We demonstrate the usefulness of ISD filters in simulations and empirical applications in finance and macroeconomics.

To address the scalability limitations of Gaussian process (GP) regression, several approximation techniques have been proposed. One such method is based on tensor networks, which utilizes an exponential number of basis functions without incurring exponential computational cost. However, extending this model to a fully probabilistic formulation introduces several design challenges. In particular, for tensor train (TT) models, it is unclear which TT-core should be treated in a Bayesian manner. We introduce a Bayesian tensor train kernel machine that applies Laplace approximation to estimate the posterior distribution over a selected TT-core and employs variational inference (VI) for precision hyperparameters. Experiments show that core selection is largely independent of TT-ranks and feature structure, and that VI replaces cross-validation while offering up to 65x faster training. The method's effectiveness is demonstrated on an inverse dynamics problem.

Zero-shot anomaly classification and segmentation (AC/AS) aim to detect anomalous samples and regions without any training data, a capability increasingly crucial in industrial inspection and medical imaging. This dissertation aims to investigate the core challenges of zero-shot AC/AS and presents principled solutions rooted in theory and algorithmic design. We first formalize the problem of consistent anomalies, a failure mode in which recurring similar anomalies systematically bias distance-based methods. By analyzing the statistical and geometric behavior of patch representations from pre-trained Vision Transformers, we identify two key phenomena - similarity scaling and neighbor-burnout - that describe how relationships among normal patches change with and without consistent anomalies in settings characterized by highly similar objects. We then introduce CoDeGraph, a graph-based framework for filtering consistent anomalies built on the similarity scaling and neighbor-burnout phenomena. Through multi-stage graph construction, community detection, and structured refinement, CoDeGraph effectively suppresses the influence of consistent anomalies. Next, we extend this framework to 3D medical imaging by proposing a training-free, computationally efficient volumetric tokenization strategy for MRI data. This enables a genuinely zero-shot 3D anomaly detection pipeline and shows that volumetric anomaly segmentation is achievable without any 3D training samples. Finally, we bridge batch-based and text-based zero-shot methods by demonstrating that CoDeGraph-derived pseudo-masks can supervise prompt-driven vision-language models. Together, this dissertation provides theoretical understanding and practical solutions for the zero-shot AC/AS problem.

Models of imitation and herding behavior often underestimate the role of individualistic actions and assume symmetric boundary conditions. However, real-world systems (e.g., electoral processes) frequently involve asymmetric boundaries. In this study, we explore how arbitrarily placed boundary conditions influence the mean first passage time in the symmetric noisy voter model, and how individualistic behavior amplifies this asymmetry. We derive exact analytical expressions for mean first passage time that accommodate any initial condition and two types of boundary configurations: (i) both boundaries absorbing, and (ii) one absorbing and one reflective. In both scenarios, mean first passage time exhibits a clear asymmetry with respect to the initial condition, shaped by the boundary placement and the rate of independent transitions. Symmetry in mean first passage time emerges only when absorbing boundaries are equidistant from the midpoint. Additionally, we show that Kramers' law holds in both configurations when the rate of independent transitions is large. Our analytical results are in excellent agreement with numerical simulations, reinforcing the robustness of our findings.

Inverse problems arise across scientific and engineering domains, where the goal is to infer hidden parameters or physical fields from indirect and noisy observations. Classical approaches, such as variational regularization and Bayesian inference, provide well established theoretical foundations for handling ill posedness. However, these methods often become computationally restrictive in high dimensional settings or when the forward model is governed by complex physics. Physics Informed Neural Networks (PINNs) have recently emerged as a promising framework for solving inverse problems by embedding physical laws directly into the training process of neural networks. In this paper, we introduce a new perspective on the Bayesian Physics Informed Neural Network (BPINN) framework, extending classical PINNs by explicitly incorporating training data generation, modeling and measurement uncertainties through Bayesian prior modeling and doing inference with the posterior laws. Also, as we focus on the inverse problems, we call this method BPINN-IP, and we show that the standard PINN formulation naturally appears as its special case corresponding to the Maximum A Posteriori (MAP) estimate. This unified formulation allows simultaneous exploitation of physical constraints, prior knowledge, and data-driven inference, while enabling uncertainty quantification through posterior distributions. To demonstrate the effectiveness of the proposed framework, we consider inverse problems arising in infrared image processing, including deconvolution and super-resolution, and present results on both simulated and real industrial data.

Stochastic models of reaction networks are widely used to capture intrinsic noise in complex systems in the life sciences. Typical formulations of these models are based on Markov processes for which there is extensive research on efficient simulation and inference. However, there are complex processes in biology, such as gene transcription and translation, that introduce history dependent dynamics requiring non-Markovian processes to accurately capture the stochastic dynamics of the system. This greater realism comes with additional computational challenges for simulation and parameter inference. We develop efficient stochastic simulation algorithms for well-mixed non-Markovian stochastic reaction networks with stochastic delays that depend on system state and time. Our methods generalize the next reaction method and $\tau$-leaping method to support arbitrary inter-event time distributions while preserving computational scalability. We also introduce a coupling scheme to generate exact non-Markovian sample paths that are positively correlated to an approximate non-Markovian $\tau$-leaping sample path. This enables substantial computational gains for simulation and Bayesian inference through multilevel Monte Carlo and multifidelity schemes. We demonstrate the effectiveness of our approach using several non-Markovian examples, showing substantial gains in both simulation accuracy and inference efficiency. These results extend the practical applicability of non-Markovian models in systems biology and beyond.

The stochastic Polyak step size (SPS) has proven to be a promising choice for stochastic gradient descent (SGD), delivering competitive performance relative to state-of-the-art methods on smooth convex and non-convex optimization problems, including deep neural network training. However, extensions of this approach to non-smooth settings remain in their early stages, often relying on interpolation assumptions or requiring knowledge of the optimal solution. In this work, we propose a novel SPS variant, Safeguarded SPS (SPS$_{safe}$), for the stochastic subgradient method, and provide rigorous convergence guarantees for non-smooth convex optimization with no need for strong assumptions. We further incorporate momentum into the update rule, yielding equally tight theoretical results. Comprehensive experiments on convex benchmarks and deep neural networks corroborate our theory: the proposed step size achieves competitive performance to existing adaptive baselines and exhibits stable behavior across a wide range of problem settings. Finally, in the context of deep neural network training, the gradient norms under our step size do not collapse to (near) zero, indicating robustness to vanishing gradients.

High-throughput screening (HTS) is useful for evaluating chemicals for potential human health risks. However, given the extraordinarily large number of genes, assay endpoints, and chemicals of interest, available data are sparse, with dose-response curves missing for the vast majority of chemical-gene pairs. Although gene ontologies characterize similarity among genes with respect to known cellular functions and biological pathways, the sensitivity of various pathways to environmental contaminants remains unclear. We propose a novel Dose-Activity Response Tracking (DART) approach to predict the biological activity of chemicals across genes using information on chemical structural properties and gene ontologies within a Bayesian factor model. Designed to provide toxicologists with a flexible tool applicable across diverse HTS assay platforms, DART reveals the latent processes driving dose-response behavior and predicts new activity profiles for chemical-gene pairs lacking experimental data. We demonstrate the performance of DART through simulation studies and an application to a vast new multi-experiment data set consisting of dose-response observations generated by the exposure of HepG2 cells to per- and polyfluoroalkyl substances (PFAS), where it provides actionable guidance for chemical prioritization and inference on the structural and functional mechanisms underlying assay activation.

Efficient sampling from Boltzmann distributions over discrete variables is a fundamental operation in a wide range of applications. While fast non-MCMC samplers have recently emerged as promising alternatives to conventional MCMC methods, their practical use for probabilistic learning remains hindered by the difficulty of estimating the effective temperature of the generated samples. In this work, we begin by introducing Langevin simulated bifurcation (LSB), a Boltzmann sampler that enables fast and parallel sampling with accuracy comparable to sequential MCMC methods. To address the challenge of unknown effective temperature, we propose conditional expectation matching (CEM), an efficient estimation method applicable to energy-based models (EBMs) with exploitable conditional independence structures. Building on these components, we further develop a learning framework, termed sampler adaptive learning (SAL), which adaptively adjusts the model temperature to match that of the distribution induced by fast non-MCMC sampling. We demonstrate the effectiveness of LSB, CEM, and SAL on semi-restricted Boltzmann machines (SRBMs), a class of EBMs that are difficult to train using conventional approaches. LSB achieves orders-of-magnitude acceleration over Gibbs sampling while maintaining comparable or higher accuracy, and CEM enables accurate temperature estimation of the resulting distribution with negligible computational overhead. As a consequence, SAL enables efficient training of SRBMs and outperforms conventional Boltzmann machine learning methods on synthetic spin-glass datasets. In addition, the trained models achieve strong performance across multiple tasks. These results establish LSB as a fast and accurate Boltzmann sampler and provide key insights that enable practical applications of fast non-MCMC sampling methods via efficient temperature estimation with CEM.

We study the statistical properties of the Ostrom-Weighted Bootstrap (OWB), a hierarchical, variance-aware resampling scheme for imputing missing values and estimating archetypes in multi-agent voting data. At Level~1, under mild linear model assumptions, the ideal OWB estimator – with known persona-level (agent-level) variances – is shown to be the Gauss–Markov best linear unbiased estimator (BLUE) and to strictly dominate uniform weighting whenever persona variances differ. At Level~2, within a canonical hierarchical normal model, the ideal OWB coincides with the conditional Bayesian posterior mean of the archetype. We then analyze the feasible OWB, which replaces unknown variances with hierarchically pooled empirical estimates, and show that it can be interpreted as both a feasible generalized least-squares (FGLS) and an empirical-Bayes shrinkage estimator with asymptotically valid weighted bootstrap confidence intervals under mild regularity conditions. Finally, we establish a Zero-NaN Guarantee: as long as each petal has at least one finite observation, the OWB imputation algorithm produces strictly NaN-free completed data using only explicit, non-uniform bootstrap weights and never resorting to uniform sampling or numerical zero-filling. To our knowledge, OWB is the first resampling-based method that simultaneously achieves exact BLUE optimality, conditional Bayesian posterior mean interpretation, empirical Bayes shrinkage of precision parameters, asymptotic efficiency via FGLS, consistent weighted bootstrap inference, and provable zero-NaN completion under minimal data assumptions.

We present a transfer-learning generative downscaling framework to reconstruct fine resolution satellite images from coarse scale inputs. Our approach combines a lightweight U-Net transfer encoder with a diffusion-based generative model. The simpler U-Net is first pretrained on a long time series of coarse resolution data to learn spatiotemporal representations; its encoder is then frozen and transferred to a larger downscaling model as physically meaningful latent features. Our application uses NASA's MERRA-2 reanalysis as the low resolution source domain (50 km) and the GEOS-5 Nature Run (G5NR) as the high resolution target (7 km). Our study area included a large area in Asia, which was made computationally tractable by splitting into two subregions and four seasons. We conducted domain similarity analysis using Wasserstein distances confirmed minimal distributional shift between MERRA-2 and G5NR, validating the safety of parameter frozen transfer. Across seasonal regional splits, our model achieved excellent performance (R2 = 0.65 to 0.94), outperforming comparison models including deterministic U-Nets, variational autoencoders, and prior transfer learning baselines. Out of data evaluations using semivariograms, ACF/PACF, and lag-based RMSE/R2 demonstrated that the predicted downscaled images preserved physically consistent spatial variability and temporal autocorrelation, enabling stable autoregressive reconstruction beyond the G5NR record. These results show that transfer enhanced diffusion models provide a robust and physically coherent solution for downscaling a long time series of coarse resolution images with limited training periods. This advancement has significant implications for improving environmental exposure assessment and long term environmental monitoring.

In emergency response and other high-stakes societal applications, early-stage state estimates critically shape downstream outcomes. Yet, these initial state estimates-often based on limited or biased information-can be severely misaligned with reality, constraining subsequent actions and potentially causing catastrophic delays, resource misallocation, and human harm. Under the stationary bootstrap baseline (zero transition and no rejuvenation), bootstrap particle filters exhibit Stationarity-Induced Posterior Support Invariance (S-PSI), wherein regions excluded by the initial prior remain permanently unexplorable, making corrections impossible even when new evidence contradicts current beliefs. While classical perturbations can in principle break this lock-in, they operate in an always-on fashion and may be inefficient. To overcome this, we propose a diffusion-driven Bayesian exploration framework that enables principled, real-time correction of early state estimation errors. Our method expands posterior support via entropy-regularized sampling and covariance-scaled diffusion. A Metropolis-Hastings check validates proposals and keeps inference adaptive to unexpected evidence. Empirical evaluations on realistic hazardous-gas localization tasks show that our approach matches reinforcement learning and planning baselines when priors are correct. It substantially outperforms classical SMC perturbations and RL-based methods under misalignment, and we provide theoretical guarantees that DEPF resolves S-PSI while maintaining statistical rigor.

Generative models have the potential to transform the way we emulate Earth's changing climate. Previous generative approaches rely on weather-scale autoregression for climate emulation, but this is inherently slow for long climate horizons and has yet to demonstrate stable rollouts under nonstationary forcings. Here, we introduce Spatiotemporal Pyramid Flows (SPF), a new class of flow matching approaches that model data hierarchically across spatial and temporal scales. Inspired by cascaded video models, SPF partitions the generative trajectory into a spatiotemporal pyramid, progressively increasing spatial resolution to reduce computation and coupling each stage with an associated timescale to enable direct sampling at any temporal level in the pyramid. This design, together with conditioning each stage on prescribed physical forcings (e.g., greenhouse gases or aerosols), enables efficient, parallel climate emulation at multiple timescales. On ClimateBench, SPF outperforms strong flow matching baselines and pre-trained models at yearly and monthly timescales while offering fast sampling, especially at coarser temporal levels. To scale SPF, we curate ClimateSuite, the largest collection of Earth system simulations to date, comprising over 33,000 simulation-years across ten climate models and the first dataset to include simulations of climate interventions. We find that the scaled SPF model demonstrates good generalization to held-out scenarios across climate models. Together, SPF and ClimateSuite provide a foundation for accurate, efficient, probabilistic climate emulation across temporal scales and realistic future scenarios. Data and code is publicly available at https://github.com/stanfordmlgroup/spf .

In our previous article, we estimated excess mortality during in Aotearoa New Zealand for 2020 to 2023. Since our work was published, updated population estimates have been released by Statistics NZ. In this short letter, we provide the results of applying our original model to the new population data. Our updated excess mortality estimate of 2.0% (95% CI [0.5%, 3.3%]) is 1.3 percentage points higher than our original estimate because the new population estimates for the period 2020 to 2023 are smaller, but the main conclusions of our original article still apply.

Increasing climate change and habitat loss are driving unprecedented shifts in species distributions. Conservation professionals urgently need timely, high-resolution predictions of biodiversity risks, especially in ecologically diverse regions like Africa. We propose EcoCast, a spatio-temporal model designed for continual biodiversity and climate risk forecasting. Utilizing multisource satellite imagery, climate data, and citizen science occurrence records, EcoCast predicts near-term (monthly to seasonal) shifts in species distributions through sequence-based transformers that model spatio-temporal environmental dependencies. The architecture is designed with support for continual learning to enable future operational deployment with new data streams. Our pilot study in Africa shows promising improvements in forecasting distributions of selected bird species compared to a Random Forest baseline, highlighting EcoCast's potential to inform targeted conservation policies. By demonstrating an end-to-end pipeline from multi-modal data ingestion to operational forecasting, EcoCast bridges the gap between cutting-edge machine learning and biodiversity management, ultimately guiding data-driven strategies for climate resilience and ecosystem conservation throughout Africa.

Constructing flexible probability models that respect constraints on key functionals – such as the mean – is a fundamental problem in nonparametric statistics. Existing approaches lack systematic tools for enforcing such constraints while retaining full modeling flexibility. This paper introduces a new representation for univariate probability measures based on discrete sequential barycenter arrays (SBA). We study structural properties of SBA representations and establish new approximation results. In particular, we show that for any target distribution, its SBA-based discrete approximations converge in both the weak topology and in Wasserstein distances, and that the representation is exact for all distributions with finite discrete support. We further characterize a broad class of measures whose SBA partitions exhibit regularity and induce increasingly fine meshes, and we prove that this class is dense in standard probabilistic topologies. These theoretical results enable the construction of probability models that preserve prescribed values – or full distributions – of the mean while maintaining large support. As an application, we derive a mixture model for density estimation whose induced mixing distribution has a fixed or user-specified mean. The resulting framework provides a principled mechanism for incorporating mean constraints in nonparametric modeling while preserving strong approximation properties. The approach is illustrated using both simulated and real data.

We introduce a compact probabilistic model for two-player and two-team (four-player) squash matches, along with a practical skill-comparison rule derived from point-scoring probabilities. Using recorded shot types and court locations, we analyze how shot distributions differ between professional-level and intermediate-level players. Our analysis shows that professional players use a wider variety of shots and favor backcourt play to maintain control, while intermediate players concentrate more on mid-court shots, generate more errors, and exercise less positional control. These results quantify strategic differences in squash, offer a simple method to compare player and team skill, and provide actionable insights for sports analytics and coaching.

We propose the Polyads estimator, a new method to estimate structural parameters in weighted multi-way networks while controlling for rich, arbitrary structures of fixed effects. The method is based on a series of classification tasks and is agnostic to both the number and structure of fixed effects. Unlike full maximum likelihood, our estimator does not suffer from the incidental parameter problem: it is consistent and satisfies a Central Limit Theorem with no asymptotic bias, even when some dimensions of the network are short. For sparsely connected networks, it is also computationally faster than PPML. We provide experimental evidence that our estimator yields more reliable confidence intervals, i.e., better empirical coverage, than PPML and its bias-correction strategies. These improvements hold even under model misspecification and are more pronounced in sparse settings. While PPML remains competitive in dense, low-dimensional data, our approach offers a robust alternative for multi-way models that scales efficiently with sparsity. We apply the method to French health insurance claims data to study how a 2017 physician fee reform affected the geography and gender composition of doctor-patient connections.

Two-phase sampling offers a cost-effective way to validate error-prone covariate measurements in biomedical databases. Inexpensive or easy-to-obtain information is collected for the entire study in Phase I. Then, a subset of patients undergoes cost-intensive validation (e.g., expert chart review) to collect more accurate data in Phase II. When balancing primary and secondary analyses, competing models and priorities can result in poorly defined objectives for the most informative Phase II sampling criterion. Extreme tail sampling (ETS), wherein patients with the smallest and largest values of a particular quantity (like a covariate or residual) are selected, can offer great statistical efficiency in two-phase studies when focusing on a single analytic objective by targeting observations with the biggest contributions to the Fisher information. We propose an intuitive, easy-to-use approach that extends ETS to balance and prioritize explaining the largest amount of variability across multiple models of interest. Using principal components analysis, we succinctly summarize the inherent variability of all models' error-prone exposures. Then, we sample patients with the most extreme values of the first principal component for validation. Through extensive simulations and an application to the National Health and Nutrition Examination Survey (NHANES), the proposed strategy offered simultaneous efficiency gains across multiple models of interest. Its advantages persisted across various real-world scenarios, including correlated or heterogeneous measurement error. When designing a validation study, concentrating on a single model may be short-sighted. Strategically allocating resources more broadly balances multiple analytical goals simultaneously. Employing dimension reduction before sampling will allow this strategy to scale up well to big-data applications with many error-prone exposures.

In nonclinical pharmaceutical development, tolerance intervals are critical in ensuring product and process quality. They are statistical intervals designed to contain a specified proportion of the population with a given confidence level. Parametric and non-parametric methods have been developed to obtain tolerance intervals. The former work with small samples but can be affected by distribution misspecification. The latter offer larger flexibility but require large sample sizes. As an alternative, we propose Dirichlet process-based Bayesian nonparametric tolerance intervals to overcome the limitations. We develop a computationally efficient tolerance interval construction algorithm based on the analytically tractable quantile process of the Dirichlet process. Simulation studies show that our new approach is very robust to distributional assumptions and performs as efficiently as existing tolerance interval methods. To illustrate how the model works in practice, we apply our method to the tolerance interval estimation for potency data.

Timely assessment of current conditions is essential especially for small, open economies such as Singapore, where external shocks transmit rapidly to domestic activity. We develop a real-time nowcasting framework for quarterly GDP growth using a high-dimensional panel of approximately 70 indicators, encompassing economic and financial indicators over 1990Q1-2023Q2. The analysis covers penalized regressions, dimensionality-reduction methods, ensemble learning algorithms, and neural architectures, benchmarked against a Random Walk, an AR(3), and a Dynamic Factor Model. The pipeline preserves temporal ordering through an expanding-window walk-forward design with Bayesian hyperparameter optimization, and uses moving block-bootstrap procedures both to construct prediction intervals and to obtain confidence bands for feature-importance measures. It adopts model-specific and XAI-based explainability tools. A Model Confidence Set procedure identifies statistically superior learners, which are then combined through simple, weighted, and exponentially weighted schemes; the resulting time-varying weights provide an interpretable representation of model contributions. Predictive ability is assessed via Giacomini-White tests. Empirical results show that penalized regressions, dimensionality-reduction models, and GRU networks consistently outperform all benchmarks, with RMSFE reductions of roughly 40-60%; aggregation delivers further gains. Feature-attribution methods highlight industrial production, external trade, and labor-market indicators as dominant drivers of Singapore's short-run growth dynamics.