Papers

Proper scoring rules are essential for evaluating probabilistic forecasts. We propose a simple algebraic rearrangement of the Yates covariance decomposition of the Brier score into three independently non-negative terms: a variance mismatch term, a correlation deficit term, and a calibration-in-the-large term. This rearrangement makes the optimality conditions for perfect forecasting transparent: the optimal forecast must simultaneously match the variance of outcomes, achieve perfect positive correlation with outcomes, and match the mean of outcomes. Any deviation from these conditions results in a positive contribution to the Brier score.

We provide uniform convergence rates for kernel averages on $[0,1]$ under equally-spaced fixed design points of the form $x_{t,T}=t/T,\ t\in\{1,\dotsc, T\},\ T\in\mathbb{N}$. The rates of weak and strong uniform consistency are derived under strong mixing and moment conditions and do not require stationarity. The analysis exploits the grid structure and thus complements existing random-design results such as those of Hansen (2008) and Kristensen (2009), which rely on density-based conditioning arguments. The framework accommodates dependent triangular arrays and is particularly relevant for nonparametric methods applied to time series observed on deterministic grids. As an application, we derive uniform convergence rates for the local linear estimator in a nonparametric regression model with time-varying autoregressive errors. The theoretical results are illustrated through Monte Carlo experiments and an empirical application.

Deep learning (DL) methods are currently being explored to restore images from sparse-view-, limited-data-, and undersampled-based acquisitions in medical applications. Although outputs from DL may appear visually appealing based on likability/subjective criteria (such as less noise, smooth features), they may also suffer from hallucinations. This issue is further exacerbated by a lack of easy-to-use techniques and robust metrics for the identification of hallucinations in DL outputs. In this work, we propose performing Fourier Ring Correlation (FRC) analysis over small patches and concomitantly (s)canning across DL outputs and their reference counterparts to detect hallucinations (termed as sFRC). We describe the rationale behind sFRC and provide its mathematical formulation. The parameters essential to sFRC may be set using predefined hallucinated features annotated by subject matter experts or using imaging theory-based hallucination maps. We use sFRC to detect hallucinations for three undersampled medical imaging problems: CT super-resolution, CT sparse view, and MRI subsampled restoration. In the testing phase, we demonstrate sFRC's effectiveness in detecting hallucinated features for the CT problem and sFRC's agreement with imaging theory-based outputs on hallucinated feature maps for the MR problem. Finally, we quantify the hallucination rates of DL methods on in-distribution versus out-of-distribution data and under increasing subsampling rates to characterize the robustness of DL methods. Beyond DL-based methods, sFRC's effectiveness in detecting hallucinations for a conventional regularization-based restoration method and a state-of-the-art unrolled method is also shown.

In this paper we consider a population process evolving on a dynamic random graph. The dynamic random graph is an Erdős–Rényi graph that is resampled every time unit, independently of the previous ones, with `edge existence probability' $p$. The population process consists of $M$ individuals which reside at the vertices of the dynamic graph. At each point in time any of the $M$ individuals, supposing it resides at a vertex with $k$ neighbors, jumps to an adjacent vertex with probability $k/(k+1)$ (where this adjacent vertex is picked uniformly at random), and with probability $1/(k+1)$ it stays where it is. We suppose we observe the numbers of individuals at each of the vertices, but not the evolving random graph itself. We propose two estimators for $p$, and establish their consistency and asymptotic normality.

Independence testing is a fundamental problem in statistical inference: given samples from a joint distribution $p$ over multiple random variables, the goal is to determine whether $p$ is a product distribution or is $\epsilon$-far from all product distributions in total variation distance. In the non-parametric finite-sample regime, this task is notoriously expensive, as the minimax sample complexity scales polynomially with the support size. In this work, we move beyond these worst-case limitations by leveraging the framework of augmented distribution testing. We design independence testers that incorporate auxiliary, but potentially untrustworthy, predictive information. Our framework ensures that the tester remains robust, maintaining worst-case validity regardless of the prediction's quality, while significantly improving sample efficiency when the prediction is accurate. Our main contributions include: (i) a bivariate independence tester for discrete distributions that adaptively reduces sample complexity based on the prediction error; (ii) a generalization to the high-dimensional multivariate setting for testing the independence of $d$ random variables; and (iii) matching minimax lower bounds demonstrating that our testers achieve optimal sample complexity.

Regression is the workhorse of statistics, and is often faced with real data that contain outliers. When these are casewise outliers, that is, cases that are entirely wrong or belong to a different population, the issue can be remedied by existing casewise robust regression methods. It is another matter when cellwise outliers occur, that is, suspicious individual entries in the data matrix containing the regressors and the response. We propose a new regression method that is robust to both casewise and cellwise outliers, and handles missing values as well. Its construction allows for skewed distributions. We show that it obeys the first breakdown result for cellwise robust regression. It is also the first such method that is geared to making robust out-of-sample predictions. Its performance is studied by simulation, and it is illustrated on a substantial real dataset.

K-Means is usually treated as a discrete procedure outside gradient-based learning, whereas normalized radial basis function (RBF) layers are smooth. We make precise the sense in which K-Means is the zero-temperature limit of such a layer. Relaxing the K-Means assignments to the simplex with a Shannon entropy penalty yields the normalized Gaussian RBF responsibilities and a reduced objective $F_\sigma$ with $0\le J-F_\sigma\le 2n\sigma^2\log k$, so $F_\sigma$ $\Gamma$-converges to the K-Means distortion $J$. We keep four levels of statement apart. For the objective, minimal values and minimizers converge, and above the critical temperature $\sigma^2=\lambda_{\max}$ all centroids at the mean form a strict local minimizer. For optimization, alternating minimization is a preconditioned gradient method on $F_\sigma$ whose hard limit is Lloyd's algorithm. For one update, under a margin $\Delta_{\min}>0$, the soft centroid map approaches Lloyd's at rate $O(e^{-\Delta_{\min}/2\sigma^2})$. For fixed points and trajectories, every nondegenerate Lloyd fixed point has a nearby soft local minimizer, and soft iterates keep Lloyd's partitions while Lloyd's path keeps a margin. With the Tsallis entropy of order 3/2, Entmax-1.5 recovers the hard assignments, the Lloyd update and, along a path with margin, Lloyd's trajectory exactly for $\sigma\le\sqrt{\Delta_{\min}}/2$, a sharp threshold. Experiments on sixteen datasets confirm every bound, rate and threshold, and the trajectory statements at the edge of their hypotheses. As a differentiable K-Means term, $F_\sigma$ shows the predicted effects: its gradients do not vanish at low temperature, its closed-form centroid update needs no learning rate, a fixed temperature crosses the critical one as representations contract, and soft responsibilities keep a vector-quantized codebook in use.

When multiple datasets describe complementary information about the same set of entities, for example, brain scans of an individual over time, global trade network across years, or user information across social media platforms, integrating these snapshots allows us to see a more holistic picture. A common way of identifying structure in data is through clustering, but while clustering may be applied to each dataset separately, we learn more in the multi-view setting by identifying joint clusters. We consider a clustering problem where each view conflates some of these joint clusters, only revealing partial information, and seek to recover the true joint cluster structure. We introduce this multi-view clustering model and a method for recovering it: the transposed Khatri-RAo Framework for joinT cluster recoverY (KRAFTY). The model is flexible and can accommodate a variety of data-generating processes, including latent positions in random dot product graphs and Gaussian mixtures. A key advantage of KRAFTY is that it represents joint clusters in a space with sufficient dimension so that each joint cluster occupies an orthogonal subspace in the transposed Khatri-Rao matrix, which results in a sharp drop in the scree plot at the true number of joint clusters, enabling easy model selection. Our simulations show that when the number of joint clusters exceeds the sum of the numbers of clusters in each individual view, our method outperforms existing methods in both joint clustering accuracy and estimation of the number of joint clusters.

Survey sampling is concerned with the estimation of finite population parameters. In practice, survey data suffer from item nonresponse, which is commonly handled through imputation, i.e., replacing missing values with predicted values. As a result, the properties of the resulting imputed estimator depend critically on the properties of the prediction method used. In turn, prediction methods themselves depend on the choice of variables and tuning parameters used to fit the imputation model. In this article, we study the problem of variable selection for linear regression imputation. Although variable selection has been widely studied across many fields, primarily for identification or prediction, its role in imputation for survey data has received comparatively little attention. We introduce the notion of an optimal imputation model defined through an oracle loss function and show that, with probability tending to one, the optimal model coincides with the true model. We also examine the consequences of using misspecified models – either omitting relevant covariates or including irrelevant ones – on consistency and asymptotic variance. We then develop a complete methodological framework for constructing confidence intervals after model selection. The proposed confidence intervals are shown to be asymptotically valid and optimal among all candidate models. Simulation studies indicate that the proposed methodology performs well in finite samples.

This study introduces a deep learning-based framework for forecasting weather-related traffic crash risk using heterogeneous spatiotemporal data. Given the complex, non-linear relationship between crash occurrence and factors such as road characteristics, and traffic conditions, we propose an ensemble of Convolutional Long Short-Term Memory (ConvLSTM) models trained over overlapping spatial grids. This approach captures both spatial dependencies and temporal dynamics while addressing spatial heterogeneity in crash patterns. North Carolina was selected as the study area due to its diverse weather conditions, with historical crash, weather, and traffic data aggregated at 5-mi by 5-mi grid resolution. The framework was evaluated using Mean Squared Error (MSE), Root Mean Squared Error (RMSE), and spatial cross-K analysis. Results show that the ensembled ConvLSTM significantly outperforms baseline models, including linear regression, ARIMA, and standard ConvLSTM, particularly in high-risk zones. The ensemble approach effectively combines the strengths of multiple ConvLSTM models, resulting in lower MSE and RMSE values across all regions, particularly when data from different crash risk zones are aggregated. Notably, the model performs exceptionally well in volatile high-risk areas (Cluster 1), achieving the lowest MSE and RMSE, while in stable low-risk areas (Cluster 2), it still improves upon simpler models but with slightly higher errors due to challenges in capturing subtle variations.

The Hybrid Online Learning Problem, where features are drawn i.i.d. from an unknown distribution but labels are generated adversarially, is a well-motivated setting positioned between statistical and fully-adversarial online learning. Prior work has presented a dichotomy: algorithms that are statistically-optimal, but computationally intractable (Wu et al., 2023), and algorithms that are computationally-efficient (given an ERM oracle), but statistically-suboptimal (Wu et al., 2024). This paper takes a significant step towards achieving statistical optimality and computational efficiency simultaneously in the Hybrid Learning setting. To do so, we consider a structured setting, where the Adversary is constrained to pick labels from an expressive, but fixed, class of functions $R$. Our main result is a new learning algorithm, which runs efficiently given an ERM oracle and obtains regret scaling with the Rademacher complexity of a class derived from the Learner's hypothesis class $H$ and the Adversary's label class $R$. As a key corollary, we give an oracle-efficient algorithm for computing equilibria in stochastic zero-sum games when action sets may be high-dimensional but the payoff function exhibits a type of low-dimensional structure. Technically, we develop a number of tools for the design and analysis of our learning algorithm, including a novel Frank-Wolfe reduction with "truncated entropy regularizer" and a new tail bound for sums of "hybrid" martingale difference sequences.

With the advent of effective pre-exposure prophylaxis agents, active-controlled HIV prevention trials have become a common study design. Nevertheless, estimating absolute efficacy relative to a placebo remains important. In this paper, we introduce a novel application of proximal causal inference methods to estimate the counterfactual cumulative HIV incidence under placebo for participants in an active-controlled trial of cabotegravir, using external control data from a placebo-controlled trial with similar eligibility criteria. We leverage baseline sexually transmitted infection status and geographic region as negative control outcome and exposure variables, respectively. We address two key challenges: unmeasured differences in HIV risk between trials and statistical difficulties arising from low HIV incidence rates in both studies. To overcome these challenges, we develop two proximal inference approaches: (1) a semiparametric inverse probability of censoring weighting estimator, and (2) a two-stage regression-based strategy tailored to low-event-rate settings. Our theoretical and numerical investigations demonstrate these methods yield reliable estimates of the counterfactual one-year cumulative HIV incidence under placebo, and provide robust evidence of the superior efficacy of cabotegravir compared with placebo. These findings highlight the potential of proximal inference methods to estimate placebo-controlled effects in both single-arm and active-controlled trials by leveraging external controls.

Statistics educators recommend teaching with real data with relevant contexts, but defining relevancy is challenging and varies by student. We investigated whether providing student choice of data context increases engagement through a quasi-experiment in two sections of an introductory probability and statistics course at a large public university (n=65 consenting students). Sections alternated as treatment and control: during their treatment, students chose weekly homework from three similar instructor-provided options varying by data context; during control weeks, they received randomly assigned contexts. We found no significant difference in homework grades between treatment and control conditions. However, thematic analysis revealed students with choice reported enhanced engagement and motivation, greater appreciation for statistics' real-world value, and increased autonomy. Students overwhelmingly preferred contexts relevant to their interests, experiences, daily lives, and career paths-though preferences varied considerably across individuals. Based on these findings, we provide four recommendations for statistics educators: (1) use real data with authentic contexts, (2) select contexts students care about, (3) incorporate variety across data contexts, and (4) consider choice as a pedagogical tool.

Modern approaches for learning from non-Markovian time series, such as recurrent neural networks, neural controlled differential equations or transformers, typically rely on implicit memory mechanisms that can be difficult to interpret or to train over long horizons. We propose the Volterra signature $\mathrm{VSig}(x;K)$ as a principled, explicit feature representation for history-dependent systems. By developing the input path $x$ weighted by a temporal kernel $K$ into the tensor algebra, we leverage the associated Volterra–Chen identity to derive rigorous learning-theoretic guarantees. Specifically, we prove an injectivity statement (identifiability under augmentation) that leads to a universal approximation theorem on the infinite dimensional path space, which in certain cases is achieved by linear functionals of $\mathrm{VSig}(x;K)$. Moreover, we demonstrate applicability of the kernel trick by showing that the inner product associated with Volterra signatures admits a closed characterization via a two-parameter integral equation, enabling numerical methods from PDEs for computation. For a large class of exponential-type kernels, $\mathrm{VSig}(x;K)$ solves a linear state-space ODE in the tensor algebra. Combined with inherent invariance to time reparameterization, these results position the Volterra signature as a robust, computationally tractable feature map for data science. We demonstrate its efficacy in dynamic learning tasks on real and synthetic data, where it consistently improves classical path signature baselines.

We study the Collatz total stopping time $\tau(n)$ over $n\le 10^7$ from a probabilistic machine learning viewpoint. Empirically, $\tau(n)$ is a skewed and heavily overdispersed count with pronounced arithmetic heterogeneity. We develop two complementary models. First, a Bayesian hierarchical Negative Binomial regression (NB2-GLM) predicts $\tau(n)$ from simple covariates ($\log n$ and residue class $n \bmod 8$), quantifying uncertainty via posterior and posterior predictive distributions. Second, we propose a mechanistic generative approximation based on the odd-block decomposition: for odd $m$, write $3m+1=2^{K(m)}m'$ with $m'$ odd and $K(m)=v_2(3m+1)\ge 1$; randomizing these block lengths yields a stochastic approximation calibrated via a Dirichlet-multinomial update. On held-out data, the NB2-GLM achieves substantially higher predictive likelihood than the odd-block generators. Conditioning the block-length distribution on $m\bmod 8$ markedly improves the generator's distributional fit, indicating that low-order modular structure is a key driver of heterogeneity in $\tau(n)$.

Discovering causal direction from temporal observational data is particularly challenging for symbolic sequences, where functional models and noise assumptions are often unavailable. We propose a novel \emph{Dictionary Based Pattern Entropy ($DPE$)} framework that infers both the direction of causation and the specific subpatterns driving changes in the effect variable. The framework integrates Algorithmic Information Theory (AIT) and Shannon Information Theory. Causation is interpreted as the emergence of compact, rule based patterns in the candidate cause that systematically constrain the effect. $DPE$ constructs direction-specific dictionaries and quantifies their influence using entropy-based measures, enabling a principled link between deterministic pattern structure and stochastic variability. Causal direction is inferred via a minimum-uncertainty criterion, selecting the direction exhibiting stronger and more consistent pattern-driven organization. As summarized in Table 7, $DPE$ consistently achieves reliable performance across diverse synthetic systems, including delayed bit-flip perturbations, AR(1) coupling, 1D skew-tent maps, and sparse processes, outperforming or matching competing AIT-based methods ($ETC_E$, $ETC_P$, $LZ_P$). In biological and ecological datasets, performance is competitive, while alternative methods show advantages in specific genomic settings. Overall, the results demonstrate that minimizing pattern level uncertainty yields a robust, interpretable, and broadly applicable framework for causal discovery.

Skewed distributions are fundamental in modelling asymmetric data on the d-dimensional torus. In this context, asymmetry is introduced through the sine-skewing mechanism, which is the only skewing mechanism that has been proposed on the hyper-torus in the literature. Some sine-skewed models are known to suffer from a singular Fisher information matrix in the vicinity of symmetry, which poses a significant issue for inferential purposes. It is an open question to determine for which sine-skewed models Fisher information singularity occurs. In this paper, a general characterization of the class of models that exhibit this singularity is given in the general d-dimensional setting.

This paper establishes a comparison theorem for the maximum eigenvalue of a sum of independent random symmetric matrices. The theorem states that the maximum eigenvalue of the matrix sum is dominated by the maximum eigenvalue of a Gaussian random matrix whose statistics match the sum, and it strengthens previous results of this type. Corollaries address the minimum eigenvalue and the spectral norm; the proof strategy also extends to matrix martingale sequences. The comparison methodology is powerful because of the vast arsenal of tools for treating Gaussian random matrices. As applications, the paper improves on existing eigenvalue bounds for random matrices arising in spectral graph theory, quantum information theory, high-dimensional statistics, and numerical linear algebra. In particular, these techniques deliver the first complete proof that a sparse random dimension reduction map has the injectivity properties conjectured by Nelson & Nguyen in 2013.

Geometric (also known as spatial) quantiles, introduced by Chaudhury and representing one of the three principal approaches to defining multivariate quantiles, have been well studied in the literature. In this work, we focus on the extremal behaviour of these quantiles. We establish new extremal properties, namely general lower and upper bounds for the norm of extreme geometric quantiles, free of any moment conditions. We discuss the impact of such results on the characterization of distribution behaviour. Importantly, the lower bound can be directly linked to univariate quantiles and to halfspace (Tukey) depth central regions, highlighting a novel connection between these two fundamental notions of multivariate quantiles.

Clustered and personalised federated learning (FL) needs a signal telling the server which clients should share a model. Most methods derive it from losses or model updates that must be recomputed during training. We study pTopoFL, which derives it once, before training, from a compact persistent-homology (PH) descriptor of each client's feature distribution: the server clusters clients on these descriptors, weights them within clusters, and runs blended clustered local gradient descent, returning one personalised model per cluster. For strongly convex, smooth losses we analyse the complete procedure: for any partition, one round is a contraction with factor (1-eta*mu)^tau; the fixed point is characterised by a local-step drift bound, an exact formula for the effective strength of blending (which yields a calibration rule) and a stochastic floor exposing a bias-variance trade-off of clustering; and personalisation lowers the heterogeneity floor in proportion to a measurable share of the dispersion of client optima. Experiments on synthetic federations, a label-skew benchmark and a real four-hospital dataset confirm the theory and delimit the method. When feature geometry and decision rules co-vary, the PH partition recovers the latent client groups, including differences a linear-subspace descriptor misses, and pTopoFL is competitive with the strongest clustered baselines; on the real federation it lowers the test log-loss of FedAvg from 0.463 to 0.438, on par with the best personalised methods. When heterogeneity is invisible in feature geometry, it offers no advantage over FedAvg. pTopoFL transmits model parameters and is no more private than FedAvg; we give a record-level differential-privacy accounting and show that privatising the descriptor destroys the partition. Code reproduces every number.

To characterize the community structure in network data, researchers have developed various block-type models, including the stochastic block model, the degree-corrected stochastic block model, the mixed membership block model, the degree-corrected mixed membership block model, and others. A critical step in applying these models effectively is determining the number of communities in the network. However, to the best of our knowledge, existing methods for estimating the number of network communities either rely on explicit model fitting or fail to simultaneously accommodate network sparsity and a diverging number of communities. In this paper, we propose a model-free spectral inference method based on eigengap ratios that addresses these challenges. The inference procedure is straightforward to compute, requires no parameter tuning, and can be applied to a wide range of block models without the need to estimate network distribution parameters. Furthermore, it is effective for both dense and sparse networks with a divergent number of communities. Technically, we show that the proposed spectral test statistic converges to a {function of the type-I Tracy-Widom distribution via the Airy kernel} under the null hypothesis, and that the test is asymptotically powerful under weak alternatives. Simulation studies on both dense and sparse networks demonstrate the efficacy of the proposed method. Three real-world examples are presented to illustrate the usefulness of the proposed test.

Exponential Random Graph Models (ERGMs) provide a statistical framework for testing hypotheses about how ties form using network structure and node attributes. Their usefulness depends on model specification, which often requires researchers to repeatedly propose models, fit them, check how well they reproduce the observed network, and revise them when they do not. We present Forge (Formation-Oriented Reasoning with Guarded ERGMs), an agentic system that performs this process using a language model and external statistical tools. Given an observed network and a domain description, Forge proposes hypotheses about tie formation, translates them into candidate ERGM specifications, evaluates them statistically, refines the best candidate using goodness-of-fit feedback, and returns a human-readable interpretation of the final model. On 16 benchmark networks, Forge improves on the best baseline on 13 networks and matches it on the other three, with a median 24.8% improvement in goodness of fit. On 60 controlled networks with known generating specifications, Forge achieves exact specification recovery in 78.3% of cases and attains 90.8% term-level F1. These results show that Forge can reduce the manual trial-and-error involved in ERGM specification while making the process more reproducible and keeping model selection grounded in statistical evidence.

The progression of chronic diseases often follows highly variable trajectories, and the underlying factors remain poorly understood. Standard mixed-effects models typically represent inter-patient differences as random deviations around a common reference, which may obscure meaningful subgroups. We propose a probabilistic mixture extension of a mixed effects model, the Disease Course Mapping model, to identify distinct disease progression subtypes within a population. The mixture structure is introduced at the latent individual parameters, enabling clustering based on both temporal and spatial variability in disease trajectories. We evaluated the model through simulation studies to assess classification performance and parameter recovery. Classification accuracy exceeded 90% in simpler scenarios and remained above 80% in the most complex case, with particularly high recall and precision for fast-progressing clusters. Compared to a post hoc classification approach, the proposed model yielded more accurate parameter estimates, smaller biases, lower root mean squared errors, and reduced uncertainty. It also correctly recovered the true three-cluster structure in 93% of the simulations. Finally, we applied the model to a longitudinal cohort of CADASIL patients, identifying two clinically meaningful clusters, differentiating patients with early versus late onset and fast versus slow progression, with clear spatial patterns across motor and memory scores. Overall, this probabilistic mixture framework offers a robust, interpretable approach for clustering patients based on spatiotemporal disease dynamics.

This paper develops a comprehensive Markov-based framework for modelling reservoir behaviour and assessing key performance measures such as reliability and resilience. We first formulate a stochastic model for a finite-capacity dam, analysing its long-term storage dynamics under both independent and identically distributed inflows, following the Moran model, and correlated inflows represented by an ergodic Markov chain in the Lloyd formulation. For this finite case, we establish stationary water balance relations and derive asymptotic results, including a central limit theorem for storage levels. The analysis is then extended to an infinite-capacity reservoir, for which normal limit distributions and analogous long-term properties are obtained. A continuous-state formulation is also introduced to represent reservoirs with continuous inflow processes, generalizing the discrete-state framework. On this basis, we define and evaluate reliability and resilience metrics within the proposed Markovian context. The applicability of the methodology is demonstrated through a real-world case study of the Quiebrajano dam, illustrating how the developed models can support efficient and sustainable reservoir management under hydrological uncertainty.

We introduce inference methods for score decompositions, which partition scoring functions for predictive assessment into three interpretable components: miscalibration, discrimination, and uncertainty. Our estimation and inference relies on a linear recalibration of the forecasts and is applicable to general point forecasts such as means and quantiles due to its validity for non-smooth scoring functions. This approach ensures non-negative decomposition terms in finite samples, enables asymptotic inference under model misspecification, and establishes a direct connection to the classical Mincer-Zarnowitz regression. The resulting inference framework facilitates novel tests for equal linearized forecast calibration or discrimination, which yield three key advantages. They enhance the information content of predictive ability tests by decomposing scores, can improve detection power in scenarios where predictive differences are attributable to specific score components, and formally connect scoring-function-based evaluation to traditional calibration tests, such as financial backtests. Applications demonstrate the method's utility. We find that for survey inflation forecasts, discrimination abilities can differ significantly even when overall predictive ability does not. In an application to financial risk models, our tests provide deeper insights into the calibration and information content of volatility and Value-at-Risk forecasts. By disentangling forecast accuracy from backtest performance, the method exposes critical shortcomings in current banking regulation.

Accurate estimation of Marginal Emission Factors (MEFs) is critical for evaluating the decarbonization potential of low-carbon technologies and demand-side management. However, canonical methodologies, predominantly relying on linear regression and differencing techniques, fail to capture the structural non-linearities inherent in the merit order, i.e. the marginal technology setting electricity prices. Utilizing Markov switching autoregressive models with exogenous regressors (MS-ARX) and hourly US data (2019-2025), we identify distinct, mutually exclusive regimes governed by fuel-price dynamics. We find that linear models overestimate abatement potential by masking the dichotomy between a gas-driven and coal-driven marginal system. Furthermore, using robust structural break detection, we link regime instability to a specific structural shift in natural gas pricing in May 2022. Our results indicate that post-2022, the grid has transitioned into a correction phase where the coal-driven regime is less persistent but highly volatile, necessitating state-dependent policy metrics rather than static annual averages.

Experimentation is central to modern digital businesses, but many operational decisions cannot be randomized at the user level. In such cases, cluster-level experiments, where clusters are usually geographic, come to the rescue. However, such experiments often suffer from low power due to persistent cluster heterogeneity, strong seasonality, and autocorrelated outcome metrics, as well as common shocks that move many clusters simultaneously. On an example of airline pricing - where policies are typically applied at the route level and thus the A/B test unit of analysis is a route - we study switchback designs to remedy these problems. In switchback designs, each cluster (route in our case) alternates between treatment and control on a fixed schedule, creating within-route contrasts that mitigate time-invariant heterogeneity and reduce sensitivity to low-frequency noise. We provide a unified Two-Way Fixed Effects interpretation of switchback experiments that makes the identifying variation explicit after partialling out route and time effects, clarifying how switching cadence interacts with temporal dependence to determine precision. Empirically, we evaluate weekly and daily switchback cadences using calibrated synthetic regimes and operational airline data from ancillary pricing. In our evaluations, switchbacks decrease standard errors by up to 67%, with daily switching yielding the largest gains over short horizons and weekly switching offering a strong and simpler-to-operationalize alternative.

Producing reliable estimates of health and demographic indicators at fine areal scales is crucial for examining heterogeneity and supporting localized health policy. However, many surveys release outcomes only at coarser administrative levels, thereby limiting their relevance for decision-making. We propose a fully Bayesian, single-stage spatial modeling framework for area-level disaggregation that generates fine-scale estimates of indicators directly from coarsely aggregated survey data. By defining a latent spatial process at the target resolution and linking it to observed outcomes through an aggregation step, the framework adopts small-area estimation techniques while incorporating covariates and delivering coherent uncertainty quantification. The proposed methods are implemented with inlabru to achieve computational efficiency. We evaluate performance through a simulation study of general fertility rates in Kenya to demonstrate the models' ability to recover fine-scale variation across diverse data-generating scenarios. We further apply the framework to two national surveys to produce district-level fertility estimates from the 2022 Kenya Demographic and Health Survey and, more importantly, district-level indicators for unpaid care and domestic work and mass media usage from the 2021 Kenya Time Use Survey.

We introduce Latent Space Distribution Matching (LSDM), a novel framework for semi-supervised generative modeling of conditional distributions. LSDM operates in two stages: (i) learning a low-dimensional latent space from both paired and unpaired data, and (ii) performing joint distribution matching in this space via the 1-Wasserstein distance, using only paired data. This two-step approach minimizes an upper bound on the 1-Wasserstein distance between joint distributions, reducing reliance on scarce paired samples while enabling fast one-step generation. Theoretically, we establish non-asymptotic error bounds and demonstrate a key benefit of unpaired data: enhanced geometric fidelity in generated outputs. Furthermore, by extending the scope of its two core steps, LSDM provides a coherent statistical perspective that connects to a broad class of latent-space approaches. Notably, Latent Diffusion Models (LDMs) can be viewed as a variant of LSDM, in which joint distribution matching is achieved indirectly via score matching. Consequently, our results also provide theoretical insights into the consistency of LDMs. Empirical evaluations on real-world image tasks, including class-conditional generation and image super-resolution, demonstrate the effectiveness of LSDM in leveraging unpaired data to enhance generation quality.

Density aggregation is a central problem in machine learning, for instance when combining predictions from a Deep Ensemble. The choice of aggregation remains an open question with two commonly proposed approaches being linear pooling (probability averaging) and geometric pooling (logit averaging). In this work, we address this question by studying the normalized generalized mean of order $r \in \mathbb{R} \cup \{-\infty,+\infty\}$ through the lens of log-likelihood, the standard evaluation criterion in machine learning. This provides a unifying aggregation formalism and shows different optimal configurations for different situations. We show that the regime $r \in [0,1]$ is the only range ensuring systematic improvements relative to individual distributions, thereby providing a principled justification for the reliability and widespread practical use of linear ($r=1$) and geometric ($r=0$) pooling. In contrast, we show that aggregation rules with $r \notin [0,1]$ may fail to provide consistent gains with explicit counterexamples. Finally, we corroborate our theoretical findings with empirical evaluations using Deep Ensembles on image and text classification benchmarks.