Papers

We introduce a new notion of positive dependence, namely multivariate total positivity of order two for conditional distributions, denoted cMTP$_2$, that explicitly incorporates the conditioning variables. This property is weaker than multivariate total positivity of order two for densities, but stronger than multivariate total positivity of order two for distribution functions, stochastic monotonicity, and tail monotonicity. It thus provides a natural intermediate concept linking these classical notions of positive dependence. We verify the cMTP$_2$ property for several distributions and copula families, including Archimedean copulas, and establish stability under Markov product transformations. As a consequence, we derive comparison results for measures of directed dependence arising from Markov structures, including Chatterjee's rank correlation and a related sensitivity measure.

We develop kernel-based specification tests for semiparametric conditional moment models with high-dimensional nuisance parameters, extending existing conditional moment tests—which typically require asymptotically linear nuisance estimators—to accommodate modern machine-learning methods. The proposed locally robust kernel tests combine Neyman-orthogonal moments, cross-fitting, and reproducing kernel Hilbert space methods, yielding inference that is first-order insensitive to nuisance estimation error. We establish oracle equivalence between the feasible and infeasible test processes under local alternatives and weak nuisance-rate conditions, and characterize the resulting local power. A fast multiplier bootstrap avoids nuisance re-estimation. Applications include specification testing in high-dimensional linear and logistic regression, significance testing with machine-learning regressions, and tests of constant conditional treatment effects. Monte Carlo simulations and an application to the National Supported Work program illustrate the finite-sample performance of the proposed tests.

High-dimensional data with sparse structure and spatio-temporal dependence arise in many scientific domains. We develop a Bayesian feature-extraction framework for spatio-temporal settings that employs Gaussian and Diffused-gamma priors to induce structured sparsity. The modeling framework specifies a general likelihood via Bregman divergence, enabling compatibility with a range of loss functions and measurement models. Posterior computation is carried out via Markov chain Monte Carlo (MCMC), and we introduce a two-stage feature-extraction procedure based on posterior samples to stabilize selection across space and time. We illustrate the method with a multi-subject electroencephalography (EEG) case study examining the relationship between chronic alcohol exposure and activity in different brain regions. We first fit binary classification models at each time point, then use false discovery rate-controlled screening and subsequent clustering in a two-stage feature-extraction pipeline to identify active brain regions. The analysis demonstrates that our proposed priors improve recovery of sparse features and enhance interpretability in the presence of spatio-temporal dependence. The framework is broadly applicable to high-dimensional, structured problems where accurate feature selection and inference are required. The code to implement the model is publicly available via GitHub.

We introduce a class of goodness-of-fit tests for the spherical Cauchy model on the unit hypersphere. The proposed procedures exploit the invariance of the spherical Cauchy family under Möbius transformations: after estimating the parameter by the sample Möbius mean, the observations are transformed to approximate spherical uniformity, and a projection-based uniformity statistic is applied to the resulting sample. We show that, under mild conditions, the resulting tests are exactly distribution-free under the null hypothesis, so that exact critical values can be arbitrarily well approximated by Monte Carlo simulation. We study the Möbius mean as a population functional, establish its existence and uniqueness under mild conditions, and prove equivariance and asymptotic linearity of its empirical counterpart, which coincides with the spherical Cauchy maximum likelihood estimator. We derive the asymptotic null distribution of the test statistic and show that it coincides with that of the underlying uniformity statistic after removing the degree-one spherical-harmonic component, which corresponds to the tangent space of the spherical Cauchy model. We establish consistency against fixed alternatives and characterize local powers through the spherical-harmonic decomposition of contiguous alternatives. Monte Carlo experiments demonstrate the finite-sample accuracy of the asymptotic approximations and the empirical power of the proposed tests. A real data example is treated.

Self-reported numerical variables in sample surveys are frequently subject to coarsening, as respondents tend to report rounded or heaped values rather than the exact underlying quantity. While the statistical literature offers various model-based solutions, official statistics and public health surveillance routinely require design-based inference on finite-population indicators under complex sampling designs. This paper introduces a general framework that bridges this gap by treating the observed response as a coarsened manifestation of a latent variable, modeling reporting regimes of increasing coarseness jointly with the latent distribution via a survey-weighted pseudo-likelihood approach. The fitted model is used to generate posterior predictive replicates of the latent values, to which standard design-based estimators are applied, formally propagating the additional uncertainty through an explicit variance decomposition. Simulation studies assess the finite-sample performance and robustness of the proposed method under various misspecification and sampling scenarios. Finally, its practical relevance is demonstrated through an application to behavioural data from the Italian PASSI surveillance system, illustrating how coarsening affects different functionals, such as means, quantiles, and threshold-based prevalence indicators in heterogeneous ways.

Classical bootstrap methods can behave poorly in high-dimensional linear models: the pairs bootstrap often yields overly conservative inference, whereas the residual bootstrap can be anti-conservative, reflecting systematic failures in variance calibration. We propose a diffusion-based pairs bootstrap that replaces the empirical joint distribution with a learned generative law. We establish variance consistency under a score approximation assumption, using complementary SDE and PDE arguments. Counterexamples show that terminal $W_4$ convergence alone is insufficient for variance consistency. Experiments indicate that diffusion pairs bootstrap improves variance calibration and generally improves Type~I error calibration, including in settings not covered by our theory.

Classical early-warning signals assume that recovery slows near a tipping point, but in a well-studied CESM simulation of AMOC collapse, autocorrelation and variance decrease instead. We develop a preregistered diagnostic that uses only past data to estimate the slowest mode of a memory operator fitted to the evolving overturning structure. The operator ensemble produces an exploratory alarm 77 years before collapse, compared with 29 years for a physics-based freshwater-transport indicator. A blind test on the recovery branch does not validate the same timing rule, supporting interpretation of the diagnostic as a proximity measure rather than a universal clock. In nine additional simulations, it warns before all four finite-rate forced transitions but not before three rapid noise-induced collapses available only as scalar AMOC records. Matched ablations show that the signal depends on long-timescale memory and vertical overturning structure rather than trend, forcing, or multivariate information alone.

Fréchet regression is well developed for Euclidean predictors, but local linear methods remain limited for general manifold-valued predictors. We propose local constant and local linear estimators for predictors lying on a general Riemannian manifold and responses taking values in a general metric space. The proposed local linear estimator is the first local linear Fréchet regression method in this setting. Our construction uses geodesic neighborhoods, logarithmic-map coordinates, volume-density correction, and frame-invariant scalar equivalent weights. For both estimators, we establish not only pointwise consistency and convergence rates but also uniform consistency and convergence rates. Simulations and real data applications demonstrate the finite-sample performance and practical applicability of the proposed methods across diverse predictor and response geometries.

Over the past 20 years, kernel discrepancies have been leveraged as a highly powerful tool for quantifying the disagreement of distributions, with numerous successful applications in two-sample, goodness-of-fit, and independence testing, among others. Their fastest estimators are known to converge at a parametric rate—$n^{-1/2}$—under mild conditions. While this rate is known to be minimax optimal on $\mathbb R^d$ under strict assumptions with bounded kernels, little is known about its optimality beyond the finite-dimensional Euclidean setting with unbounded kernels. In this work, we prove that the minimax lower bound of estimation of the most popular kernel discrepancies (maximum mean discrepancy, Hilbert-Schmidt independence criterion and kernel Stein discrepancy; MMD, HSIC, KSD) is $n^{-1/2}$ on general topological spaces, and under mild assumptions on the kernel; the same rates are shown (as corollaries) to hold for the estimation of the mean embedding and the centered cross-covariance operator. Our results settle the question of optimal estimation of these kernel discrepancies.

The Gini index remains the most important measure of economic inequality worldwide, and accurate estimates of this index are essential for effective public policies. Yet, Gini estimates for the same country and year vary considerably across data sources, a problem that remains largely unresolved. The paper reviews the largest global and regional databases providing Gini estimates, surveys the related literature, and constructs a unified dataset of 122,351 Gini observations spanning 222 countries and territories and 158 years, from 1867 to 2024. The analysis of this new dataset shows that income-based Ginis exceed consumption-based ones by 4.7 points on average globally, and by as much as 10 points in some regions, with these gaps widening over time. The gross–net income distinction and the use of alternative equivalence scales together with several other measurement choices add further systematic differences. Based on these findings, the paper provides correction factors that can be used to harmonise Ginis built on different welfare concepts. We further show that overall divergence across databases has grown only modestly since 1960, and mainly through the proliferation of databases rather than through genuine divergence among long-standing sources. Thus, improving on the existing discrepancies across Ginis globally is possible, but ultimately depends on database administrators disclosing full details of Gini construction and on users selecting Ginis built on comparable measures.

Causal inference is often focused on average effects, which can hide important aspects of the effect distributions. Here we consider the entire posterior effects distribution by estimating full counterfactual outcome distributions. We propose a methodology for inference on counterfactual distributions which builds upon the martingale posterior framework of Fong et al. (2023). This provides a highly flexible approach to estimating densities, distribution functions, and derived quantities such as quantiles, which coherently quantifies the epistemic uncertainty on any target estimand of interest. As the predictive recursions are based on an underlying nonparametric model (a Dirichlet process mixture model), our method naturally inherits robustness with respect to restrictive parametric assumptions. In addition, implementation of our method is typically very fast. This approach can be applied to marginal or conditional counterfactual distributions and is easily extended to an instrumental variables setup. Using the concept of almost conditionally identically distributed random variables, we prove convergence of the martingale posterior inference on the counterfactual outcome distributions for the causal models considered in the paper. We illustrate our approach on both simulated and real data. Using the latter, we investigate the effect of zinc lozenges on common cold duration, the impact of vitamin A supplementation on children's survival rates with one-sided non-compliance (analysed in Imbens and Rubin, 1997a) and the effect of job training (LaLonde, 1986).

We study the contextual dynamic pricing problem under non-stationarity, where a firm sells products to $T$ sequentially arriving consumers that behave according to an unknown demand model that can change over time. The demand model is assumed to be a generalized linear model (GLM), allowing for a feature vector in $\mathbb{R}^d$ that encodes products and consumer information. To achieve optimal revenue (i.e., least regret), the firm needs to learn and exploit the unknown GLMs while monitoring for potential changes. We propose a multiscale change-point detection based algorithm that achieves a regret of order $\widetilde{O}(\sqrt{s_TdT}\wedge\{V_T^{1/3}d^{1/3}T^{2/3}+\sqrt{dT}\})$, where $s_T$ is the number of piecewise stationary segments and $V_T$ is a newly defined notion of design-adjusted variation budget of model parameters. Our algorithm is adaptive and does not require knowing $s_T$ or $V_T$. Moreover, to our knowledge, this is the first dynamic pricing algorithm that is adaptive to the nature of changes and achieves the best-of-both-worlds rate, thus closing a long-standing gap in the literature. We remark that, due to the varying contexts, existing works in the adaptive non-stationary bandit literature cannot be applied to achieve optimality for contextual dynamic pricing. The regret is further accompanied with a newly constructed minimax lower bound, confirming the optimality of our algorithm (up to logarithmic factors). Extensive numerical experiments are conducted to illustrate the efficiency and robustness of the proposed algorithm in non-stationary dynamic pricing.

In many applications, a diffusion trajectory is observed without distortion only while it remains inside a time-varying region; outside this region, only its nearest boundary point and an indicator of visibility are recorded. We formalize this setting through a censoring scheme for multidimensional stochastic differential equations, in which the latent state is observed via its Euclidean projection onto a random, time-dependent closed convex set. Classical arguments handle the one-dimensional case. In higher dimensions, however, the projection generates additional finite-variation terms, and it is not immediate that the local information required for drift estimation is preserved under censoring. We show that it is. Under a suitable regularity condition on the projection map, allowing the censoring region to be nonsmooth, the observed process is a continuous semimartingale and admits a generalized Itô decomposition, whose finite-variation correction term assigns no mass to visible times. Consequently, stochastic integrals over visible times coincide exactly for the observed and latent processes. Building on this identity, we construct a Nadaraya-Watson-type drift estimator with a data-driven bandwidth selection rule and establish oracle inequalities. We also derive anisotropic minimax lower bounds for both the full-observation and censored experiments.

Bayes factors provide a coherent Bayesian measure of evidence for competing hypotheses and have recently been used as the basis for single-arm phase II trial designs with binary endpoints. In contrast to classical power analyses based on test statistics and p-values, Bayes-factor based sample size calculations target high probabilities of obtaining compelling evidence either for a relevant treatment effect or for the null hypothesis, given pre-specified Bayes-factor thresholds. This paper explains how to design single-arm phase II binomial trials using Bayes factors with a focus on simulation-free calibration of Bayesian and frequentist power, type-I-error, and the probability of compelling evidence for the null. Two oncology-motivated examples illustrate the approach and are implemented in the bfbin2arm R package, with code provided in an appendix. The methodology fits naturally into current efforts to innovate and modernize clinical trial design through Bayesian and adaptive methods.

Count data models are ubiquitous in many fields, yet Bayesian data augmentation algorithms for such models frequently encounter challenges with Markov chain Monte Carlo efficiency. Posterior simulation is especially demanding when modeling data with a high proportion of zero outcomes. In this paper, we address this issue by introducing a marginal data augmentation approach for semi-parametric Bayesian count data regression models, based on a working parameter that rescales latent outcomes corresponding to zero-count observations. This strategy alleviates the strong posterior dependencies that typically reduce the efficiency of standard data augmentation schemes and leads to substantial gains in sampling efficiency. Synthetic data examples and simulation studies are used to demonstrate the improvements in mixing compared to conventional sampling methods. A demographic application using latent factor analysis to model subnational mortality counts in Austria further underscores the broader applicability of the proposed methodology.

Over-parameterized linear regression has been widely studied over the last decade. However, most existing works assume that the covariates are independent and that their covariance matrices are non-degenerate. In this paper, we relax both assumptions and derive deterministic equivalents for the prediction risk in a vanishing-ridge regime. We show that degeneracy of the covariance matrices and dependence can lead to multiple descent, and characterize where the corresponding peaks can occur. Our proofs use a novel graph representation of the variance profile. We show that maximum matchings and the Dulmage–Mendelsohn decomposition of the associated bipartite graph identify the configurations at which the variance becomes singular.

We propose a methodology for computing marginal likelihoods for block models. The proposed estimator computes the marginal likelihood from Markov chain Monte Carlo (MCMC) samples and is simulation-consistent, even when the size of the dataset is fixed. Moreover, it is asymptotically normal, of finite variance, invariant to label switching and can be computed efficiently, even for models with an arbitrarily large number of components. We evaluate the method through simulation studies in settings where the true marginal likelihood is available analytically. Finally, we apply the approach to a social network dataset based on the 2023 United Nations Climate Change Conference (COP28) and discuss the resulting insights.

We establish sharp minimax limits for two-sample testing of Hölder-smooth densities under central differential privacy. Given two independent samples, the goal is to decide whether the underlying distributions are identical or separated in $L_1$ distance, while releasing only an $\varepsilon$-differentially private decision. We show that privacy changes the classical smooth-testing boundary through multiple regimes: the optimal separation radius is the maximum of four terms, consisting of the classical nonprivate rate and three distinct privacy-induced barriers. Which barrier is active depends on the privacy budget and the smoothness-to-dimension ratio, yielding a sharp phase diagram. Our upper bound discretizes the samples, applies a private discrete two-sample test to the resulting histograms, and chooses the bin resolution to balance approximation bias, sampling fluctuations, and privacy noise. The procedure also admits a permutation-calibrated implementation with finite-sample type~I error control. For the lower bounds, we combine smooth perturbation constructions with privacy-specific coupling and transport inequalities, showing that all four terms are unavoidable. Finally, when the smoothness is unknown, we develop a multiscale private test that attains the optimal adaptive rate and prove a matching lower bound. Adaptation costs exactly an iterated-logarithmic factor, and this cost appears only in the classical nonprivate term.

Let $X = [ \xi_1, \,\, \xi_2,...\,\, ,\xi_d]^\top$ be a zero-mean random vector of large dimension $d$ ($d \rightarrow \infty$) with (hidden) covariance matrix $M = (m_{ij})_{1 \leq i, j \leq d},$ where $m_{ij} = m_{ji} = \textbf{Cov}(\xi_i, \xi_j).$ Let $X_1, X_2, \dots, X_n$ be $n$ iid samples of $X$. Consider the sample covariance matrix $$\textstyle \tilde{M} := \frac{1}{n} \sum_{i=1}^{n} X_i X_i^\top.$$ In practice, one frequently uses the eigenvectors and eigenspaces of $\tilde M$ as estimators for those of $M$. A central task is to provide an error analysis for these estimators. In this paper, we provide an optimal error analysis, obtaining upper and lower bounds of matching order of magnitude, for a wide range of parameters $d$ and $n$, under mild assumptions on $M$. As corollaries, we obtain new necessary and sufficient conditions for the consistency of the estimators. In these conditions, we only require the number of samples $n$ to depend linearly on the effective rank of $M$, which can be much smaller than the dimension $d$.

High dimensional statistical theory has established the importance of constant aspect ratio, when the number of dimensions ($d$) and samples ($n$) satisfy $n,d\to\infty$ with $n/d\to \gamma\in(0,\infty)$, in understanding the limits of canonical estimation problems. In particular, for estimating the top eigenvector of a $d\times d$ population covariance matrix from $n$ iid samples, the BBP phase transition gives a precise threshold – a simple functional of the aspect ratio – such that the top sample principal component attains nonzero asymptotic correlation with the truth only when the leading population eigenvalue exceeds it. In this paper, we show that for online / streaming algorithms the story is very different, and constant aspect ratio is insufficient for nonzero overlap. We study Oja's algorithm, the most popular method for online PCA. Let $\Sigma=\theta^2 v_0v_0^\top+I\in\mathbb{R}^{d\times d}$, and run Oja's algorithm with step size $\delta/d$ on $n$ iid samples $X_k\sim\mathcal{N}(0,\Sigma)$, with output $\hat v_n$. Then, as $n,d\to\infty$ with $n/d\log d\to\gamma\in(0,\infty)$, we establish a phase transition: $|\langle\hat v_n,v_0\rangle|\to 0$ when $\gamma<\gamma_*$, and $\to\rho_*$ when $\gamma>\gamma_*$. Here $\rho_*=\rho_*(\theta,\delta)=\sqrt{(\theta^2-\delta/2)_+/\theta^2(1+\delta/2)}$ and $\gamma_*=\gamma_*(\theta,\delta)=1/2\delta(\theta^2-\delta/2)_+$. Further, at criticality, when $n=[\gamma_*d\log d+\eta d]$ and $d\to\infty$, $\eta\in\mathbb{R}$, the correlation is random: $|\langle\hat v_n,v_0\rangle|\stackrel{w}{\to}\rho_*|G|\exp(\eta/2\gamma_*)/\sqrt{\rho_*^4+G^2\exp(\eta/\gamma_*)}$ where $G\sim\mathcal{N}(0,1)$. This is in stark contrast to ordinary high dimensional PCA, where nonzero overlap is possible at constant $n/d$ and improves as $n/d$ increases.

We obtain explicit formulas for the expected number and height distribution of critical points of smooth isotropic Gaussian random fields on $\mathbb{R}^d$. The expected number density formula is expressed in terms of at most one-dimensional integrals, regardless of the dimension $d$. To obtain the formulas, we provide a variant of de Bruijn's theorem, as well as Weierstrass' convolution formula with a Gaussian random variable and its inversion.

Exposure mappings are often assumed to be known in causal spillover analyses. In environmental settings, however, they are typically induced by transport processes that are not directly observed and must instead be learned from pollution data. We study how uncertainty in learned transport processes propagates into exposure mappings and downstream spillover inference under interference. We compare mechanistic transport models with modern operator-learning approaches, including PDE, PINO, FNO, and GeoPT, using both simulation studies and an empirical analysis of California PM$_{2.5}$ data. In simulations, all four transport models achieved nearly identical pollution prediction accuracy, yet estimated spillover effects ranged from 1.78 to 2.27. Models that more accurately recovered the induced exposure mapping also produced spillover estimates closer to the true effect. Disagreement was modest for regional interventions but substantially larger for localized point-source interventions. The California analysis showed the same pattern: competing transport models produced similar predictions of observed PM${2.5}$ concentrations while implying different spillover effects under hypothetical pollution-control interventions. Our findings suggest that predictive agreement alone is insufficient for reliable causal inference when exposure mappings are learned rather than directly observed.

This paper characterizes a class of twice continuously differentiable objective-probability preference representations exhibiting endogenous reference dependence under risk. Weak rank-dependent utility (WRDU) preserves objective probabilities, partitions outcomes at an endogenous reference point, and evaluates lotteries through a gainloss representation in which the reference point maximizes a penalized functional. The first-order condition yields a virtual loss-aversion index equal to the ratio of marginal utilities across the loss and gain domains, recovering both the utility-based index of Köbberling and Wakker (2005) and the slope ratio of Tversky and Kahneman (1992) as special cases. The main theorem shows that, within a class satisfying affine admissibility, loss-factorization, dispersion monotonicity, and attenuation, the derivative-ratio form is uniquely admissible. In this class, WRDU generates the modal Allais pattern on an admissible region and blocks the Rabin calibration implication through range-dependent attenuation. The result is conditional and does not claim uniqueness over all behavioral models of risky choice.

Recurrent events and repeated measures are commonly encountered in clinical longitudinal studies, often holding strong associations with patient outcomes. Although joint models for repeated measures, recurrent events, and a terminal event have been developed to account for their correlation, limited methodologies exist to examine causal mediation mechanisms involving multiple types of mediators, especially when mediators are causally related. This study addresses this gap by proposing a novel causal mediation analysis framework to quantify natural direct and indirect effects when both recurrent events and repeated measures act as mediators with causal dependencies. We extend joint modeling approaches by incorporating shared random effects (frailties) structures, relaxing the commonly used “sequential ignorability" assumption, and accounting for unmeasured time-independent confounders through shared random effects. We apply our method to the Terry Beirn Community Programs for Clinical Research on AIDS (CPCRA) study and demonstrate that both recurrent opportunistic infections (OIs) and repeated CD4 measurements mediate the effects of prior AIDS-defining conditions on survival outcomes. Additionally, the shared random effects between repeated CD4 and survival models highlight the presence of unmeasured confounding between CD4 counts and mortality. Simulation studies demonstrate the robustness and finite sample performance of our estimators for natural direct and indirect effects. The proposed methodology enables a more comprehensive investigation of causal pathways in longitudinal studies with multiple mediators, providing insights into treatment mechanisms and informing clinical decision-making.

Nitrous oxide (N$_2$O) is the dominant ozone-depleting substance emitted in the 21st century, and the third largest contributor to anthropogenic greenhouse gases due to its high potency and long atmospheric lifetime, with more than 70% of N$_2$O emissions occurring as a result of agricultural processes. Current approaches to predicting N$_2$O flux emissions include process-based models such as DayCent and Cycles, as well as classical AI models, but the application of Physics-Informed Neural Networks (PINNs) to predicting N$_2$O flux emissions is largely underexplored. Our paper draws upon the mechanistic equations that underlie the DayCent family of process-based models to construct a rigorously derived, literature-traceable physics residual. We then build and train an MLP-based PINN on a multi-site agricultural dataset spanning four geographically distinct US agricultural sites. Across all tested values of the physics loss weighting hyperparameter $\lambda$, our PINN consistently and substantially outperformed uncalibrated Cycles simulation (R$^2=0.01$), with our MLP baseline achieving mean R$^2=0.411$ across ten random seeds. Physics constraints consistently degrade model performance in holdout validation, with marginal degradation at low $\lambda$ and significant degradation at high $\lambda$, but consistently improve model performance and reduce performance variability in leave-one-site-out validation. This suggests that physics constraints sacrifice in-distribution accuracy for out-of-distribution robustness, anchoring the model toward biogeochemically plausible behavior on unfamiliar soil conditions — though cross-site generalization remains challenging, with negative R$^2$ across all seeds and $\lambda$ values on our geographically distinct held-out site.

The assumption of conditional independence in conventional group-based trajectory modeling (GBTM) is often violated by paired repeated-measures data with heterogeneous trajectory patterns. While random-effects models can accommodate this dependence, they inflate within-group variability and blur distinct phenotypic shapes. We propose a joint GBTM framework that explicitly models hierarchical dependence in paired trajectories while allowing them to follow different latent patterns. We develop a robust two-stage approach to address estimation challenges caused by rare latent groups, and a one-stage EM algorithm that serves as a theoretical baseline under balanced group sizes. Simulations demonstrate that our methods correct the biases caused by ignoring hierarchical dependence. The proposed model was applied to real-world data from the Conservation of Hearing Study (CHEARS) Audiology Assessment Arm (AAA), a subcohort of the Nurses' Health Study II (NHS II), to identify distinct audiometric phenotypes and to investigate the association between the Dietary Approaches to Stop Hypertension (DASH) dietary adherence score and the latent audiometric patterns.

In model predictive control (MPC) with time-varying objectives, predicted signals need to be often incorporated in the cost function, such as prices in energy system operation. These are, however, often difficult to predict from the historical trajectory of these signals alone, as they may depend on other contextual events. We propose LiFT-MPC, an MPC framework that integrates a LiFT (Language-in-the-Loop Feedback Tuning) correction scheme to refine such predictions within the MPC loop. The prediction mechanism is updated online via a control-performance loss function, and we establish a performance guarantee for the resulting closed loop system. Numerical experiments using a realistic example of energy-storage management with real prices and news context to improve predictions, demonstrate an improved economic performance

When running experiments that involve humans or animals, for example in clinical or pre-clinical research, it is often the case that multiple measurements are taken on the experimental subjects. This may involve measuring subjects repeatedly over time to track any trends, administering a sequence of treatments to compare their effects within-subject, or taking multiple technical replicate samples of each subject to obtain a more reliable average response. However, it appears that there is some confusion as to what constitutes a 'repeated measure' and what does not. This paper clarifies this confusion by defining characteristics a design may possess when the subjects are assessed multiple times. These characteristics are delineated based on whether the subjects are the experimental units, if the experimental units are measured repeatedly or not, and which randomisation strategy is used. Experimental designs can then be classified using these characteristics and visualised using Hasse diagrams.

Euclidean Hamiltonian Monte Carlo (HMC) warmup must choose a step size and constant preconditioner from limited, nonstationary draws. Standard warmup follows a fixed schedule and generally requires the preconditioner structure to be specified in advance. We present a multi-chain controller that starts diagonal and, at dimension-derived window endpoints, selects between diagonal and low-rank-plus-diagonal inverse mass matrices and chooses the retained rank, subject to dimension and sample-support caps. When evidence is inconclusive, the controller gathers another scheduled window. Persistent within-/between-chain disagreement means draws do not support treating one constant preconditioner as an adequate global description; the controller retains its within-region matrix and advises a population or tempering method for regional exploration. Poor held-out score–position linearity advises reparameterization. The controller selected low rank in every evaluated headline benchmark NUTS run ($12/12$). Geometric-mean pooled ESS-per-gradient ratios relative to the prespecified Fisher low-rank warmup and Welford diagonal warmup baselines were respectively $2.451$ and $22.572$ on the synthetic ill-conditioned Gaussian benchmark, and $1.951$ and $6.264$ on the German-credit Bayesian logistic-regression posterior; all compared runs passed the post-warmup quality check. This method unifies common HMC warmup heuristics in one evidence-driven controller, reducing manual choices and turning warning signals into actionable guidance.

The usefulness of a variational autoencoder (VAE) depends on two properties of its latent space that are hard to obtain together: high encoding capacity in the individual latent variables, and a low-dimensional, disentangled organization of those variables. Weakening the Kullback-Leibler regularization raises capacity but degrades disentanglement, while strengthening it prunes latent variables away entirely. We formulate VAE training as a soft-constrained optimization problem that addresses both. First, we impose an entropy-based constraint (EC) on individual latent variables, showing that the entropy of a latent code upper-bounds the mutual information it carries about the generative factors of the data. Second, we propose a weight-filter method that exploits the slack of the soft constraint to prune low-entropy dimensions during downstream training. On dSprites, the EC raises the aggregate latent-variable activation score by 43-62% over a vanilla VAE, attains the highest FactorVAE score among the e̱ta} e̱ta}-VAE variants (0.891 vs 0.847), and lowers reconstruction error by up to 38%. On MNIST, the weight filter reduces the latent dimensionality supplied to a downstream classifier from ten to two while holding accuracy above 90%, converging in 37% fewer epochs than the same procedure without the EC. We also find that low-entropy discrete factors tend to merge into a single latent variable, whereas high-entropy continuous factors are distributed across several.