Papers

Coral bleaching is a major concern for marine ecosystems; more than half of the world's coral reefs have either bleached or died over the past three decades. Increasing sea surface temperatures, along with various spatiotemporal environmental factors, are considered the primary reasons behind coral bleaching. The statistical and machine learning communities have focused on multiple aspects of the environment in detail. However, the literature on various stochastic modeling approaches for assessing coral bleaching is extremely scarce. Data-driven strategies are crucial for effective reef management, and this review article provides an overview of existing statistical and machine learning methods for assessing coral bleaching. Statistical frameworks, including simple regression models, generalized linear models, generalized additive models, Bayesian regression models, spatiotemporal models, and resilience indicators, such as Fisher's Information and Variance Index, are commonly used to explore how different environmental stressors influence coral bleaching. On the other hand, machine learning methods, including random forests, decision trees, support vector machines, and spatial operators, are more popular for detecting nonlinear relationships, analyzing high-dimensional data, and allowing integration of heterogeneous data from diverse sources. In addition to summarizing these models, we also discuss potential data-driven future research directions, with a focus on constructing statistical and machine learning models in specific contexts related to coral bleaching.

Fatalities resulting from violence in armed conflict have long been a significant public health issue in Ethiopia. Despite the severity of this problem, more comprehensive quantitative scientific studies need to be conducted to elucidate the sequence and dynamics of these occurrences. In response, this study introduces a spatio-temporal statistical method designed to uncover the patterns of fatalities associated with violent events in Ethiopia. The research employs a two-part zero-inflated Bayesian generalized additive mixed model, which integrates a spatio-temporal component to map the fatality patterns across Ethiopian regions. The dataset utilized originates from the Armed Conflict Location and Event Data Project, covering fatality counts related to violent events from 1997 to 2022. The analysis revealed that nine out of thirteen administrative regions exhibited a probability greater than 0.6 for fatality occurrence due to violent events, with five regions surpassing a 0.7 probability threshold. These five regions include Benishangul Gumz, Gambela, Oromia, Somali, and the South West Ethiopian People's Region. Notably, the Tigray region displayed the highest probability (0.558) of experiencing more than 20 deaths per violent event, followed by the Benishangul Gumz region with a probability of 0.306. Encouragingly, the findings also indicate an average decline in fatalities per violent event over time. Specifically, the probability of more than 20 deaths per event was 0.401 in 2020, which decreased to 0.148 by 2022. These insights are invaluable for the government, policymakers, political leaders, and traditional or religious authorities in Ethiopia, enabling them to make informed, strategic decisions to mitigate and ultimately prevent violence-related fatalities in the country.

Edgeworth expansions of first and second order are established for general linear rank statistics under the null hypothesis with asymptotically ”sufficiently” small remainder terms. The methods used are the Stein method combined with an extension of a combinatorial method of Bolthausen (1984). The conditions obtained for the validity of these Edgeworth expansions are very similar to the necessary and sufficient conditions found by Bickel and Robinson (1982) for the case of sums of iid random variables. But these conditions are often difficult to prove directly. For simple linear rank statistics, however, it is possible to use a result from van Zwet (1982) to verify these assumptions. Thus, we obtain conditions for the validity of Edgeworth expansions, which on the one hand are very easy to prove and on the other hand are much more general than all previously known conditions. Finally, this result is applied to the special case of approximating and exact scores.

Contrastive learning has emerged as a cornerstone of unsupervised representation learning across vision, language, and graph domains, with InfoNCE as its dominant objective. Despite its empirical success, the theoretical underpinnings of InfoNCE remain limited. In this work, we introduce an explicit feature space to model augmented views of samples and a transition probability matrix to capture data augmentation dynamics. We demonstrate that InfoNCE optimizes the probability of two views sharing the same source toward a constant target defined by this matrix, naturally inducing feature clustering in the representation space. Leveraging this insight, we propose Scaled Convergence InfoNCE (SC-InfoNCE), a novel loss function that introduces a tunable convergence target to flexibly control feature similarity alignment. By scaling the target matrix, SC-InfoNCE enables flexible control over feature similarity alignment, allowing the training objective to better match the statistical properties of downstream data. Experiments on benchmark datasets, including image, graph, and text tasks, show that SC-InfoNCE consistently achieves strong and reliable performance across diverse domains.

This study examines the determinants of financial and digital inclusion in West and Central Africa using the World Bank Findex 2021 data. Unlike prior works that rely solely on traditional logit and probit models, we combine country-by-country analysis with robustness checks including K-fold cross-validation and Vuong test. Three samples were considered : a full sample combin- ing both regions and two separate subsamples for West and Central Africa. The results indicate that gender, educational attainment, income level, and place of residence are significant factors influencing both financial and digital inclusion in the full sample and the West African subsam- ple. In the Central African subsample, gender is not significant; however, age, education, income, and rural residence emerge as key determinants of financial and digital inclusion. Overall, Ghana stands out as the most financially inclusive country, although it trails Senegal in terms of credit access and digital payment use. Nigeria leads in formal account ownership and formal savings but falls considerably behind Ghana in mobile money account ownership and digital payments. Central African countries generally report lower levels of inclusion compared to West Africa, with Cameroon performing comparatively better.

Modeling normal behavior in dynamic, nonlinear time series data is challenging for effective anomaly detection. Traditional methods, such as nearest neighbor and clustering approaches, often depend on rigid assumptions, such as a predefined number of reliable neighbors or clusters, which frequently break down in complex temporal scenarios. To address these limitations, we introduce the Granular-ball One-Class Network (GBOC), a novel approach based on a data-adaptive representation called Granular-ball Vector Data Description (GVDD). GVDD partitions the latent space into compact, high-density regions represented by granular-balls, which are generated through a density-guided hierarchical splitting process and refined by removing noisy structures. Each granular-ball serves as a prototype for local normal behavior, naturally positioning itself between individual instances and clusters while preserving the local topological structure of the sample set. During training, GBOC improves the compactness of representations by aligning samples with their nearest granular-ball centers. During inference, anomaly scores are computed based on the distance to the nearest granular-ball. By focusing on dense, high-quality regions and significantly reducing the number of prototypes, GBOC delivers both robustness and efficiency in anomaly detection. Extensive experiments validate the effectiveness and superiority of the proposed method, highlighting its ability to handle the challenges of time series anomaly detection.

Stock trading strategies play a critical role in investment. However, it is challenging to design a profitable strategy in a complex and dynamic stock market. In this paper, we propose an ensemble strategy that employs deep reinforcement schemes to learn a stock trading strategy by maximizing investment return. We train a deep reinforcement learning agent and obtain an ensemble trading strategy using three actor-critic based algorithms: Proximal Policy Optimization (PPO), Advantage Actor Critic (A2C), and Deep Deterministic Policy Gradient (DDPG). The ensemble strategy inherits and integrates the best features of the three algorithms, thereby robustly adjusting to different market situations. In order to avoid the large memory consumption in training networks with continuous action space, we employ a load-on-demand technique for processing very large data. We test our algorithms on the 30 Dow Jones stocks that have adequate liquidity. The performance of the trading agent with different reinforcement learning algorithms is evaluated and compared with both the Dow Jones Industrial Average index and the traditional min-variance portfolio allocation strategy. The proposed deep ensemble strategy is shown to outperform the three individual algorithms and two baselines in terms of the risk-adjusted return measured by the Sharpe ratio. This work is fully open-sourced at \href{https://github.com/AI4Finance-Foundation/Deep-Reinforcement-Learning-for-Automated-Stock-Trading-Ensemble-Strategy-ICAIF-2020}{GitHub}.

Code smells indicate latent design or implementation problems that may negatively affect software maintainability. Over the past decades, numerous approaches have been proposed for code smell refactoring, including those based on software metrics, predefined rules, machine learning/deep learning (ML/DL), and, more recently, large language models (LLMs). However, traditional metric- and rule-based approaches rely heavily on manually defined criteria, while ML/DL approaches are often constrained by the availability of training data and the design of model architectures. Although LLMs provide advanced code understanding capabilities, they typically incur substantial computational and time costs, particularly when applied to large-scale software systems. In this study, we propose a graph-based deep learning approach for code smell refactoring. Specifically, we construct code graphs at both the class and method levels and employ graph- and node-level classification to detect code smells and identify corresponding refactoring opportunities for three representative code smells: Long Method, Large Class, and Feature Envy. The proposed approach is trained and evaluated using SACS, a large-scale open-source dataset constructed through a semi-automated process. In the experiments, we implement the proposed approach using three representative GNN architectures: GCN, GraphSAGE, and GAT. We further compare its performance with traditional refactoring approaches, an existing deep learning-based approach, and four representative lightweight LLMs. Experimental results show that the proposed approach outperforms the compared approaches across all evaluated code smell refactoring tasks, demonstrating that it provides both superior performance and greater efficiency.

Conformal prediction offers a distribution-free framework for constructing prediction sets with finite-sample coverage. Yet, efficiently leveraging multiple conformity scores to reduce prediction set size remains a major open challenge. Instead of selecting a single best score, this work introduces a principled aggregation strategy, COnfidence-Level Allocation (COLA), that optimally allocates confidence levels across multiple conformal prediction sets to minimize empirical set size while maintaining provable coverage. Two variants are further developed, COLA-s and COLA-f, which guarantee finite-sample marginal coverage via sample splitting and full conformalization, respectively. In addition, we develop COLA-l, an individualized allocation strategy that promotes local size efficiency while achieving asymptotic conditional coverage. Extensive experiments on synthetic and real-world datasets demonstrate that COLA achieves considerably smaller prediction sets than state-of-the-art baselines while maintaining valid coverage.

We propose the Modified Mahalanobis Distance Conformal Prediction (MMDCP), a unified framework for multi-class classification and outlier detection under label shift, where the training and test distributions may differ. In such settings, many existing methods construct nonconformity scores based on empirical cumulative or density functions combined with data-splitting strategies. However, these approaches are often computationally expensive due to their heavy reliance on resampling procedures and tend to produce overly conservative prediction sets with unstable coverage, especially in small samples. To address these challenges, MMDCP combines class-specific distance measures with full conformal prediction to construct a score function, thereby producing adaptive prediction sets that effectively capture both inlier and outlier structures. Under mild regularity conditions, we establish convergence rates for the resulting sets and provide the first theoretical characterization of the gap between oracle and empirical conformal $p$-values, which ensures valid coverage and effective control of the class-wise false discovery rate (CW-FDR). We further introduce the Summarized Class-Wise FDR (SCW-FDR), a novel global error metric aggregating false discoveries across classes, and show that it can be effectively controlled within the MMDCP framework. Extensive simulations and two real-data applications support our theoretical findings and demonstrate the advantages of the proposed method.

Persistent homology is a cornerstone of topological data analysis, offering a multiscale summary of topology with robustness to nuisance transformations, such as rotations and small deformations. Persistent homology has seen broad use across domains such as computer vision and neuroscience. Most statistical treatments, however, use homology primarily as a feature extractor, relying on statistical distance-based tests or simple time-to-event models for inferential tasks. While these approaches can detect global differences, they rarely localize the source of those differences. We address this gap by taking a graphical model-based approach: we associate each vertex with a population latent position in a conic space and model each bar's key events (birth and death times) using an exponential distribution, whose rate is a transformation of the latent positions according to an event occurring on the graph. The low-dimensional bars have simple graph-event representations, such as the formation of a minimum spanning tree or the triangulation of a loop, and thus enjoy tractable likelihoods. Taking a Bayesian approach, we infer latent positions and enable model extensions such as hierarchical models that allow borrowing strength across groups. Applications to a neuroimaging study of Alzheimer's disease demonstrate that our method localizes sources of difference and provides interpretable, model-based analyses of topological structure in complex data. The code is provided and maintained at https://github.com/zitian-wu/graphPH.

Modern epidemiological analytics increasingly use machine learning models that offer strong prediction but often lack calibrated uncertainty. Bayesian methods provide principled uncertainty quantification, yet are viewed as difficult to integrate with contemporary AI workflows. This paper proposes a unified Bayesian and AI framework that combines Bayesian prediction with Bayesian hyperparameter optimization. We use Bayesian logistic regression to obtain calibrated individual-level disease risk and credible intervals on the Pima Indians Diabetes dataset. In parallel, we use Gaussian-process Bayesian optimization to tune penalized Cox survival models on the GBSG2 breast cancer cohort. This yields a two-layer system: a Bayesian predictive layer that represents risk as a posterior distribution, and a Bayesian optimization layer that treats model selection as inference over a black-box objective. Simulation studies in low- and high-dimensional regimes show that the Bayesian layer provides reliable coverage and improved calibration, while Bayesian shrinkage improves AUC, Brier score, and log-loss. Bayesian optimization consistently pushes survival models toward near-oracle concordance. Overall, Bayesian reasoning enhances both what we infer and how we search, enabling calibrated risk and principled hyperparameter intelligence for epidemiological decision making.

We study the problem of entropy calibration, which asks whether a language model's entropy over generations matches its log loss on human text. Past work found that models are miscalibrated, with entropy per step increasing as generations grow longer, due to error accumulation. To calibrate the model and improve text quality, it has become standard practice to truncate the distribution, but this approach reduces output diversity, which we would like to avoid. Therefore, in this paper, we ask: does miscalibration improve automatically with scale, and if not, is it theoretically possible to calibrate without tradeoffs? To build intuition, we first study a simplified theoretical setting to characterize the scaling behavior of miscalibration with respect to dataset size. We find that the rate of scaling depends on the power law exponent of the data distribution – in particular, for a power law exponent close to 1, the scaling exponent is close to 0, meaning that miscalibration improves very slowly with scale. Next, we measure miscalibration empirically in language models ranging from 0.5B to 70B parameters. We find that the observed scaling behavior is similar to what is predicted theoretically: our fitted scaling exponents for text are close to 0, meaning that larger models accumulate error at a similar rate as smaller ones. This scaling (or, lack thereof) provides one explanation for why we sample from larger models with similar amounts of truncation as smaller models, even though the larger models are of higher quality. However, truncation is not a satisfying solution because it comes at the cost of increased log loss. In theory, is it even possible to reduce entropy while preserving log loss? We prove that it is possible, if we assume access to a black box which can fit models to predict the future entropy of text.

We study a deliberately simple, fully non-linguistic model of text: a sequence of independent draws from a finite alphabet of letters plus a single space symbol. A word is defined as a maximal block of non-space symbols. Within this symbol-level framework, which assumes no morphology, syntax, or semantics, we derive several structural results. First, word lengths follow a geometric distribution governed solely by the probability of the space symbol. Second, the expected number of words of a given length, and the expected number of distinct words of that length, admit closed-form expressions based on a coupon-collector argument. This yields a critical word length k* at which word types transition from appearing many times on average to appearing at most once. Third, combining the exponential growth of the number of possible strings of length k with the exponential decay of the probability of each string, we obtain a Zipf-type rank-frequency law p(r) proportional to r^{-alpha}, with an exponent determined explicitly by the alphabet size and the space probability. Our contribution is twofold. Mathematically, we give a unified derivation linking word lengths, vocabulary growth, critical length, and rank-frequency structure in a single explicit model. Conceptually, we argue that this provides a structurally grounded null model for both natural-language word statistics and token statistics in large language models. The results show that Zipf-like patterns can arise purely from combinatorics and segmentation, without optimization principles or linguistic organization, and help clarify which phenomena require deeper explanation beyond random-text structure.

We study how two information feeds, a closed-form Markov estimator of residual sojourn and an online trained actor-critic, affect reneging and jockeying in a dual M/M/1 system. Analytically, for unequal service rates and total-time patience, we show that total wait grows linearly so abandonment is inevitable and the probability of a successful jockey vanishes as the backlog approaches towards infinity. Furthermore, under a mild sub-linear error condition both information models yield the same asymptotic limits (robustness). We empirically validate these limits and quantify finite backlog differences. Our findings show that learned and analytic feeds produce different delays, reneging rates and transient jockeying behavior at practical sizes, but converge to the same asymptotic outcome implied by our theory. The results characterize when value-of-information matters (finite regimes) and when it does not (asymptotics), informing lightweight telemetry and decision-logic design for low-cost, jockeying-aware systems.

Principal Component Analysis (PCA) is a standard tool for extracting a low-rank signal from noisy observations. It is known that applying PCA to a rank-one signal corrupted by a dense, homogeneous noise, in the large matrix size limit, the celebrated BBP transition occurs, where the emergence of an outlying eigenvalue and the alignment of the corresponding eigenvector occur at the same critical signal strength. Here we study the case of sparse noise corruption. The noise matrix is modelled as the adjacency matrix of a weighted undirected graph with finite average connectivity. Using the replica method, we analytically compute the typical top eigenvalue, the top eigenvector component density, and the squared overlap with the signal, through recursive distributional equations solved by population dynamics. We identify two signal-strength transitions as functions of graph connectivity: $\theta_{\rm crit}$, marking signal recovery by the top eigenvector and generalising the BBP transition, and $\theta_{\rm b}$, where the signal-related eigenvalue detaches from the bulk. For noise with nonzero mean, these transitions need not coincide because of a structural sparse-graph outlier, leading to a discontinuous transition in the squared overlap with the top eigenvector. The same top-eigenpair formalism also predicts the overlap of the signal with the eigenvector associated with the second largest eigenvalue when the signal eigenvalue is an outlier but remains below the structural outlier, where the transition is continuous. We specialise the equations to Poissonian and Random Regular degree distributions, recover dense-noise results in the large-connectivity limit, and validate the theory by numerical diagonalisation of large matrices.

This paper proposes methods for producing compound selection decisions in a Gaussian sequence model. Given unknown, fixed parameters $\mu_ {1:n}$ and known $\sigma_{1:n}$ with observations $Y_i \sim \textsf{N}(\mu_i, \sigma_i^2)$, the decision maker would like to select a subset of indices $S$ so as to maximize utility $\frac{1}{n}\sum_{i\in S} (\mu_i - K_i)$, for known costs $K_i$. Inspired by Stein's unbiased risk estimate (SURE), we introduce an almost unbiased estimator, called ASSURE, for the expected utility of a proposed decision rule. ASSURE allows a user to choose a welfare-maximizing rule from a pre-specified class by optimizing the estimated welfare, thereby producing selection decisions that borrow strength across noisy estimates. We show that ASSURE produces decision rules that are asymptotically no worse than the optimal but infeasible decision rule in the pre-specified class. We apply ASSURE to the selection of Census tracts for economic opportunity, the identification of discriminating firms, and the analysis of $p$-value decision procedures in A/B testing.

Air sensor networks provide hyperlocal, high-frequency data on multiple pollutants, but unlike speciated particulate matter (PM) measurements, they lack direct chemical signatures for source identification. However, these networks collect data at high temporal resolution and multiple spatial locations, creating new opportunities to interpret latent factors through their relationships with spatial proximity to known origins, temporal patterns, and meteorology. We analyze 451,946 one-minute air sensor records from Curtis Bay (Baltimore, USA; October 2022 - June 2023), covering size-resolved PM, black carbon (BC), carbon monoxide (CO), nitric oxide (NO), and nitrogen dioxide (NO2), using a geometric non-negative matrix factorization (NMF) approach that scales to large datasets and yields provably unique factor attribution percentages. Three stable latent factors emerge with converging evidence toward recognizable source categories: Factor 1 explains $>$ 70% of fine and coarse PM and $\sim$30% of BC; Factor 2 dominates CO and contributes $\sim$70% of BC, NO, and NO2; Factor 3 is specific to the larger PM fractions, PM10 to PM40. Regression analyses of the estimated factor intensities with wind direction and bulldozer activity at a nearby coal terminal and a case study on a known bulldozer incident link Factors 1 and 3 to the coal terminal. Extreme-intensity episodes from Factors 1 and 3 averaged $\sim$33 and $\sim$24 minutes per day at the site nearest the coal terminal, attenuating with distance. Factor 2 reflects diurnal traffic patterns. Together, these results show that dense air sensor networks paired with the geometric NMF method can move community air monitoring beyond pollution detection toward identifying likely source categories and informing actionable mitigation strategies.

Time series forecasting is essential in a wide range of real world applications. Recently, frequency-domain methods have attracted increasing interest for their ability to capture global dependencies. However, when applied to non-stationary time series, these methods encounter the $\textit{spectral entanglement}$ and the computational burden of complex-valued learning. The $\textit{spectral entanglement}$ refers to the overlap of trends, periodicities, and noise across the spectrum due to $\textit{spectral leakage}$ and the presence of non-stationarity. However, existing decompositions are not suited to resolving spectral entanglement. To address this, we propose the Frequency Decomposition Network (FreDN), which introduces a learnable Frequency Disentangler module to separate trend and periodic components directly in the frequency domain. Furthermore, we propose a theoretically supported ReIm Block to reduce the complexity of complex-valued operations while maintaining performance. We also re-examine the frequency-domain loss function and provide new theoretical insights into its effectiveness. Extensive experiments on seven long-term forecasting benchmarks demonstrate that FreDN outperforms state-of-the-art methods by up to 10%. Furthermore, compared with standard complex-valued architectures, our real-imaginary shared-parameter design reduces the parameter count and computational cost by at least 50%.

Piecewise diffusion Markov processes (PDifMPs) form a versatile class of stochastic hybrid systems that combine continuous diffusion processes with discrete event-driven dynamics, enabling flexible modelling of complex real-world hybrid phenomena. The practical utility of PDifMP models, however, depends critically on accurate estimation of their underlying parameters. In this work, we present a novel framework for parameter inference in PDifMPs based on approximate Bayesian computation (ABC). Our contributions are threefold. First, we provide detailed simulation algorithms for PDifMP sample paths. Second, we extend existing ABC summary statistics for diffusion processes to account for the hybrid nature of PDifMPs, showing particular effectiveness for ergodic systems. Third, we demonstrate our approach on several representative example PDifMPs that empirically exhibit ergodic behaviour. Our results show that the proposed ABC method reliably recovers model parameters across all examples, even in challenging scenarios where only partial information on jumps and diffusion is available or when parameters appear in state-dependent jump rate functions. These findings highlight the potential of ABC as a practical tool for inference in various complex stochastic hybrid systems.

ReLU activations are the main bottleneck in Private Inference that is based on ResNet networks. This is because they incur significant inference latency. Reducing ReLU count is a discrete optimization problem, and there are two common ways to approach it. Most current state-of-the-art methods are based on a smooth approximation that jointly optimizes network accuracy and ReLU budget at once. However, the last hard thresholding step of the optimization usually introduces a large performance loss. We take an alternative approach that works directly in the discrete domain by leveraging Coordinate Descent as our optimization framework. In contrast to previous methods, this yields a sparse solution by design. We demonstrate, through extensive experiments, that our method is State of the Art on common benchmarks.

In regression models with missing outcomes, selection bias can arise when the missingness mechanism depends on the outcome itself. This proposal focuses on an extension of the Heckman model to a setting where the outcome is binary and both the selection process and the outcome are modeled through logistic regression. A correction term analogous to the inverse Mills' ratio is derived based on relative risks. Under given assumptions, such a strategy provides an effective tool for bias correction in the presence of informative missingness.

Molecular property prediction is fundamental to chemical engineering applications such as solvent screening. We present Socrates-Mol, a framework that transforms language models into empirical Bayesian reasoners through context engineering, addressing cold start problems without model fine-tuning. The system implements a reflective-prediction cycle where initial outputs serve as priors, retrieved molecular cases provide evidence, and refined predictions form posteriors, extracting reusable chemical rules from sparse data. We introduce ranking tasks aligned with industrial screening priorities and employ cross-model self-consistency across five language models to reduce variance. Experiments on amine solvent LogP prediction reveal task-dependent patterns: regression achieves 72% MAE reduction and 112% R-squared improvement through self-consistency, while ranking tasks show limited gains due to systematic multi-model biases. The framework reduces deployment costs by over 70% compared to full fine-tuning, providing a scalable solution for molecular property prediction while elucidating the task-adaptive nature of self-consistency mechanisms.

The Infinite Monkey Theorem states that if one monkey randomly hits the keys in front of a typewriter keyboard during an infinite amount of time, any works written by William Shakespeare will almost surely be typed out at the end of the total text. Due to the seemingly low chance of typing the exact literature works, our group are motivated to find out the expected time the Hamlet, our target text, being typed out by simulated random typing on a standard keyboard. For finding the answer, 30 users randomly typed characters into a file. Then, the frequency of each characters occurred following the previous character is calculated. This conditional probability is used to build the Markov matrix by considering all 128 times 128 cases. Finally, the expected time we estimated is about 10 to the power of 34 (min), which is surprisingly lower than the theoretical computation, and not achievable at all even in the cosmic time.

This work explores the bounds of the variance of unilaterally truncated Gaussian distributions (UTGDs) and scaled chi distributions (UTSCDs) with fixed means. For any arbitrary Gaussian distribution function, $f(x;\mu,\sigma)$, with a fixed, finite mean $M$ on the truncated domain $x \ge a$, where $a \in \mathbb{R}$, it is proven that the variance is bounded: specifically, $\sup \mathrm{Var}(x)_{|x \ge a}= \sup \mathrm{Var}(x)_{|x \le a} =(M-a)^2$. For a fixed cutoff, $a$, the variance can be considered a function of only $M$, $a$, and the location parameter $\mu$. Examples of such approximating functions, which can be used for model calibration, are developed in addition to other, related calibration methods. For UTSCDs, numerical evidence is presented indicating that for $n \in \mathbb{Z+}$ degrees of freedom, or dimensions, and a fixed, finite mean, the variance, $\mathrm{Var}(R)$, over $R \in [a,\infty)$ reaches its maximum value $M^2(\pi-2)/2$ at $a=0$, $n=1$. For a fixed cutoff value, there is a local maximum in the variance as a function of $n$, and the number of dimensions resulting in the maximal variance, $n_{\mathrm{vmx}}$, increases with cutoff value. However, for $n \in \mathbb{R}$, as the cutoff approaches $0$, $n_{\mathrm{vmx}}$ approaches $-1$, while $\mathrm{Var}(R)$ appears to grow without bound.

We study randomized experiments in bipartite systems where only a subset of treatment-side units are eligible for assignment while all units continue to interact, generating interference. We formalize eligibility-constrained bipartite experiments and define estimands aligned with full deployment: the Primary Total Treatment Effect (PTTE) on eligible units and the Secondary Total Treatment Effect (STTE) on ineligible units. Under randomization within the eligible set, we give identification conditions and develop interference-aware ensemble estimators that combine exposure mappings, generalized propensity scores, and flexible machine learning. We further introduce a projection that links treatment- and outcome-level estimands; this mapping is exact under a Linear Additive Edges condition and enables estimation on the (typically much smaller) treatment side with deterministic aggregation to outcomes. In simulations with known ground truth across realistic exposure regimes, the proposed estimators recover PTTE and STTE with low bias and variance and reduce the bias that could arise when interference is ignored. Two field experiments illustrate practical relevance: our method corrects the direction of expected interference bias for a pre-specified metric in both studies and reverses the sign and significance of the primary decision metric in one case.

The Zipf distribution is a probability distribution widely used by scientists from various disciplines due to its ubiquity. Some of these areas include linguistics, physics, genetics, and sociology, among others. In this paper, it is proved that the Zipf distribution is both a mixture of geometric distributions and a mixture of zero-truncated Poisson distributions. It is also shown that it is not the zero-truncation of a mixed Poisson distribution. These results are important because they provide insights on the data generation mechanism that leads to data from a Zipf distribution. Additionally, it is proved, as a corollary, that the Zipf-Poisson Stopped Sum distribution is a particular case of a mixed Poisson distribution. The results are illustrated analyzing the 135 chapters of the novel Moby Dick.

In this article, variational state estimation is examined from the dynamic programming perspective. This leads to two different value functional recursions depending on whether backward or forward dynamic programming is employed. The result is a theory of variational state estimation that corresponds to the classical theory of Bayesian state estimation. More specifically, in the backward method, the value functional corresponds to a likelihood that is upper bounded by the state likelihood from the Bayesian backward recursion. In the forward method, the value functional corresponds to an unnormalized density that is upper bounded by the unnormalized filtering density. Both methods can be combined to arrive at a variational two-filter formula. Additionally, it is noted that optimal variational filtering is generally of quadratic time-complexity in the sequence length. This motivates the notion of sub-optimal variational filtering, which also lower bounds the evidence but is of linear time-complexity. Another problem is the fact that the value functional recursions are generally intractable. This is briefly discussed and a simple approximation is suggested that retrieves the filter proposed by Courts et. al (2021).The methodology is examined in (i) a jump Gauss-Markov system under a certain factored Markov process approximation, and (ii) in a Gauss-Markov model with log-polynomial likelihoods under a Gauss–Markov constraint on the variational approximation. It is demonstrated that the value functional recursions are tractable in both cases. The resulting estimators are examined in simulation studies and are found to be of adequate quality in comparison to sensible baselines.

The harmful relationship between heatwaves and health has been extensively documented in medical and epidemiological literature. However, most evidence is associational and cannot be interpreted causally unless strong assumptions are made. In this paper, we first make explicit the assumptions underlying the statistical methods frequently used in the heatwave literature and demonstrate when these assumptions might break down in heatwave contexts. To address these shortcomings, we propose a causal inference framework that transparently elicits causal identification assumptions. Within this new framework, we first introduce synthetic controls (SC) for estimating heatwave effects, then propose a spatially augmented Bayesian synthetic control (SA-SC) method that accounts for spatial dependence and spillovers. Empirical Monte Carlo simulations show both methods perform well, with SA-SC reducing root mean squared error and improving posterior interval coverage under spillovers and spatial dependence. Finally, we apply the proposed methods to estimate the causal effects of heatwaves on Medicare heat-related hospitalizations among 13,753,273 beneficiaries residing in Northeastern U.S. from 2000 to 2019. This causal inference framework provides spatially coherent counterfactual outcomes and robust, interpretable, and transparent causal estimates while explicitly addressing the unexamined assumptions in existing methods that pervade the heatwave effect literature.

Consider the problem of finding the best matching in a weighted graph where we only have access to predictions of the actual stochastic weights, based on an underlying context. If the predictor is the Bayes optimal one, then computing the best matching based on the predicted weights is optimal. However, in practice, this perfect information scenario is not realistic. Given an imperfect predictor, a suboptimal decision rule may compensate for the induced error and thus outperform the standard optimal rule. In this paper, we propose multicalibration as a way to address this problem. This fairness notion requires a predictor to be unbiased on each element of a family of protected sets of contexts. Given a class of matching algorithms $\mathcal C$ and any predictor $\gamma$ of the edge-weights, we show how to construct a specific multicalibrated predictor $\hat \gamma$, with the following property. Picking the best matching based on the output of $\hat \gamma$ is competitive with the best decision rule in $\mathcal C$ applied onto the original predictor $\gamma$. We complement this result by providing sample complexity bounds, and by performing numerical experiments.