This paper analyzes and identifies a space-based Global Navigation Satellite System (GNSS) interference source that has caused scores of powerful transient wide-area interference events over continental Europe, Greenland, and Canada since 2019. While terrestrial or near-terrestrial sources are primarily responsible for the recent uptick in GNSS interference worldwide, space-based interferers are of special concern given their potential for vast geographic reach and their portent of a qualitative escalation in GNSS interference. Based on data collected between 2019 and 2026 from a network of terrestrial GNSS reference stations, this paper (1) develops a received-power-based detection framework; (2) details the spatial, temporal, and spectral patterns of wide-area interference events caused by the source; (3) presents and analyzes identification techniques that blend received-power and time-difference-of-arrival measurements; and (4) applies these techniques to confidently identify the GNSS interference source as a constellation of Russian early warning satellites in Molniya ("lightning") orbits.

Channel knowledge maps (CKMs) are designed to predict channel state information (CSI) from user locations, thereby enabling low-overhead CSI acquisition. However, existing CKM construction methods often require hours-to-days of training time and dense measurements, resulting in substantial deployment cost. In this paper, we propose Voxel-CKM, a novel voxelized radio frequency (RF) radiance field framework for fast and few-shot CKM construction. The core idea is to replace implicit neural representations with explicit voxel grids to efficiently capture the spatial variation of wireless channels. Building upon this, we further introduce a compact vector-matrix (VM) decomposition to parameterize these voxel grids using a small set of matrices and vectors, which significantly accelerates convergence and facilitates fast CKM construction. To enable few-shot learning, we incorporate a transmitter prior as an inductive bias to guide the learning process under sparse measurements. Additionally, a total-variation (TV) regularization loss is proposed to mitigate overfitting and stabilize optimization. Experiments show that Voxel-CKM substantially accelerates training convergence and improves performance in the few-shot regime.

Recently, industrial pioneers like Amazon, Tencent, ByteDance, and Huawei have been adopting BBR as their congestion control algorithm for live-streaming applications, including TikTok Live. However, BBR, originally crafted for bulk data transmission, faces multiple challenges in live-streaming scenarios. In this paper, we first explore two key issues associated with BBR due to inaccurate bandwidth estimation in live-streaming scenarios: (i) BBR cannot easily exit its startup phase, resulting in a fierce self-inflicted loss. (ii) BBR sends data at a lower rate than the available bandwidth during its stable phase. We then propose BBR-Copilot, an auxiliary congestion control component that cooperates with BBR, making BBR better adapt to live-streaming scenarios. BBR-Copilot allows for proactively generating accurate bandwidth measurement samples by smartly creating and sending extra data. We implement the BBR-Copilot prototype upon QUIC and evaluate it via testbed. Experimental evaluation results show that BBR-Copilot effectively enhances BBR's performance in live-streaming scenarios.

Multimodal multi-object tracking (MOT) under complex illumination remains challenging due to insufficient joint modeling of spatial and modal features and the limited adaptability of fixed fusion strategies. To address these issues, this paper proposes a spatial-modal convolution fusion and distillation-prompt-based multimodal MOT framework. A spatial-modal fusion backbone is first constructed, where a Basic module performs spatial feature extraction and modal interaction via decoupled 3D convolution, while a Mixed module models nonlinear cross-modal correlations through amplitude-phase decomposition. In addition, a representation collapse network is designed for adaptive multimodal fusion. A Distillation Prompt Guidance (DPG) module generates dynamic modal weights under teacher supervision, and a Global Modal Difference Aggregation (GMDA) module preserves discriminative information during multimodal representation collapse. Extensive experiments on the UniRTL dataset demonstrate the effectiveness of the proposed method. The proposed tracker achieves 63.31 HOTA and 79.21 MOTA on the RNT modality, outperforming several state-of-the-art methods while maintaining favorable inference efficiency. The source code and pretrained models are publicly available at https://github.com/QitaiSun/SMAC.

Graph signal denoising is a fundamental task in graph signal processing. While the node-oriented filtering approach enhances spatial adaptability, it suffers from spectral rigidity due to its reliance on the graph Fourier transform. Conversely, emerging fractional-domain transforms provide crucial spectral flexibility but are fundamentally limited by their globally shared filtering paradigm, failing to accommodate localized topological variations. To bridge this gap, this paper proposes a generalized node-oriented fractional filtering (NOFF) framework that seamlessly integrates localized spatial adaptability with proactive spectral modulation across various fractional transforms. However, straightforwardly assigning independent full-rank filters to all vertices incurs a prohibitive parameter space, leading to severe overfitting on random noise. To mitigate this, we introduce the low-rank NOFF (LRNOFF) architecture. By imposing a strict low-rank constraint, LRNOFF inherently acts as a powerful implicit regularizer, preventing noise memorization and ensuring the extraction of robust spectral bases. Furthermore, we develop an efficient computational implementation termed LRNOFF-Fast, which drastically reduces computational and memory overhead while preserving theoretical optimality. Experiments on real-world datasets demonstrate that the proposed framework achieves state-of-the-art performance.

Reconfigurable holographic surface (RHS)-aided integrated sensing and communication (ISAC) systems hold great promise for achieving both sensing and communication with low hardware costs and high energy efficiency. However, existing works largely overlook practical hardware impairments in RHSs, particularly faulty RHS elements with uncontrollable amplitudes, which degrade system performance if left unaddressed. This work aims to fill the gap by i) quantifying the impact of faulty RHS elements on ISAC performance and ii) optimizing the functional RHS elements to preserve the ISAC performance. Specifically, we derive the misspecified Cramer-Rao bound (MCRB) for sensing and the signal-to-interference-and-noise ratio (SINR) for communication to measure the performance loss caused by faulty elements. We then formulate an optimization problem that minimizes MCRB, subject to constraints on SINR, transmit power budget, and RHS amplitude. The high non-convexity of the formulated problem poses a significant challenge, which we address by reformulating and proposing a block coordinate descent-based solution incorporating majorization-minimization and successive convex approximation techniques. Simulation results verify that the proposed approach achieves an average 13.7% performance gain compared to the fault-unaware benchmark.

Splatting (GS)-based shared geometry framework adopts a two-stage training strategy, in which an explicit, subject-specific Gaussian scaffold encoding anatomical geometry is first learned from the isotropic structural scan and then reused to fit appearance for target modalities acquired with sparse slices. Experiments on the UK Biobank, GBM, and ABCD datasets for through-plane super-resolution across multiple modalities (T2-weighted, FLAIR, DWI, ASL), degradation factors ($\times 3$, $\times 5$, $\times 7$), and pathological abnormalities (glioblastoma) demonstrate state-of-the-art reconstruction fidelity. The shared Gaussian geometry enables arbitrary-view generation for target modalities with strong structural consistency and further shows potential for self-supervised in-plane super-resolution. This work establishes explicit geometry-guided representations as a novel, flexible, and interpretable pathway toward retrospective multi-contrast MRI harmonization and reliable clinical reference construction. Source code is available at: https://github.com/yfgao76/AtlasGS

Over-the-air computation (AirComp) is widely used for model aggregation in wireless distributed learning. Although it enhances communication efficiency, we believe the AirComp aggregation has limited effectiveness due to the difference between its target problem and that of distributed learning. In this paper, we develop a rigorous formulation for optimal model aggregation in wireless distributed learning. Using this formulation, we show that AirComp aggregation generally assumes a mismatched statistical model for local parameters. We then propose a statistical framework for model aggregation, called global unknown estimation (GUE). It captures the statistical relation between the local and global model parameters, allowing to interpret model aggregation as an inference task. We validate the efficiency of GUE through numerical experiments. Our results show that, in the low SNR regime, GUE can reduce the required power for model aggregation by approximately 15 dB compared to AirComp aggregation. Remarkably, this gain is obtained without additional computational overhead

Ultrasound localization microscopy (ULM) enables micrometer-scale microvascular imaging by localizing and tracking intravascular microbubbles, but its dependence on exogenous contrast agents and long acquisition times limits clinical translation. This study presents a high-frame-rate contrast-free super-resolution ultrasound microvascular imaging method based on high-frequency ultrafast ultrasound and nonlinear beamforming of backscatter signals from native blood flow. Using only 125 milliseconds of in vivo ultrafast data per image, the proposed method achieved an imaging frame rate of 8 frames/s in a rabbit kidney model. The reconstructed microvascular images resolved vessels with a global spatial resolution of 22.2 um over a field of view of 23.04 x 15.18 mm2, where the wavelength of ultrasound was 67.5 um. This corresponds to a three-fold improvement over conventional power Doppler imaging under the same acquisition duration. Compared with conventional flow imaging, the proposed method provided improved microvascular contrast and finer vessel delineation without microbubble injection. These results demonstrate a practical pathway toward high frame rate, contrast-free super-resolution ultrasound imaging for microvascular assessment.

In this study, we address the IMU-based heave motion estimation problem for inertial navigation systems. Unlike existing approaches, we propose a data-driven framework in which a bank of IIR filters, each associated with a specific frequency range, is optimized using a synthetically generated dataset of realistic heave-acceleration tuples. The synthetic heave signal generation pipeline starts by synthesizing random wave signals from established wave energy spectra and then processing them through heave response amplitude operators reported in the literature. The corresponding vertical acceleration measurements are obtained by double-differentiating the heave signals and corrupting them with realistic low- and high-frequency disturbances observed in real IMU recordings. A Fourier-transform-based method is used to estimate the mean peak period and select the appropriate filter. Simulation results from both offline and real-time tests demonstrate that the proposed method is robust to varying sea regimes and provides accurate heave estimation, with a maximum RMSE not exceeding the larger of 5 cm or 5% of the significant heave height.

Aggregated relational data (ARD) consists of survey responses to questions of the form ``how many people do you know who~$X$?'' and is widely used in survey statistics for indirect inference about populations and social networks. The dominant ARD inference target is hidden-population size estimation via the Network Scale-Up Method (NSUM), but ARD is also used for personal-network-size estimation, mixing-pattern recovery, and inference about latent network structure. Bayesian inference for ARD almost universally assumes that, conditional on a respondent's degree, the counts reported for different subpopulations are independent. There are, however, reasons to question this assumption, as homophily, latent-space clustering, and imperfect recall may all induce cross-population dependence. We develop a simulation-based neural estimation framework for ARD which requires only a simulator, so it can be applied to generative models whose likelihood cannot be written down or efficiently evaluated. The framework trains a permutation-invariant neural Bayes estimator that returns, for each marginal parameter, a posterior median and a 95% credible interval, by minimising a multi-quantile pinball loss with a cumulative-gap construction that rules out quantile crossing by design. We demonstrate the framework on three structurally distinct intractable extensions of NSUM-style ARD inference: a stochastic block model, a latent-space model, and a recall-subset model. We apply the framework to ARD Household Survey collected in Rwanda. The framework provides inference on any new survey drawn from the training distribution, and extends the reach of ARD modelling to network-structure and cognitive-process assumptions beyond those currently accessible to likelihood-based inference.

The fraction of variance explained (FVE) in a linear model quantifies the extent to which predictors account for outcome variability. In high-dimensional settings, where traditional FVE estimators do not apply, modern FVE estimators such as GWASH or linear mix-effect model estimated through the restricted maximum likelihood (LMM-REML) struggle with strong correlation among predictors, often found, for example, in brain imaging data. We propose a decomposition framework that partitions the FVE into two components: a low-dimensional component capturing the strong correlation, estimable by low dimensional methods, and a high-dimensional component with remaining weak correlation, estimable by high dimensional methods. Simulations demonstrate that decomposing dominant principal components (PCs) and estimating the high-dimensional FVE using GWASH or LMM-REML leads to improved bias reduction compared to directly applying standard approaches such as GWASH and LMM-REML. Our method shows consistent performance asymptotically as both the number of predictors and the number of samples increase. We illustrate the method in an analysis of the Adolescent Brain Cognitive Development (ABCD) brain imaging dataset, capturing nuanced heritability signals in the FVE of cognitive measures predicted by high-resolution brain imaging data.

Realized volatility has become a standard tool for measuring latent variation in financial assets, and its forecasting is crucial for a wide range of financial applications. We propose a network-based model for forecasting a vector of realized variance processes through the heterogeneous autoregressive (HAR) approach. The generalised network HAR (GNHAR) model incorporates cross-sectional spillovers through a directed graph inferred from Granger-causality tests or connectedness indices, yielding a parsimonious multivariate time series model specification. In an application to ten equities over tranquil and crisis regimes, the proposed GNHAR model improves upon common HAR model benchmarks under both short- and long-term forecasting. We also compare the network-based specification when the jump-continuous decomposition or node-specific option-implied variances are considered. Finally, unlike overparameterised models, our approach yields a concise set of parameters that track the strengthening or weakening of cross-market dependencies, providing a time-varying quantitative assessment of market stability.

Paired comparison models are useful for estimating latent abilities or preferences from binary outcomes, but maximum likelihood estimation can be unstable or fail when the comparison graph is disconnected or nearly separated. Ridge regularization addresses these difficulties by shrinking ability parameters toward a common center, but it can obscure the simple likelihood interpretation that makes Bradley-Terry and Thurstone-Mosteller models attractive to practitioners. This paper describes two data-augmentation perspectives on regularization. The first adds fractional pseudo-games between every pair of competitors. The second adds a fixed-strength phantom player and gives each real competitor a weighted pseudo-win and pseudo-loss against that player. Both approaches yield finite, shrunken estimates; the phantom-player construction also resolves the usual location nonidentifiability without an explicit linear constraint. For the Bradley-Terry model, the two augmentations lead to transparent penalty functions that can be compared directly with ridge penalties. An application to the 2025 Major League Baseball regular season illustrates that tuned pseudo-game and phantom-player regularization can closely reproduce ridge-regularized strength estimates while retaining an intuitive augmented-data representation.

Outliers are known to significantly distort the results of many commonly used clustering methods, often leading to unreliable partitions. To address this issue, several robust clustering approaches have been developed that not only reduce their influence but also facilitate the detection of meaningful outliers. This presentation focuses on robust clustering methods based on trimming, especially TCLUST, which extends the type of trimming used by MCD in one-population problems to the more general case of multiple and unknown clusters. While TCLUST performs well on low-dimensional data, it struggles with high-dimensional datasets due to the complexity of estimating a large number of parameters. The Robust Linear Grouping (RLG) method offers an alternative by assuming clusters lie near lower-dimensional subspaces, thereby combining clustering with dimensionality reduction. However, RLG has limitations when subspaces intersect and assumes overly simplistic isotropic orthogonal errors. A robust clustering method extending TCLUST will be presented, building on the High Dimensional Data Clustering (HDDC) approach by incorporating trimming and eigenvalue constraints. This new approach, called tHHDC, combines TCLUST and RLG, requiring careful modification and integration of both methodologies within that HDDC framework. A study of the theoretical properties of this approach, together with a feasible algorithm for its implementation, will be presented. The interest of the proposed methodology, along with the issue of selecting input parameters, will be illustrated through a simulation study and a real-data example.

TThis paper develops a Dynamic Mini-Max (DMM) framework for repeated surveys comprising a Dynamic Mini-Max Design and a Sequential Hierarchical Bayes Update (SHBU). The DMM jointly optimizes sample size and wave overlap subject to simultaneous precision constraints for levels and movements, a respondent burden limit, and a fieldwork budget. The methods are illustrated using 2021 Australian Census data (t = 1) and simulated waves t = 2, 3, 4. Both the DMM and the classical design start from the same 5% proportional allocation of n_A = 42,018 units. The DMM reduces this to n* = 40,251 while meeting all precision constraints, achieving a cost saving of approximately 6.3%. Level coverage is comparable between the two designs (maximum absolute relative error (MARE) ratio 0.844--1.263). Movement coverage diverges markedly: the DMM achieves 100% across all 27 domain-variable cells, while the classical design achieves only 82%--96% (87.5%--95.0% nationally). The classical confidence interval understates movement uncertainty because it addresses sampling variance only and does not account for the model variance component V_mod_hat. Additional benefits of the DMM framework -- including coherent joint inference for levels and movements, sequential updating without ad hoc composite-estimator chaining, and small area estimation -- are outlined in the paper.

We study projection-based diagnostics for distinguishing directional asymmetry from tail-ratio departure in multivariate data. The procedure reduces the problem to one-dimensional projections and computes two quantile-based summaries: a directional skewness measure evaluated over several quantile levels, and an interquantile tail-ratio evaluated relative to a chosen benchmark. The two summaries lead to a four-regime classification: symmetric benchmark-tail, symmetric tail-departed, skewed benchmark-tail, and skewed tail-departed. The quantile formulation avoids relying on third and fourth moments, which can be unstable in heavy-tailed settings. We establish population properties under central symmetry and ellipticity, uniform finite-sample bounds over the searched directions, and consistency of the threshold classifier under separated regimes. A sparse rank-one calculation is also used to show why coordinate directions can complement random directions in high dimensions. The resulting diagnostic is meant to guide subsequent modelling choices, for example whether a symmetric, skewed, tail-departed, or combined multivariate model is appropriate.

In many risk prediction problems, covariates and a response surrogate are routinely available for a large target population, whereas the true response is costly to ascertain and is observed only for a limited subset. This creates a design problem: one must decide which observations should receive response measurement in order to build a prediction model under a fixed measurement budget. We propose a surrogate-assisted optimal sampling framework for risk prediction under measurement constraints. In the target setting, the surrogate identifies confirmed positive cases, while responses for surrogate-negative observations remain unobserved and can be selectively measured, and thus the sampling design determines how the response measurement budget is allocated. Our framework constructs an optimal sampling design minimizing the leading term of the expected out-of-sample cross-entropy loss and incorporates the resulting design into an inverse-probability-weighted cross-entropy estimator. The proposed design depends only on covariates, the surrogate, and a preliminary estimator, and therefore does not require responses from unlabeled observations at the design stage. We establish consistency, asymptotic normality, and leading-order prediction optimality of the resulting estimator. Extensive simulation studies and two real data applications demonstrate that the proposed design improves prediction performance and exhibits robustness under surrogate misspecification and rare outcome settings.

Modeling high-dimensional data is challenging, yet essential to understanding many complex systems. Maximum entropy models such as Ising and Potts models have been used extensively to capture pairwise interactions from correlation patterns in data, allowing to infer graphical representations of complex systems from observations (e.g., from protein sequences or neural population activity). Recently, there has been growing interest in modeling higher-order correlation patterns involving simultaneously three or more variables. While progress has been made in binary data with high-order Ising models, we extend this framework to the more general case of discrete data. We introduce q-state spin models, a complete family of maximum entropy models that generalize the vector Potts model to include long-range and arbitrary high-order interactions. In the pairwise case, our models allow for more diverse interaction types compared to the standard vector Potts model. We discuss their statistical interpretation with examples and relate them to discrete Fourier analysis. Using a loop expansion of the partition function, we show that the statistical properties of spin models are fully captured by the algebraic structure of their interactions. We define gauge transformations under which this structure, and thus the partition function, remains invariant. Models equivalent under gauge transformations can be seen as different representations of the same abstract statistical model, despite generally having interactions of different orders, extending results from the binary case. For practical application to data analysis, we focus on a subset of models known in the binary case as Minimally Complex Models, generalizing them to discrete data. We obtain a closed-form expression for the marginal likelihood of these models, enabling fast model selection. We illustrate their use with simple real-world examples.

This paper presents a post-Bayesian approach to online filtering in nonlinear state-space models, capable of avoiding over-confident inferences in settings where either the dynamical model, the measurement model, or both, could be misspecified. This is addressed using predictively oriented (PrO) posteriors, an emerging paradigm in which learning (i.e., posterior concentration) occurs if and only if the overall model is well-specified, without strict adherence to Bayes' theorem. As the characterisation of PrO posteriors is challenging, our main technical contribution is a fast approximate linear-Gaussian update procedure, analogous to an (iterated) extended Kalman filter. The methodology, which we call EKF-PrO, has no tunable hyper-parameters and has a computational cost comparable to that of existing filtering methods. Performance is empirically assessed on a range of linear and non-linear applications, in which the state-space model is systematically misspecified.

Active Statistical Inference is a new framework to make precise claims about population parameters with provable statistical guarantees. It uses a predictive "black-box" machine learning (ML) model to strategically decide which data points to label, roughly prioritizing samples for which the ML model is unsure about their label values. A major issue is that the framework can be brittle when uncertainty estimates are noisy. This paper introduces OPAL (Optimized Policy for Allocation of Labels), which learns a labeling strategy within a tractable class of smooth policies to yield estimators with the lowest variance. In effect, OPAL is an end-to-end pipeline that turns a black-box model's uncertainty scores into a data-adaptive labeling strategy and then performs inference on the collected samples. We evaluate OPAL on real datasets spanning medical imaging data, computational social science, and proteomics. As a concrete example, we consider predicting breast cancer subtype from histopathology images and using OPAL to form valid confidence intervals for odds ratios for different demographic groups. We show that OPAL achieves nominal coverage in finite samples and has the accuracy one expects from methods which have far more labeled samples.

Tail index regression studies how covariates affect tail heaviness in heavy-tailed data. In many applications, data are distributed across heterogeneous sources, where direct pooling is infeasible due to privacy or regulatory constraints. Existing methods mainly focus on single-dataset analysis and do not address heterogeneous federated settings. We develop a personalized federated framework for high-dimensional tail index regression that accommodates client heterogeneity while exploiting latent similarities across clients. The proposed estimator combines sparsity regularization with nonconcave fusion penalties to perform coefficient estimation, variable selection, and group recovery. We establish non-asymptotic convergence rates and show that the estimator enjoys an oracle property by consistently recovering the underlying grouping structure. For computation, we develop an ADMM-based federated algorithm with adaptive gradient updates and establish its convergence guarantees. We further propose a debiased federated inference procedure based on adaptive weighted aggregation across related clients, yielding valid confidence intervals and hypothesis tests with improved efficiency over target-only inference. Simulation studies and real-data analysis demonstrate the effectiveness of the proposed methods.

Count data with excess zeros arise frequently in health economics and epidemiology. The standard Poisson Hurdle Model (PHM) parametrises the underlying Poisson rate directly, so its count-component coefficients are log-rate ratios rather than log-ratios of the marginal mean. Consequently, the incidence density ratio (IDR) from the PHM is neither exact nor constant across covariate profiles, complicating applied reporting. We propose the Marginalised Poisson Hurdle Model (MPHM), which reparametrises the count component so that the coefficient vector beta directly governs the marginal mean E[Y]. A nonlinear connector equation links the structural Poisson rate to this parametrised mean. We prove existence and uniqueness of the connector solution, develop a vectorised Brent's-method solver, derive the score equations and block-diagonal Fisher information, establish asymptotic normality, and prove that exp(beta) is exactly constant across all covariate values. A simulation study with n in {100, 250, 500, 1000}, zero proportion pi in {0.2, 0.4, 0.6, 0.8}, and R = 200 replications confirms consistency, near-zero bias, and 95% Wald coverage of 0.905-0.975 across all 16 scenarios. Applied to the NMES1988 physician visit data (n = 4,406), the MPHM yields IDR = 1.163 (95% CI: 1.150-1.177) per additional chronic condition - an exact, population-wide effect not derivable from the PHM. The MPHM resolves the non-constant IDR problem by directly parametrising E[Y]. The resulting IDR holds for every individual and the whole population without further marginalisation, substantially simplifying the reporting of covariate effects in health utilisation research.

Switchback experiments -- in which treatment is assigned at the level of a cluster crossed with a time period -- are widely used in marketplace and platform settings, yet no closed-form power formula exists for them. We fill this gap by deriving a closed-form, multi-level asymptotic variance approximation for the individual-level OLS estimator, facilitating power budgeting. Using this formula, we reveal a structural floor on statistical power: while idiosyncratic noise vanishes with observation density, macro-level shocks are multiplicatively penalized by cluster size imbalance. We confirm through analytical derivations and Monte Carlo simulations that the formula is exact across typical parameters and serves as a mathematically conservative upper bound in extreme boundary regimes. We study three methodological applications. First, we prove that advanced assignment designs like stratification only partially eliminate the penalty of cluster size imbalance on power. Second, we demonstrate that variance reduction techniques targeting macro-level shocks yield disproportionately greater efficiency gains than those targeting residual noise. Third, we formalize the finite-sample power trade-offs between individual-level and cell-level estimators.

The Galton--Watson process (GWP) is a discrete-time branching process model that provides a powerful tool for analyzing epidemic data and estimating key epidemiological parameters such as the basic reproduction number. When used with surveillance-based cluster size data, the GWP can also elicit information about the extent of transmission heterogeneity, even when each transmission process is not directly observable. When cluster size distribution data are available, the parameters that govern the transmission can be statistically inferred by using the probability mass function that corresponds to the observed cluster size data. For multi-type GWPs, however, real-world applications remain limited, possibly because of the absence of conceptually and practically straightforward approaches for deriving the closed-form solution of the final size distribution. In the present study, we propose a framework for computing the final size distribution of multi-type GWPs, using a method for the choice of the Cauchy integral contour. We provide examples of how our framework can be applied to both simulated data and real-world data of Middle East respiratory syndrome, and discuss potential pitfalls surrounding the identifiability of parameters for statistical inference when using likelihoods that are not conditioned on extinction.

Neural posterior estimation (NPE) is a simulation-based approach to Bayesian inference that trains a neural network to approximate the posterior distribution from simulated parameter - data pairs, bypassing likelihood evaluation. We apply NPE -- to our knowledge for the first time -- to stochastic susceptible-infectious-removed (SIR) epidemic models observed through final outcome data, considering both homogeneously mixing and household-structured populations. Such data arise naturally in retrospective outbreak investigations and household transmission studies, yet inference is computationally challenging: data-augmentation Markov chain Monte Carlo (MCMC) can be slow to mix in large populations and difficult to implement, while Approximate Bayesian Computation (ABC) suffers from low acceptance rates, particularly for large populations or unlikely outcomes. The discrete, low-dimensional nature of such observations makes this setting particularly well suited to NPE. We show that a logNormal posterior approximation, parameterised by a feed-forward neural network, accurately recovers reference posteriors across a range of population sizes and transmission regimes, and extends naturally to joint inference on global and local transmission rates in the household model. Once trained, the network produces approximate posterior distributions in seconds and generalises reliably to population sizes and structures not seen during training. Performance on both synthetic and real outbreak datasets is consistently strong, with results in close agreement with published analyses.

Mediation analysis plays an essential role in uncovering the mechanisms by which an exposure influences an outcome through intermediate pathways. While methodological advances for single-mediator settings are well established, rigorous tools for handling multiple, sequentially ordered mediators remain underdeveloped. Such settings are common in applications like longitudinal cohort studies, where exposures operate through complex chains of mediators over time. In this paper, we establish a general framework for sequentially ordered mediators that enables the identification and formal decomposition of the total effect into component path-specific effects. We also develop estimation procedures for mediation estimands with both continuous and categorical outcomes. Furthermore, we introduce a new testing strategy to conduct inference using a studentized statistic combined with data-splitting. This approach achieves valid Type I error control under the composite null across diverse data-generating mechanisms. Through extensive simulations and applications to two large-scale empirical studies, we demonstrate that the proposed methodology provides reliable estimation, valid inference, and improved power for discovering novel mediation pathways.

Computer experiments with both quantitative and qualitative inputs have become common across various areas. However, constructing accurate and computationally efficient emulators for such experiments at large scales remains a significant challenge. We propose a novel, scalable framework for emulating computer experiments with mixed inputs. Our approach is based on a new covariance function integrating additive Gaussian Processes (GPs) to handle the mixed inputs, with Vecchia approximation for scalability. We demonstrate that methods for large-scale computer experiments can be effectively extended when paired with our proposed modeling framework.

Visual and quantitative goodness-of-fit diagnostics are an important tool in the practitioner's toolbox. The need for convincing and reliable diagnostics is particularly clear when fitting extreme value regression models, which are used for extrapolation far beyond the observable range of the response variable, and often evaluated at unobserved covariate values. Despite this, few diagnostics have been developed for extreme value regression models, and those available often suffer in terms of interpretability or scalability on low-dimensional or non-Euclidean covariate domains, often encountered in modern applications. Moreover, existing methods tend to offer a global perspective on model fit; that is, they quantify goodness-of-fit across the entire dataset, without offering insight into regions of the covariate space where the model fit may be poor. We propose two novel visual diagnostics for extreme value regression models: the standardised tail plot and the normalised residual plot. By considering the asymptotic distribution of normalised exceedance probabilities, we show that uncertainty bounds for our plots are approximately independent of the sample size used in their construction. This allows us to propose visual diagnostics which can efficiently and consistently compare goodness-of-fit at both a global and regional level, despite varying sample sizes over regions of the covariate domain. Following a discussion of summary statistics for global and regional goodness-of-fit, we provide two applications of extreme value regression models that illustrate how our diagnostics can be used to perform model comparison (across thousands of candidate models) and provide actionable findings that support model design.

Integrating over model uncertainty in factorial designs via Bayesian model averaging is hindered by the combinatorial explosion of interpretable interaction effects, often yielding a multimodal posterior, where standard Markov chain Monte Carlo algorithms encounter significant convergence issues. We propose a general computational framework that repurposes Rashomon sets, collections of high-performing models traditionally valued for prediction and interpretability, as a strategic "warm start" for estimating the full posterior. Our method, Rashomon-seeded annealing, initializes annealed importance sampling (AIS) by anchoring the starting density within these pre-identified, high-evidence regions while preserving global support over the entire model space. Rather than restricting inference to the Rashomon set and understating uncertainty, the AIS correction restores full posterior inference, turning the Rashomon certificate from an inferential truncation into a proposal mechanism. We demonstrate this approach using Rashomon Partition Sets (RPS) as a rigorous, certified seed constructor for factorial designs. The resulting algorithm yields consistent self-normalized posterior summaries, such as model-averaged cell means, credible intervals, and uncertainty summaries without exhaustive enumeration of the complete model space. This bridges the gap between high-evidence model discovery and rigorous Bayesian inference, and outlines a general strategy in which any high-posterior seed set can provide computational leverage for AIS-based model averaging.