Optimal experimental design is a classic topic in statistics, with many well-studied problems, applications, and solutions. The design problem we study is the placement of sensors to monitor spatiotemporal processes, explicitly accounting for the temporal dimension in our modeling and optimization. We observe that recent advancements in computational sciences often yield large datasets based on physics-based simulations, which are rarely leveraged in experimental design. We introduce a novel model-based sensor placement criterion, along with a highly-efficient optimization algorithm, which integrates physics-based simulations and Bayesian experimental design principles to identify sensor networks that "minimize information loss" from simulated data. Our technique relies on sparse variational inference and (separable) Gauss-Markov priors, and thus may adapt many techniques from Bayesian experimental design. We validate our method through a case study monitoring air temperature in Phoenix, Arizona, using state-of-the-art physics-based simulations. Our results show our framework to be superior to random or quasi-random sampling, particularly with a limited number of sensors. We conclude by discussing practical considerations and implications of our framework, including more complex modeling tools and real-world deployments.

Deep neural networks often fail when deployed in real-world contexts due to distribution shift, a critical barrier to building safe and reliable systems. An emerging approach to address this problem relies on \emph{disagreement discrepancy} -- a measure of how the disagreement between two models changes under a shifting distribution. The process of maximizing this measure has seen applications in bounding error under shifts, testing for harmful shifts, and training more robust models. However, this optimization involves the non-differentiable zero-one loss, necessitating the use of practical surrogate losses. We prove that existing surrogates for disagreement discrepancy are not Bayes consistent, revealing a fundamental flaw: maximizing these surrogates can fail to maximize the true disagreement discrepancy. To address this, we introduce new theoretical results providing both upper and lower bounds on the optimality gap for such surrogates. Guided by this theory, we propose a novel disagreement loss that, when paired with cross-entropy, yields a provably consistent surrogate for disagreement discrepancy. Empirical evaluations across diverse benchmarks demonstrate that our method provides more accurate and robust estimates of disagreement discrepancy than existing approaches, particularly under challenging adversarial conditions.

Accurate real-time waypoints estimation for the UAV-based online Terrain Following during wildfire patrol missions is critical to ensuring flight safety and enabling wildfire detection. However, existing real-time filtering algorithms struggle to maintain accurate waypoints under measurement noise in nonlinear and time-varying systems, posing risks of flight instability and missed wildfire detections during UAV-based terrain following. To address this issue, a Residual Variance Matching Recursive Least Squares (RVM-RLS) filter, guided by a Residual Variance Matching Estimation (RVME) criterion, is proposed to adaptively estimate the real-time waypoints of nonlinear, time-varying UAV-based terrain following systems. The proposed method is validated using a UAV-based online terrain following system within a simulated terrain environment. Experimental results show that the RVM-RLS filter improves waypoints estimation accuracy by approximately 88$\%$ compared with benchmark algorithms across multiple evaluation metrics. These findings demonstrate both the methodological advances in real-time filtering and the practical potential of the RVM-RLS filter for UAV-based online wildfire patrol.

In this paper, we propose a recurrent neural network (RNN)-based framework for estimating the parameters of the fractional Poisson process (FPP), which models event arrivals with memory and long-range dependence. The Long Short-Term Memory (LSTM) network estimates the key parameters $μ>0$ and $β\in(0,1)$ from sequences of inter-arrival times, effectively modeling their temporal dependencies. Our experiments on synthetic data show that the proposed approach reduces the mean squared error (MSE) by about 55.3\% compared to the traditional method of moments (MOM) and performs reliably across different training conditions. We tested the method on two real-world high-frequency datasets: emergency call records from Montgomery County, PA, and AAPL stock trading data. The results show that the LSTM can effectively track daily patterns and parameter changes, indicating its effectiveness on real-world data with complex time dependencies.

Analyzing decision problems under uncertainty commonly relies on idealizing assumptions about the describability of the world, with the most prominent examples being the closed world and the small world assumption. Most assumptions are operationalized by introducing states of the world, conditional on which the decision situation can be analyzed without any remaining uncertainty. Conversely, most classical decision-theoretic approaches are not applicable if the states of the world are inaccessible. We propose a decision model that retains the appeal and simplicity of the original theory, but completely overcomes the need to specify the states of the world explicitly. The main idea of our approach is to address decision problems in a radically empirical way: instead of specifying states and consequences prior to the decision analysis, we only assume a protocol of observed act--consequence pairs as model primitives. We show how optimality in such empirical decision problems can be addressed by using protocol-based empirical choice functions and discuss three approaches for deriving inferential guarantees: (I) consistent statistical estimation of choice sets, (II) consistent statistical testing of choice functions with robustness guarantees, and (III) direct inference for empirical choice functions using credal sets. We illustrate our theory with a proof-of-concept application comparing different prompting strategies in generative AI models.

The main objective of this study is to propose an optimal transport based semi-supervised approach to learn from scarce labelled image data using deep convolutional networks. The principle lies in implicit graph-based transductive semi-supervised learning where the similarity metric between image samples is the Wasserstein distance. This metric is used in the label propagation mechanism during learning. We apply and demonstrate the effectiveness of the method on a GNSS real life application. More specifically, we address the problem of multi-path interference detection. Experiments are conducted under various signal conditions. The results show that for specific choices of hyperparameters controlling the amount of semi-supervision and the level of sensitivity to the metric, the classification accuracy can be significantly improved over the fully supervised training method.

As artificial intelligence and machine learning tools become more accessible, and scientists face new obstacles to data collection (e.g., rising costs, declining survey response rates), researchers increasingly use predictions from pre-trained algorithms as substitutes for missing or unobserved data. Though appealing for financial and logistical reasons, using standard tools for inference can misrepresent the association between independent variables and the outcome of interest when the true, unobserved outcome is replaced by a predicted value. In this paper, we characterize the statistical challenges inherent to drawing inference with predicted data (IPD) and show that high predictive accuracy does not guarantee valid downstream inference. We show that all such failures reduce to statistical notions of (i) bias, when predictions systematically shift the estimand or distort relationships among variables, and (ii) variance, when uncertainty from the prediction model and the intrinsic variability of the true data are ignored. We then review recent methods for conducting IPD and discuss how this framework is deeply rooted in classical statistical theory. We then comment on some open questions and interesting avenues for future work in this area, and end with some comments on how to use predicted data in scientific studies that is both transparent and statistically principled.

We consider the problem of learning the parameters of a $N$-dimensional stochastic linear dynamics under both full and partial observations from a single trajectory of time $T$. We introduce and analyze a new estimator that achieves a small maximum element-wise error on the recovery of symmetric dynamic matrices using only $T=\mathcal{O}(\log N)$ observations, irrespective of whether the matrix is sparse or dense. This estimator is based on the method of moments and does not rely on problem-specific regularization. This is especially important for applications such as structure discovery.

We formulate the Fast-Weights Homeostatic Reentry Network (FHRN) as a continuous-time neural-ODE system, revealing its role as a norm-regulated reentrant dynamical process. Starting from the discrete reentry rule $x_t = x_t^{(\mathrm{ex})} + γ\, W_r\, g(\|y_{t-1}\|)\, y_{t-1}$, we derive the coupled system $\dot{y}=-y+f(W_ry;\,x,\,A)+g_{\mathrm{h}}(y)$ showing that the network couples fast associative memory with global radial homeostasis. The dynamics admit bounded attractors governed by an energy functional, yielding a ring-like manifold. A Jacobian spectral analysis identifies a \emph{reflective regime} in which reentry induces stable oscillatory trajectories rather than divergence or collapse. Unlike continuous-time recurrent neural networks or liquid neural networks, FHRN achieves stability through population-level gain modulation rather than fixed recurrence or neuron-local time adaptation. These results establish the reentry network as a distinct class of self-referential neural dynamics supporting recursive yet bounded computation.

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