A new perspective for slope reliability analysis: hyper-spherical ring-enhanced adaptive Bayesian failure probability inference

Nocifensive behavior (NB) is a protective response to noxious stimuli that threaten tissue damage. However, similar motor responses, termed nocifensive-like behavior (NLB), can be evoked by unexpected innocuous stimuli. This observation challenges strict “labeled-line” models of pain, raising a fundamental question: how does the nervous system discriminate true threats from false alarms? We review evidence suggesting NB and NLB exist on a shared behavioral continuum, where defensive responses aren’t determined solely by sensory input but by the brain’s integrated threat assessment. This assessment computes the probability of harm by weighing somatosensory input against contextual factors like prior experience and multisensory cues. We propose this process is governed by a threat prediction error (TPE) mechanism, which is computationally analogous to the reward prediction error (RPE) mechanism encoded by the dopaminergic system. Under this framework, defensive responses are scaled to the magnitude of the TPE – the discrepancy between expected and actual sensory outcomes. Critically, this means the surprise of a benign touch in a dangerous environment can produce a larger TPE – and a stronger withdrawal – than the anticipation of a noxious pinprick in a safe environment. Furthermore, while NLB represents an adaptive response that can be permanently resolved as the stimulus is learned to be non-threatening, NB represents an innate response, permitting only transient suppression due to the real risk of injury. This model positions defensive behaviors as dynamic perceptual decisions arising from probabilistic inference, offering a unified theory for how context and expectation gate the expression of protective motor programs.

Proportional information is important for a range of everyday actions, from infants' and toddler's probabilistic inferences to adults' medical and financial decisions. Unfortunately, children and adults frequently make systematic errors in some proportional reasoning contexts. For example, people tend to focus more on the numerators, rather than the proportional relations, when proportions are discrete (i.e., with enumerable units) or when the subcomponents are spatially separated. Importantly, it is not that people cannot reason proportionally, as they do not make these same errors with continuous proportions presented as part of a single coherent whole. Although format-dependent variation has been shown across many studies with both children and adults, no work has systematically manipulated multiple aspects of visual, nonsymbolic proportional stimuli simultaneously to better understand which spatial factors impact proportional reasoning, and how. Here, we manipulate proportional stimuli in three ways: the availability of enumerable units (i.e., discreteness), predictability of the proportional information, and spatial separateness of the proportion subcomponents. We also formalize competing strategy explanations using mathematical models to infer people's strategies. Overall, we find that discreteness, predictability, and spatial separateness (as operationalized here) significantly impact adults' performance and strategies. Furthermore, all features interact with each other, and qualitative patterns suggest that spatial separateness and predictability may be particularly important, despite being less well-studied. By systematically varying the spatial features of proportions, we provide insight into the mechanisms that underlie proportional reasoning and highlight important interactions between spatial, numerical, and relational information. (PsycInfo Database Record (c) 2026 APA, all rights reserved).

Communication and control in biological systems is mediated by the timing of discharges -spikes- from excitable cells such as neurons and muscle fibers. Each spike is associated to a characteristic waveform that can be captured by sensors. The waveform's characteristics depend on the cell's biophysical properties and the recording modality. Depending on the technique, e.g., electrical recordings with electrodes, optical imaging, ultrasound, the observed signals are mixtures of waveforms emitted from active cells/sources (multiunit data/signals). Recovering the timing and identity of these sources (multiunit or spike decoding) is central to neuroscience, clinical diagnostics, and neural interfacing, yet it remains challenging due to waveform superposition, non-stationarity, limited training labels, and the computational demands of high-density recordings. This review provides a unified methodological perspective on spike decoding by formalizing the problem as a sparse source separation task under a convolutive mixing model. Rather than organizing the literature by application domain, we group and critically compare methods by their underlying principles: classical spike sorting, Bayesian and probabilistic inference, blind source separation, and data-driven approaches, including deep learning and hybrid schemes. For each class of methods, we present the core mathematical formulation and algorithmic strategies and discuss assumptions and limitations. Our synthesis highlights parallels in signal processing across physical recording modalities and clarifies when and why particular approaches succeed or fail. By bridging previously compartmentalized literature, this survey aims to accelerate crosspollination of ideas between application areas and to provide a roadmap for selecting, adapting, and advancing decoding methods across diverse multiunit recording modalities.

Abstract Stability selection is a versatile framework for structure estimation and variable selection in high-dimensional settings, primarily grounded in frequentist principles. In this paper, we propose an enhanced methodology that integrates Bayesian analysis to refine the inference of selection probabilities within the stability selection framework. Traditional approaches rely on selection frequencies for decision-making, often overlooking domain-specific knowledge. Our methodology uses prior information to derive posterior distributions of selection probabilities, thereby improving both inference and decision-making. We present a two-step process for engaging with domain experts, enabling statisticians to construct prior distributions informed by expert knowledge, while allowing experts to control the weight of their input on the final results. Using posterior distributions, we offer Bayesian credible intervals to quantify uncertainty in the variable selection process. Furthermore, we demonstrate how incorporating prior knowledge improves selection stability by reducing the variance of selection probabilities and how it contributes to the per-family error rate. Our approach preserves the versatility of stability selection and is suitable for a broad range of structure estimation challenges.

Global warming and increasing heat events necessitate long-term assessments of passive design strategies to ensure thermal resilience under future climatic conditions. Although machine-learning-based Surrogate Models (SMs) offer timely approximation of building performance compared to conventional simulation-based approaches, the lack of uncertainty quantification raises concerns about the reliability of their design optimization outcomes. This study aims to develop a robust surrogate-assisted optimization framework, based on a probabilistic Bayesian Neural Network (BNN) model and supported by an uncertainty-aware objective function. The framework is applied to an affordable housing case study in Surakarta, Indonesia, evaluating its generalizability under current and future climatic scenarios for 2050, 2070, and 2090. Thermal resilience is assessed through overheating hours exceeding acceptability limits in Southeast Asian context, using a parametric workflow implemented in Ladybug-tools and Grasshopper 3D. Compared to simulated test data, the BNN model demonstrates reliable predictive accuracy and probabilistic inference (R2 = 0.99, MAE = 0.52%, CRPS = 0.38%). Furthermore, validation against re-evaluated optimal solutions shows low error ranges (RMSE = 0.43%, MAE = 0.33%), outperforming the deterministic SM optimization approach—using Artificial Neural Networks—by a factor of five. Overall, the uncertainty-aware framework provides a feasible, overconfidence-resistant, and reliable surrogate-assisted optimization method, identifying optimal solutions closely matching those from simulation-based optimization while reducing computational time by 96%.

Censored geochemical data, particularly below detection limits, challenge mineral exploration by biasing anomaly delineation and spatial patterns. This study presents a multi-stage framework combining Bayesian Gaussian Random Field (BGRF) modeling with Random Forest (RF) learning, enhanced by fractal-based background separation, to accurately predict censored Au concentrations. 14 samples with gold concentrations below 5 ppb were hypothesized as censored data to enable a more accurate evaluation of the model's performance based on their real Au concentrations. Unlike constant substitution methods, the framework preserves censored information and reconstructs spatial variability through probabilistic inference and nonlinear learning. The BGRF model incorporates spatial coordinates and Cu as the principal covariate to capture spatial autocorrelation and inter-element associations, producing probabilistic estimates for hypothesized censored data (HCD) that are then used to train the RF under a 5-fold out-of-fold scheme. The HCD estimated by spatial BGRF covariate model were performed as inputs for RF prediction model. A targeted calibration and scaling procedure reduces detection-limit bias and improves low-range predictions. Comparative analyses show that the calibrated and scaled RF-BGRF model substantially enhances accuracy and preserves realistic geochemical structures, outperforming half the detection limit (LD-half) or the detection limit divided by the square root of two (LD-rad2) approaches. This framework offers a promising tool for refining left-censored geochemical data in complex geological environments.

By enhancing transient fidelity before geometric inversion, this work revisits the classical LCT-based non line-of-sight (NLOS)imaging paradigm and establishes a unified Bayesian sparse-enhancement framework for reconstructing hidden objects under photon-starved and hardware-limited conditions. We introduce sparse Bayesian learning (SBL) as a dedicated front-end transient restoration module, leveraging adaptive sparsity modeling to suppress background fluctuations while preserving physically consistent multipath returns. This lightweight and geometry-agnostic design enables seamless integration into existing LCT processing pipelines, granting the framework strong compatibility with diverse acquisition configurations. Comprehensive simulations and experiments on complex reflective targets demonstrate significant improvements in spatial resolution, boundary sharpness, and robustness to IRF-induced temporal blurring compared with traditional LCT and f-k migration methods. The results validate that transient quality remains a critical bottleneck in practical NLOS deployment, and addressing it via probabilistic sparsity inference offers a scalable and computationally affordable pathway toward stable, high-fidelity NLOS reconstruction. This study provides an effective signal-domain enhancement solution that strengthens the practicality of NLOS imaging in real-world environments, paving the way for future extensions toward dynamic scenes, multi-view fusion, and high-throughput computational sensing.

Inverse material design, which seeks microstructures yielding desired macroscopic properties, is inherently ill-posed due to non-uniqueness and the existence of unattainable targets. While data-driven generative models offer powerful empirical solutions, they often lack rigorous theoretical guarantees. This paper establishes a formal probabilistic learning framework to address these challenges. We first prove that the forward homogenization map, which predicts effective properties from a microstructure descriptor field, is Frechet differentiable and locally Lipschitz continuous under physically reasonable assumptions. This foundational result justifies the use of gradient-based methods and sensitivity analysis. Building upon this, we demonstrate the probabilistic well-posedness of the Bayesian inverse problem: the posterior distribution over microstructures is well-defined and depends continuously on the target property data. Furthermore, we prove Bayesian consistency, showing that as observational uncertainty vanishes, the posterior measure concentrates on the true set of solutions. This theoretical foundation validates advanced probabilistic inference techniques (e.g., MCMC, variational inference) for robustly exploring the solution manifold and quantifying uncertainty, thereby enabling a more complete and practical exploration of the material design space.

Adaptive behavior requires maintaining and updating probabilistic beliefs about the world, yet how distributed brain circuits implement such computations remains unknown. We recorded from over 1,400 neurons across six brain regions in monkeys performing a multi-dimensional inference task requiring them to infer hidden rules through trial-and-error learning. Behavior was well-described by models based on Bayesian updating of beliefs over rule features. Neural representations of both observable variables (stimuli, rewards) and latent beliefs (rule preferences, confidence) were broadly distributed across hippocampus, amygdala, prefrontal cortex, anterior cingulate, striatum, and inferior temporal cortex. Belief representations were present throughout all task periods but exhibited region- and epoch-specific dynamics. Critically, trial-to-trial changes in population activity reflected Bayesian belief updating: neural responses evolved according to the integration of prior beliefs with new evidence. Additionally, we identified confidence representations that were independent of specific beliefs and showed distinct temporal profiles. These results demonstrate that probabilistic inference emerges from coordinated dynamics across distributed brain systems, with different regions contributing flexibly according to computational demands at different states of learning and decision-making.

ABSTRACTIn 2020, Sao Caetano do Sul city, located in the metropolitan region of Sao Paulo State, Brazil, established a web-based platform to provide primary care to suspected COVID-19 patients, integrating clinical and demographic data and sample metadata. Here we describe lineage-specific spatiotemporal dynamics of infections, clinical symptoms, and disease severity during the first year of the epidemic, which included circulation of the poorly characterised Gamma variant of concern. From April 6, 2020, to April 30, 2021, we gathered clinical, demographic, spatial and epidemiological data from the city's platform. We selected and sequenced 879 PCR+ swab samples (8% of all reported cases), obtaining a spatially and temporally representative set of sequences. Daily lineage-specific prevalence was estimated with a moving-window approach, allowing inference of cumulative cases and symptom probability stratified by lineage using integrated data from the platform. Most infections were caused by B.1.1.28 (41.3%), followed by Gamma (31.7%), Zeta (9.6%), and B1.1.33 (9.0%). Gamma and Zeta correlated with larger prevalence of dyspnoea (respectively, 81.3% and 78.5%) and persistent fever (84.7% and 61.1%) compared with B.1.1.28 and B.1.1.33. Ageusia, anosmia, and coryza were respectively 18.9%, 20.3%, and 17.8% less commonly caused by Gamma, whereas altered mental status was 108.9% more common in Zeta. Case incidence was spatially heterogeneous and larger in poorer and younger districts. Our study reveals that Gamma was associated with more severe presentation of the disease, emphasising its role in the heightened mortality levels in Brazil.

Abstract: This study investigates a sensing-to-action pipeline for GPS-denied autonomy that explicitly couples navigation uncertainty to safety-constrained decision-making. GPS denial is intrinsic to subsea operations and frequently arises in space and lunar environments where satellite navigation is unavailable or unreliable, and where perception is degraded by scattering, aliasing, and extreme illumination. A factor-graph formulation implemented in GTSAM is used to express multi-sensor navigation as probabilistic inference, enabling posterior covariances and estimator-health diagnostics to be produced alongside state estimates. Quantum-limited sensing is introduced as a physically grounded way to bound inertial uncertainty by clamping process noise and bias evolution to experimentally demonstrated performance envelopes from quantum accelerometry and quantum rotation sensing. The empirical foundation uses two real-world, public datasets that capture GPS-denied conditions in domains relevant to space and marine robotics. The AQUALOC underwater harbor sequences combine monocular imagery, inertial measurements, and pressure-derived depth, thereby capturing feature intermittency and scale/altitude challenges typical of underwater SLAM. The DLR S3LI planetary analog dataset was recorded on Mount Etna in volcanic terrain using stereo vision, solid-state LiDAR with limited field of view and minimum range, and inertial sensing, thereby capturing perceptual aliasing and sparse geometry. Published benchmark results on these datasets are consolidated into inline tables and figures to quantify accuracy–robustness trade-offs that directly affect safety. Results show (i) consistent underwater accuracy gains from pressure-aided fusion but sensitivity to tracking loss, (ii) pronounced completion–accuracy trade-offs on planetary-analog terrain, and (iii) orders-of-magnitude differences in inertial drift bounds when quantum-limited accelerometry and rotation sensing envelopes are used as uncertainty floors. A risk proxy based on chance-constraint tails illustrates how reduced uncertainty can justify smaller safety buffers for a fixed probability-of-violation target, improving mission feasibility in constrained environments. The resulting blueprint treats uncertainty as a first-class output, validates it through consistency tests, and consumes it in a planner that enforces probabilistic safety constraints. Keywords:GPS-denied navigation; factor graphs; GTSAM; uncertainty quantification; quantum inertial sensing; risk-aware planning; underwater SLAM; planetary robotics; safety constraints.

The quantification of uncertainty in scientific modeling is fundamentally divided between the classical (frequentist) and Bayesian paradigms, compelling practitioners to adopt an either/or approach that often discards valuable information. This paper introduces a novel, unified mathematical framework that synthesizes the inferential outputs of both paradigms. Leveraging the likelihood function as a common foundation, the framework employs a linear pooling operator to combine the classical confidence distribution and the Bayesian posterior distribution into a single, more comprehensive representation of uncertainty, the primary output is a "Unified Uncertainty Interval" (UUI), which inherits both the long-run frequency guarantees of confidence intervals and the intuitive, belief-based interpretation of credible intervals. Case studies involving binomial proportion estimation, particularly under conditions of prior-data conflict, demonstrate that the UUI provides a robust and balanced measure of uncertainty, the framework offers a pragmatic solution to bridge the gap between classical and Bayesian approaches, providing a richer, more nuanced tool for decision-making under uncertainty and moving beyond paradigmatic dogmatism towards a more holistic inferential practice

The Dakwäkäda (Haines Junction) area is in a tectonically active region of Yukon, Canada, with significant natural hazard potential. Despite this, little knowledge exists about local site properties, which influence earthquake shaking intensity and duration (site effects). This work constrains sediment properties to quantify these effects. Passive seismic recordings at 14 sites are used to extract dispersion measurements and probabilistically infer 1D subsurface shear-wave velocity (VS), including rigorous model uncertainty quantification. The VS models are used to classify sites according to proxies for site rigidity. Results, including uncertainties, are propagated into estimates of linear site amplification factors for earthquake ground motion determination. Our results indicate much of the area can be characterized by site class C and modest amplification potential. Spatial variability in our results are predominantly attributed to hydrologic and cryospheric processes. The presence of permafrost in the area may currently mitigate amplification of earthquake shaking. Our results point to the need to understand seasonal and long-term changes in site effects, particularly in response to permafrost thaw within the warming climate. Results from this work can contribute to strategic community planning that mitigates natural hazards in the Dakwäkäda area, and other seismically active areas throughout the global North.

BackgroundAdvances in single-cell and spatial transcriptomics have transformed our understanding of tumor cell states and lineage dynamics, enabling high-resolution investigation of cellular heterogeneity and evolution.MotivationBuilding on Schiffman et al.’s Markovian framework for inferring cell state transitions from single-cell lineage tracing, there is a need for models that integrate spatial context to better capture the dynamics of tumor evolution.Method and resultsWe introduce StateSim, a spatial–temporal model that simulates tumor cell state transitions within tissue, incorporating spatial growth and mutation accumulation (Waclaw, et al. 2015). StateSim assumes that daughter cells are spatial neighbors, shaping the spatial organization of cell states, and models two cell states with distinct birth and death rates. To quantify spatial patterns, we developed StateMap, a network-based approach that maps tumor cell states and their spatial relationships, summarizing transition patterns through network statistics. Applying StateSim under various transition scenarios, we demonstrate that distinct transition modes yield unique spatial statistics, robustly correlated with transition rates (Pearson r = 0.9938, P = 6.87e-10). Using spatial transcriptomics data from glioma samples (Greenwald, et al. 2024), StateMap identified subgroups with distinct transition patterns, further validated by spatial statistics such as bivariate Moran’s I. Approximate Bayesian computation with StateSim enabled inference of posterior probabilities for cell state transition rates and phylogenetic trajectories.ConclusionOur framework enables inference of cell state transitions and in-silico lineage tracing from spatial data, advancing studies of tumor heterogeneity and evolution.SignificanceThis work provides a novel computational approach for integrating spatial and temporal information to decipher the dynamics of cell state transitions and lineage development during cancer evolution, offering new insights into tumor heterogeneity and progression.

Network neuroscience has proven essential for understanding the principles and mechanisms underlying complex brain (dys)function and cognition. In this context, whole-brain network modeling—also known as virtual brain modeling—combines computational models of brain dynamics (placed at each network node) with individual brain imaging data (to coordinate and connect the nodes), advancing our understanding of the complex dynamics of the brain and its neurobiological underpinnings. However, there remains a critical need for automated model inversion tools to estimate control (bifurcation) parameters at large scales associated with neuroimaging modalities, given their varying spatio-temporal resolutions. This study aims to address this gap by introducing a flexible and integrative toolkit for efficient Bayesian inference on virtual brain models, called Virtual Brain Inference (VBI). This open-source toolkit provides fast simulations, taxonomy of feature extraction, efficient data storage and loading, and probabilistic machine learning algorithms, enabling biophysically interpretable inference from non-invasive and invasive recordings. Through in-silico testing, we demonstrate the accuracy and reliability of inference for commonly used whole-brain network models and their associated neuroimaging data. VBI shows potential to improve hypothesis evaluation in network neuroscience through uncertainty quantification and contribute to advances in precision medicine by enhancing the predictive power of virtual brain models.

Network neuroscience has proven essential for understanding the principles and mechanisms underlying complex brain (dys)function and cognition. In this context, whole-brain network modeling-also known as virtual brain modeling-combines computational models of brain dynamics (placed at each network node) with individual brain imaging data (to coordinate and connect the nodes), advancing our understanding of the complex dynamics of the brain and its neurobiological underpinnings. However, there remains a critical need for automated model inversion tools to estimate control (bifurcation) parameters at large scales associated with neuroimaging modalities, given their varying spatio-temporal resolutions. This study aims to address this gap by introducing a flexible and integrative toolkit for efficient Bayesian inference on virtual brain models, called Virtual Brain Inference (VBI). This open-source toolkit provides fast simulations, taxonomy of feature extraction, efficient data storage and loading, and probabilistic machine learning algorithms, enabling biophysically interpretable inference from non-invasive and invasive recordings. Through in-silico testing, we demonstrate the accuracy and reliability of inference for commonly used whole-brain network models and their associated neuroimaging data. VBI shows potential to improve hypothesis evaluation in network neuroscience through uncertainty quantification and contribute to advances in precision medicine by enhancing the predictive power of virtual brain models.

This article shows how inference is treated within the context of Eigenlogic projection operators in linear algebra. In Eigenlogic, operators represent logical connectives, their eigenvalues the truth-values and the associated eigenvectors the logical models. By extension, a probabilistic interpretation is proposed using vectors outside the eigensystem of the Eigenlogic operators. The probability is calculated by the quantum mean value (Born rule) of the logical projection operators. We look here for possible connections between the Born rule in quantum mechanics and Bayes' theorem from probability theory and show that Eigenlogic offers an innovative approach to address the probabilistic version of logical inference (material implication) in a quantum context. This article is part of the theme issue 'Quantum theory and topology in models of decision making (Part 2)'.

Abstract Predictive coding, as proposed by the Bayesian brain hypothesis, and surrealism present an intriguing overlap. The Bayesian brain hypothesis views the brain as a probabilistic inference system that updates its beliefs based on sensory inputs, while surrealism explores the unconscious mind by challenging conventional thought and societal norms. This paper first demonstrates how the Bayesian brain hypothesis serves as a neo-surrealistic framework for understanding brain function. It then explores how the Bayesian brain hypothesis and surrealist techniques can be integrated to generate valuable insights about the human unconscious for art therapy. This convergence broadens scientific understanding by opening new avenues for research and practical applications at the intersection of neuroscience and art therapy, ultimately enhancing therapeutic outcomes for individuals seeking psychological support.

Impulsive, non-Gaussian interference in urban 5G/6G wireless scenarios invalidates Gaussian-noise-based assumptions of conventional detectors. This work proposes the use of the Machine Learning-Enhanced Bayesian Detector for DS-CDMA systems over α-stable noise channels. The framework merges probabilistic Bayesian inference with a recurrent neural-network estimator that continuously learns α-stable parameters α, β, γ, and δ from the received data. Closed-form derivations of the detection and false alarm probabilities are obtained using characteristic-function-based likelihood ratios, whereas the proposed approach is corroborated via MATLAB simulations. The results demonstrate that ML-BD provides a 3-dB SINR gain, ≈ 45% BER reduction, and ≈ 15% increase in the detection probability compared to classical Bayesian and energy detectors. This work demonstrates that the marriage of adaptive learning with Bayesian reasoning results in a robust, interpretable, and computationally efficient detector for interference-limited 5G/6G metropolitan networks.