Nonstationary Model Research Articles

Hydrological drought assessment of the Yellow River Basin based on non-stationary model

Study Regionthe Yellow River Basin Study FocusNon-stationary hydrological conditions are becoming increasingly common due to climate change and human activities, and pose a novel challenge to the management of water resources and related risks, especially for large basins. However, prevalent research on drought assessment often ignores the non-stationary characteristics of hydrological processes. In this study, we investigated the stationarity of the runoff of the Yellow River Basin (YRB), the second-longest basin in China. We used an approach for assessing non-stationary droughts based on the generalized additive model for location, scale, and shape to establish a standardized runoff index containing covariates (SRI_cov) to identify hydrological droughts in the basin from 1986 to 2015. New Hydrological Insights for the RegionThe results show that the runoff was non-stationary in the YRB. Based on SRI_cov, hydrological drought predominantly occurred in the entire YRB in spring. From 1986, the number of months in which droughts occurred in the YRB exhibited a general trend of increase and peaked around 2002. After that, the total number of droughts significantly decreased but extreme droughts had become more prominent since 2005. The drought was more severe in the middle reaches of the Yellow River, and was characterized by a high frequency, intensity, and severity. Our analysis enhances the understanding of hydrological modeling and drought assessment under non-stationary conditions.

Regularization of the Ensemble Kalman Filter using a non-parametric, non-stationary spatial model

The sample covariance matrix of a random vector is a good estimate of the true covariance matrix if the sample size is much larger than the length of the vector. In high-dimensional problems, this condition is never met. As a result, in high dimensions the Ensemble Kalman Filter’s (EnKF) ensemble does not contain enough information to specify the prior covariance matrix accurately. This necessitates the need for regularization of the analysis (observation update) problem. We propose a regularization technique based on a new spatial model. The model is a constrained version of the general Gaussian process convolution model. The constraints include local stationarity and smoothness of local spectra. We regularize EnKF by postulating that its prior covariances obey the spatial model. Placing a hyperprior distribution on the model parameters and using the likelihood of the prior ensemble data allows for an optimized use of both the ensemble and the hyperprior. A linear version of the respective estimator is shown to be consistent. A more accurate nonlinear neural-Bayes implementation of the estimator is developed. In simulation experiments, the new technique led to substantially better EnKF performance than several existing techniques.

Increasing extreme hourly precipitation risk for New York City after Hurricane Ida.

The remnants of Hurricane Ida caused major damage and death in the United States on September 1st, 2021, and 11 people drowned in flooded basement apartments within New York City (NYC). It was catastrophic because the maximum hourly precipitation intensity, recorded as 3.47 inches (88.1mm) per hour at Central Park, was unprecedentedly high for the NYC region. The stormwater infrastructure in NYC is built for 1.75 inches (44.5mm) per hour, and so understanding the dynamic risk associated with Ida can inform city planning efforts for climate change's impact on short duration extreme precipitation events. We contextualize this storm's record-breaking hourly intensity within the historical record as well as project its risk in the near- to medium-term future using nonstationary stochastic models. These models are conditioned on average temperature (Tavg) and cooling degree day (CDD) projections from three climate models as a covariate, each with a SSP 126 and SSP 370 scenario. The likelihood of such a storm was slowly increasing even before Ida happened, but the projected aggregate reoccurrence risk of an event of Ida's magnitude over time from the non-stationary models ranges from 4 to 52 times higher than the risk given by the stationary model. Using CDD as a covariate resulted in risks that were more than twice the magnitude than when using Tavg. Presenting both covariates provides a broader envelope of uncertainty, which highlights the importance and nuances in the choice of a regionally appropriate covariate for non-stationary risk analysis.

Development of Rainfall Intensity Duration Frequency Curves for Debre Tabor Town, Ethiopia Using Non-stationary Method

Stationary rainfall intensity duration frequency curves have historically influenced urban infrastructure designs. In contrast to the stationary model, which takes constant parameters into account throughout the observation periods, the non-stationary method takes into account changes in the extreme parameters that determine the distribution of precipitation over time. The parameters were estimated using maximum likelihood estimator method. The best model were computed using the R-studio software by comparing information criteria then model parameters, return levels, rainfall intensity are computed. The National Meteorological Agency, situated in Addis Ababa, Ethiopia, provided the essential historical rainfall data of the Debre Tabor rainfall station for this study, Tests and trends were looked for in the rainfall data. Due to its ability to produce the lowest Akaike, corrected Akaike information criteria, and diagnosis test of goodness of fitness Model Type-MV was chosen for Debre Tabor stations. The parameters of the best models were used to forecast the return levels for each of the following return periods: 2, 5, 10, 25, 50, and 100 years. Because the non-stationary technique has varied intensity levels over time, the annual maximum rainfall from the best appropriate model was calculated using its exceedance probability. Using the 95% of exceedance of the return level, the highest rainfall in each fit was determined. In comparison to the stationary model, the non-stationary model produced higher rainfall intensity values. Therefore, when developing IDF curves, the non-stationary approach should be taken into consideration.

Investigation of the Influence of Environmental Thermal Characteristics on Thermal Modes of Transparent Boxes

This paper presents the results of experiments to investigate the influence of thermal characteristics of the environment on the thermal modes of transparent boxes. To conduct experiments on the non-stationary thermal model of solar greenhouses developed by us, two identical transparent boxes with dimensions of 0.80 x 0.65 x 0.80 m were constructed. The transparent boxes have rectangular shapes. One transparent box has glass walls and the other with polyethylene walls. The influence of the thermal characteristics of the environment and the thermal conditions inside the transparent boxes with film and glass transparent walls are investigated. The experimental results show that at a maximum ambient air temperature of 42 °C on 27.06.2024 at 13:48 hours, the air temperature increases to 10% and 23% in transparent boxes with polyethylene and with glass walls, respectively, and at 05:10 hours, the humidity decreases to 8% and 11%, respectively. Thus, the influence of the thermal characteristics of the environment on the thermal conditions of transparent boxes with glass walls, at the maximum ambient temperature, is greater by 1.2 times than in transparent boxes with polyethylene walls, and humidity decreases by half.

Spike and Slab Regression for Nonstationary Gaussian Linear Mixed Effects Modeling of Rapid Disease Progression

ABSTRACTSelect measures of social and environmental determinants of health (referred to as “geomarkers”), predict rapid lung function decline in cystic fibrosis (CF), defined as a prolonged decline relative to patient and/or center‐level norms. The extent to which hyper‐localization, defined as increasing the spatiotemporal precision of geomarkers, aids in prediction of rapid lung decline remains unclear. Linear mixed effects (LME) models with specialized covariance functions have been used for predicting rapid lung function decline, but there are few options to properly incorporate spatial correlation into the covariance functions while inducing simultaneous variable selection. Our innovative Bayesian model uses a spike and slab prior for simultaneous variable selection and offers additional advantages when coupled with nonstationary Gaussian LME modeling. This model also incorporates spatial correlation through an additional random effect term that accounts for spatial correlation based on ZIP code distances. We validated the model with simulations and applied it to real CF data from a Midwestern CF Center. We demonstrate how a combination of demographic, clinical, and geomarker variables can be selected as optimal predictors using Bayesian false discovery rate controlling rule. Our results indicate that incorporating spatiotemporal effects and geomarkers into this novel Bayesian stochastic LME model enhances the dynamic prediction of rapid CF disease progression.

High-resolution acoustic-impedance inversion based on a deep-learning-aided representation model of nonstationary seismic data

Building a high-resolution acoustic-impedance (AI) model based on nonstationary seismic data plays a key role in reservoir predictions. However, the common AI inversion methods are faced with two main shortcomings. First, because of the nonstationary feature of seismic data, a multiparameter inverse problem should be considered to not only estimate AI but also to estimate a time-varying wavelet or a quality factor ( Q) model, leading the problem to be more ill posed. Second, the resolution of the estimated AI is limited due to the band-limited nature of nonstationary seismic data. To address these issues, we develop a new nonstationary seismic AI inversion method. Notably, we develop a deep-learning-aided representation model to replace the nonstationary convolution model to solve the forward problem in inversion. Benefiting from multisource information (seismic data and well-log data) and the powerful nonlinear function fitting ability of deep learning, this model can map high-resolution AI to band-limited nonstationary seismic data without requiring a time-varying wavelet or a Q model. A new deep-learning architecture is developed for processing the spatio-temporal seismic data with better accuracy. In addition, total-variation regularization is adopted to enforce a physically reasonable AI model. The results of our 3D synthetic and field data experiments clearly demonstrate that our method has significant advantages over other common methods in building a high-resolution AI model.

Spectral cluster supertree: fast and statistically robust merging of rooted phylogenetic trees.

The algorithms for phylogenetic reconstruction are central to computational molecular evolution. The relentless pace of data acquisition has exposed their poor scalability and the conclusion that the conventional application of these methods is impractical and not justifiable from an energy usage perspective. Furthermore, the drive to improve the statistical performance of phylogenetic methods produces increasingly parameter-rich models of sequence evolution, which worsens the computational performance. Established theoretical and algorithmic results identify supertree methods as critical to divide-and-conquer strategies for improving scalability of phylogenetic reconstruction. Of particular importance is the ability to explicitly accommodate rooted topologies. These can arise from the more biologically plausible non-stationary models of sequence evolution. We make a contribution to addressing this challenge with Spectral Cluster Supertree, a novel supertree method for merging a set of overlapping rooted phylogenetic trees. It offers significant improvements over Min-Cut supertree and previous state-of-the-art methods in terms of both time complexity and overall topological accuracy, particularly for problems of large size. We perform comparisons against Min-Cut supertree and Bad Clade Deletion. Leveraging two tree topology distance metrics, we demonstrate that while Bad Clade Deletion generates more correct clades in its resulting supertree, Spectral Cluster Supertree's generated tree is generally more topologically close to the true model tree. Over large datasets containing 10,000 taxa and 500 source trees, where Bad Clade Deletion usually takes 2 h to run, our method generates a supertree in on average 20 s. Spectral Cluster Supertree is released under an open source license and is available on the python package index as sc-supertree.

Driving Forces of the Consumer Price Index During the Crises in the Eurozone: Heterogeneous Panel Approach

This paper examines key driving forces of inflationary pressures, taking into account supply and demand side determinants and actions of policy makers, during the pandemic and geopolitical crises in the Eurozone. Using heterogeneous nonstationary macro-panel models, especially the Mean Group (MG) and Pooled Mean Group (PMG) methods in the period 2020q1–2024q4, it is concluded that the dominant determination of inflationary pressures comes from the supply side. There is a long-run positive equilibrium relationship between the growth of energy prices and the growth of the consumer price index (CPI), and between the index representing supply bottlenecks (SBI) and the growth of CPI, while the relationship with the unemployment rate is insignificant. Also, the existence of a long-run equilibrium between the interest rate and CPI is homogeneous due to the unique monetary policy on a sample, and negative, indicating the efficiency of that policy. However, the speed of adjustment of individual economies is heterogeneous, and in the case of Greece and Ireland, insignificant. The heterogeneous or insignificant response of Eurozone member states, especially related to core-periphery asymmetry, refers to the vulnerability and structural weakness of the Eurozone economies, and the need for deeper integration.

Multi-covariate non-stationary flood frequency analysis for assessing flood hazard over the Mahanadi River basin, India

ABSTRACT Due to climate change and anthropogenic activities, the river’s peak flow is changing, which prompts exploring the non-stationary flood frequency analysis. Most of the past studies modelled the non-stationarity of floods, considering time and/or a single dominant covariate influencing the flood flows, but they are inadequate. This study proposes a multi-covariate non-stationary flood frequency model (MC-NSFFM) and investigates the influence of different covariates, such as rainfall, modified reservoir index (MRI), and climate indices, for the Mahanadi River basin in India. The models’ performances are evaluated by comparing them with the results of stationary and single-covariate non-stationary flood frequency models (SC-NSFFMs) using standard performance measures and return period analysis. The study showed that the MC-NSFFMs performed better than stationary and SC-NSFFMs. The flood return levels corresponding to the MC-NSFFMs are 4% to 22% higher than the stationary models, indicating the rise in flood risks due to climate change and anthropogenic activities.

Research on a Non-Stationary Groundwater Level Prediction Model Based on VMD-iTransformer and Its Application in Sustainable Water Resource Management of Ecological Reserves

The precise forecasting of groundwater levels significantly influences plant growth and the sustainable management of ecosystems. Nonetheless, the non-stationary characteristics of groundwater level data often hinder the current deep learning algorithms from precisely capturing variations in groundwater levels. We used Variational Mode Decomposition (VMD) and an enhanced Transformer model to address this issue. Our objective was to develop a deep learning model called VMD-iTransformer, which aims to forecast variations in the groundwater level. This research used nine groundwater level monitoring stations located in Hangjinqi Ecological Reserve in Kubuqi Desert, China, as case studies to forecast the groundwater level over four months. To enhance the predictive performance of VMD-iTransformer, we introduced a novel approach to model the fluctuations in groundwater levels in the Kubuqi Desert region. This technique aims to achieve precise predictions of the non-stationary groundwater level conditions. Compared with the classic Transformer model, our deep learning model more effectively captured the non-stationarity of groundwater level variations and enhanced the prediction accuracy by 70% in the test set. The novelty of this deep learning model lies in its initial decomposition of multimodal signals using an adaptive approach, followed by the reconfiguration of the conventional Transformer model’s structure (via self-attention and inversion of a feed-forward neural network (FNN)) to effectively address the challenge of multivariate time prediction. Through the evaluation of the prediction results, we determined that the method had a mean absolute error (MAE) of 0.0251, a root mean square error (RMSE) of 0.0262, a mean absolute percentage error (MAPE) of 1.2811%, and a coefficient of determination (R2) of 0.9287. This study validated VMD and the iTransformer deep learning model, offering a novel modeling approach for precisely predicting fluctuations in groundwater levels in a non-stationary context, thereby aiding sustainable water resource management in ecological reserves. The VMD-iTransformer model enhances projections of the water level, facilitating the reasonable distribution of water resources and the long-term preservation of ecosystems, providing technical assistance for ecosystems’ vitality and sustainable regional development.

Non-stationarity of runoff and sediment load and its drivers under climate change and anthropogenic activities in Dongting Lake Basin

Analysing non-stationarity in runoff and sediment load is crucial for effective water resource management in the Dongting Lake basin amid climate change and human impacts. Using the Mann-Kendall test, Generalized Additive Models for Location, Scale, and Shape framework, and Random Forest models, we evaluated non-stationarity and its drivers in the annual runoff and annual sediment load series at eight hydrological stations from 1961 to 2021. These stations include three inflow sites at the Jingjiang Three Outlets (Ouchi, Songzi, and Hudu Rivers), four inflow sites in the Four Rivers basin (Xiang, Zi, Yuan, and Li Rivers), and one outflow site at Chenglingji. Results revealed a significant decrease in annual runoff at the Three Outlets and Chenglingji, while the Four Rivers basin showed no significant trend. The non-stationary models with multiple physically-based covariates better captured non-stationarity compared to single covariate models. Annual rainfall was a key contributor to annual runoff in the Four Rivers basin, while reservoir storage capacity played a more dominant role in the Three Outlets. At Chenglingji station, both factors significantly influenced annual runoff. For annual sediment load, reservoir storage capacity emerged as the most critical factor across all regions. These findings provide a basis for improving runoff and sediment regulation in the Dongting Lake basin.

Integrating heterogeneous information for modeling non-stationarity of extreme precipitation in the Yangtze River Basin

Extreme precipitation exhibits non-stationary characteristics due to climate change and land use/cover change in recent years. In the literature, probability distributions with varying parameters associated with covariates have been applied to describe the non-stationarity of extreme precipitation. However, there is no consensus on the optimal distributions and the number and type of covariates for constructing non-stationary models. This study comprehensively investigates and determines the optimal distribution models, the type of covariates, and the number of covariates to best characterize the non-stationarity of extreme precipitation, using the Yangtze River Basin as the study area. The time series of four indices representing extreme precipitation of different durations and intensities are fitted by stationary and non-stationary Generalized Additive Models for Location, Scale, and Shape. The models are constructed using seven distributions and four types (time, global climate, local climate, and land cover) of covariates. Each model incorporates one to three covariates simultaneously. The results show that the most preferred distribution is the Generalized Extreme Value distribution for very wet-day precipitation, while the Log-Normal distribution is more suitable for other extreme precipitation indices. For the type of covariates, when using a single covariate, the proportion of stations using a global climate covariate as the best covariate (22.3 %–33.2 % of 193 stations) is close to that using a local climate covariate as the best covariate (22.3 %–27.5 %). The proportion of stations using land cover as the best covariate is much lower (7.3 %–10.9 %), while that using time as the best covariate is the lowest (1.6 %–4.1 %). When using multiple covariates, the models with both global and local climate covariates are mostly selected (8.3 % to 17.6 %) for all extreme precipitation indices. For the number of covariates, one or two covariates are enough to describe the non-stationary behaviors of all extreme precipitation indices. This study emphasizes the necessity to use non-stationary models for extreme precipitation frequency analysis with careful consideration and selection of distributions and covariates.

Assessing extreme significant wave height in China’s coastal waters under climate change

Accurately estimating the return values of significant wave height is essential for marine and coastal infrastructure, particularly as climate change intensifies the frequency and intensity of extreme wave events. Traditional models, which assume stationarity in wave data, often underestimate future risks by neglecting the impacts of climate change on wave dynamics. Combining time series decomposition and recurrence analysis, the research develops a nonstationary framework to predict significant wave height. The stochastic component is modelled using a stationary probability distribution, while the deterministic component is predicted based on sea surface temperature projections from CMIP6 climate scenarios. The model evaluation demonstrates strong predictive capability for both stochastic and deterministic components. Application of the model to China’s coastal waters reveals significant discrepancies between stationary and nonstationary return value estimates. Compared to conventional distribution models, the nonstationary model predicts substantial increases in extreme wave heights. These findings underscore the importance of adopting nonstationary models to more accurately assess future risks posed by extreme wave events in a changing climate.

Overtaking risk assessment based on extreme value theory and intelligent network information

In order to evaluate the overtaking risk level of intelligent connected vehicles when providing different connected information, and to make up for the neglect of driver factors in traditional risk assessment and the inadequate evaluation of complex traffic scenarios by a single traffic conflict indicator, this paper introduces the Block maxima (BM) and Peak over threshold (POT) methods to fit the extreme value distribution for two conflict scenarios involved in overtaking events (following vehicle conflict and frontal vehicle conflict), so as to evaluate the risk of following vehicle accidents and frontal collision accidents during overtaking. In each conflict scenario, a non-stationary extreme value model considering driver factors and a binary extreme value model considering different traffic conflict indicators are constructed, and the model is verified by the overtaking test data of intelligent connected vehicles in a two-way two-lane vehicle. Overtaking events were extracted from the original test data and conflict indicators were calculated: including the collision time GAP with the front vehicle at the beginning of the overtaking event, the collision time TTC_t1 with the oncoming vehicle, the deceleration DRAC, and the collision time TTC with the oncoming vehicle and the headway time THW with the front vehicle at the end of the overtaking event. The probability of the event with a negative time conflict indicator or DRAC greater than MADR was used to characterize the degree of collision risk. The results show that in the following vehicle conflict scenario, the binary extreme value model constructed with different conflict indicators has different error results, among which the binary extreme value model constructed with THW&DRAC has the most accurate evaluation result (standard error MAE = 0.00028); in the front vehicle conflict scenario, the binary extreme value model constructed with TTC&DRAC has the most accurate evaluation result ( MAE = 0.006 ). In different conflict scenarios, the non- stationary extreme value model considering the driver factor significantly improves the risk assessment accuracy compared with the model without considering the driver factor (small AIC and BIC values). In addition, different intelligent network information (real-time distance, overtaking advice, speed advice) brings different overtaking risks, and when the intelligent network information is speed advice, the vehicle's overtaking risk is the lowest. Therefore, the non- stationary extreme value model and binary extreme value model considering driver factors proposed in this paper can effectively evaluate driving risks through traffic conflict indicators. Secondly, the experimental data of intelligent networked vehicles show that the extreme value theory model proposed in this paper can accurately evaluate the overtaking risk level of intelligent networked vehicles when providing different network information.

Validation and Comparison of Non-stationary Cognitive Models: A Diffusion Model Application

AbstractCognitive processes undergo various fluctuations and transient states across different temporal scales. Superstatistics are emerging as a flexible framework for incorporating such non-stationary dynamics into existing cognitive model classes. In this work, we provide the first experimental validation of superstatistics and formal comparison of four non-stationary diffusion decision models in a specifically designed perceptual decision-making task. Task difficulty and speed-accuracy trade-off were systematically manipulated to induce expected changes in model parameters. To validate our models, we assess whether the inferred parameter trajectories align with the patterns and sequences of the experimental manipulations. To address computational challenges, we present novel deep learning techniques for amortized Bayesian estimation and comparison of models with time-varying parameters. Our findings indicate that transition models incorporating both gradual and abrupt parameter shifts provide the best fit to the empirical data. Moreover, we find that the inferred parameter trajectories closely mirror the sequence of experimental manipulations. Posterior re-simulations further underscore the ability of the models to faithfully reproduce critical data patterns. Accordingly, our results suggest that the inferred non-stationary dynamics may reflect actual changes in the targeted psychological constructs. We argue that our initial experimental validation paves the way for the widespread application of superstatistics in cognitive modeling and beyond.

Mathematical Modelling of Spatially Inhomogeneous Non-Stationary Interaction of Pests with Transgenic and Non-Modified Crops Considering Taxis

Introduction. This paper addresses a unified spatially inhomogeneous, non-stationary model of interaction between genetically modified crop resources (corn) and the corn borer pest, which is also present on a relatively small section of non-modified corn. The model assumes that insect pests influence both types of crops and are capable of independent movement (taxis) towards the gradient of plant resources. It also considers diffusion processes in the dynamics of all components of the unified model, biomass growth, genetic characteristics of both types of plant resources, processes of crop consumption, phenomena of growth and degradation, diffusion, and mutation of pests. The model allows for predictive calculations aimed at reducing crop losses and increasing the resistance of transgenic crops to pests by slowing down the natural mutation rate of the pest. Materials and Methods. The mathematical model is an extension of Kostitsin’s model and is formulated as an initial-boundary value problem for a nonlinear system of convection-diffusion equations. These equations describe the spatiotemporal dynamics of biomass density changes in two types of crops — transgenic and non-modified — as well as the specific populations (densities) of three genotypes of pests (the corn borer) resulting from mutations. The authors linearized the convection-diffusion equations by applying a time-lag method on the time grid, with nonlinear terms from eachequation taken from the previous time layer. The terms describing taxis are presented in a symmetric form, ensuring the skew-symmetry of the corresponding continuous operator and, in the case of spatial grid approximation, the finite-difference operator. Results. A stable monotonic finite-difference scheme is developed, approximating the original problem with second-order accuracy on a uniform 2D spatial grid. Numerical solutions of model problems are provided, qualitatively corresponding to observed processes. Solutions are obtained for various ratios of modified and non-modified sections of the field. Discussion and Conclusion. The obtained results regarding pest behavior, depending on the type of taxis, could significantly extend the time for pests to acquire Bt resistance. The concentration dynamics of pests moving in the direction of the food gradient differs markedly from the concentration of pests moving towards a mate for reproduction.

Experts still needed: boosting long-term android malware detection with active learning

The continuous evolution of cyber threats imposes a critical challenge to malware detection systems, so operational detection solutions in real-world settings must keep up-to-date malware knowledge databases. Machine learning-based solutions are not exempt from this requirement as handling concept drift constitutes the primary building block for keeping high detection performance in the long term. However, maintaining non-stationary malware detection models is highly demanding due to the high cost of labeling. This study applies several active learning-based approaches for maintaining a non-stationary model for Android malware detection in a 7-year-long time frame and conducts a comprehensive analysis to understand the impact of feature space selection, different data balancing techniques, and timestamping methods, utilized for locating the instances along the historical timeline, on the model’s detection performance over time. The detection accuracy and labeling costs are compared with various baselines. Additionally, the study investigates the resilience of such models against noisy labeling, a common problem in production environments due to unintentional expert errors and adversarial attacks. This research fills a significant gap in the literature by conducting a comprehensive analysis of active learning approaches to address concept drift in non-stationary settings established for mobile malware detection.

Bayesian inference for group-level cortical surface image-on-scalar regression with Gaussian process priors.

In regression-based analyses of group-level neuroimage data, researchers typically fit a series of marginal general linear models to image outcomes at each spatially referenced pixel. Spatial regularization of effects of interest is usually induced indirectly by applying spatial smoothing to the data during preprocessing. While this procedure often works well, the resulting inference can be poorly calibrated. Spatial modeling of effects of interest leads to more powerful analyses; however, the number of locations in a typical neuroimage can preclude standard computing methods in this setting. Here, we contribute a Bayesian spatial regression model for group-level neuroimaging analyses. We induce regularization of spatially varying regression coefficient functions through Gaussian process priors. When combined with a simple non-stationary model for the error process, our prior hierarchy can lead to more data-adaptive smoothing than standard methods. We achieve computational tractability through a Vecchia-type approximation of our prior that retains full spatial rank and can be constructed for a wide class of spatial correlation functions. We outline several ways to work with our model in practice and compare performance against standard vertex-wise analyses and several alternatives. Finally, we illustrate our methods in an analysis of cortical surface functional magnetic resonance imaging task contrast data from a large cohort of children enrolled in the adolescent brain cognitive development study.

A Non-Stationary Beam-Enabled Stochastic Channel Model and Characterization over Non-Reciprocal Beam Patterns

A Non-Stationary Beam-Enabled Stochastic Channel Model and Characterization over Non-Reciprocal Beam Patterns