arXiv subjects

Ingelin Steinsland

Publications and source records attributed to Ingelin Steinsland.

13 recordsLinked to original sources

arXiv2026

On the spatial statistics of free-surface turbulence and the complementarity of 'dimples' and 'scars'

The air--water interface governs the exchange of heat and gas between natural water bodies and their surrounding environment. Turbulence beneath the free surface imprints characteristic features: near-circular depressions (`dimples') and elongated indentations (`scars'). Recent studies have shown that these are linked to sub-surface flow features in a temporal sense. For instance, rapid increases in mean-square surface divergence due to upwelling events, precede dimple count surges. Yet the spatial structure of these connections remains unquantified. We employ spatial statistics to consider the spatial and temporal correlations between dimples and scars and two key velocity-derived fields, surface divergence $β=\partial_x u+\partial_y v$ and vertical vorticity $ω=\partial_x v-\partial_y u$. The dimples and scars are modelled as inhomogeneous Poisson point-processes, with intensity fields driven by the local variance of $β$ and $ω$. Parameters, including spatial support radius $r$ and time lag $τ$, are estimated by maximum likelihood against six DNS datasets, quantifying the spatial and temporal connection between dimples, scars, surface divergence and vorticity. Our results demonstrate a clear complementarity: Dimples show strong local connection to the vertical vorticity field but has weak spatial connection with surface divergence and a spatially ``global'' model is required for dimples to work as estimators of surface divergence; scars, in a similar but opposite manner, couple locally to surface divergence but globally to the vertical vorticity. The complementarity sheds new light on the way dimples and scars may be used to infer fluxes across the surface, e.g., in remote sensing contexts.

physics.flu-dyn↗

arXiv2024

A Spatial-statistical model to analyse historical rutting data

Pavement rutting poses a significant challenge in flexible pavements, necessitating costly asphalt resurfacing. To address this issue comprehensively, we propose an advanced Bayesian hierarchical framework of latent Gaussian models with spatial components. Our model provides a thorough diagnostic analysis, pinpointing areas exhibiting unexpectedly high rutting rates. Incorporating spatial and random components, and important explanatory variables like annual average daily traffic (traffic intensity), asphalt type, rut depth and lane width, our proposed models account for and estimate the influence of these variables on rutting. This approach not only quantifies uncertainties and discerns locations at the highest risk of requiring maintenance, but also uncover spatial dependencies in rutting (millimetre/year). We apply our models to a data set spanning eleven years (2010-2020). Our findings emphasise the systematic unexplained spatial rutting effect, where some of the rutting variability is accounted for by spatial components, asphalt type, in conjunction with traffic intensity, is also found to be the primary driver of rutting. Furthermore, the spatial dependencies uncovered reveal road sections experiencing more than 1 millimeter of rutting beyond annual expectations. This leads to a halving of the expected pavement lifespan in these areas. Our study offers valuable insights, presenting maps indicating expected rutting, and identifying locations with accelerated rutting rates, resulting in a reduction in pavement life expectancy of at least 10 years.

stat.AP↗

arXiv2023

Learning Physics between Digital Twins with Low-Fidelity Models and Physics-Informed Gaussian Processes

A digital twin is a computer model that represents an individual, for example, a component, a patient or a process. In many situations, we want to gain knowledge about an individual from its data while incorporating imperfect physical knowledge and also learn from data from other individuals. In this paper, we introduce a fully Bayesian methodology for learning between digital twins in a setting where the physical parameters of each individual are of interest. A model discrepancy term is incorporated in the model formulation of each personalized model to account for the missing physics of the low-fidelity model. To allow sharing of information between individuals, we introduce a Bayesian Hierarchical modelling framework where the individual models are connected through a new level in the hierarchy. Our methodology is demonstrated in two case studies, a toy example previously used in the literature extended to more individuals and a cardiovascular model relevant for the treatment of Hypertension. The case studies show that 1) models not accounting for imperfect physical models are biased and over-confident, 2) the models accounting for imperfect physical models are more uncertain but cover the truth, 3) the models learning between digital twins have less uncertainty than the corresponding independent individual models, but are not over-confident.

stat.ML↗

arXiv2023

New spatial models for integrating standardized detection-nondetection and opportunistic presence-only data: application to estimating risk factors associated to powerline-induced death of birds

The constant increase in energy consumption has created the necessity of extending the energy transmission and distribution network. Placement of powerlines represent a risk for bird population. Hence, better understanding of deaths induced by powerlines, and the factors behind them are of paramount importance to reduce the impact of powerlines. To address this concern, professional surveys and citizen science data are available. While the former data type is observed in small portions of the space by experts through expensive standardized sampling protocols, the latter is opportunistically collected by citizen scientists. We set up full Bayesian spatial models that 1) fusion both professional surveys and citizen science data and 2) explicitly account for preferential sampling that affects professional surveys data and for factors that affect the quality of citizen science data. The proposed models are part of the family of latent Gaussian models as both data types are interpreted as thinned spatial point patterns and modeled as log-Gaussian Cox processes. The specification of these models assume the existence of a common latent spatial process underlying the observation of both data types. The proposed models are used both on simulated data and on real-data of powerline-induced death of birds in the Trondelag in Norway. The simulation studies clearly show increased accuracy in parameter estimates when both data types are fusioned and factors that bias their collection processes are properly accounted for. The study of powerline-induced deaths shows a clear association between the density of the powerline network and the risk that powerlines represent for bird populations. The choice of model is relevant for the conclusions from this case study as different models estimated the association between risk of powerline-induced deaths and the amount of exposed birds differently.

stat.ME↗

arXiv2023

Bayesian Calibration of Imperfect Computer Models using Physics-Informed Priors

We introduce a computational efficient data-driven framework suitable for quantifying the uncertainty in physical parameters and model formulation of computer models, represented by differential equations. We construct physics-informed priors, which are multi-output GP priors that encode the model's structure in the covariance function. This is extended into a fully Bayesian framework that quantifies the uncertainty of physical parameters and model predictions. Since physical models often are imperfect descriptions of the real process, we allow the model to deviate from the observed data by considering a discrepancy function. For inference, Hamiltonian Monte Carlo is used. Further, approximations for big data are developed that reduce the computational complexity from $\mathcal{O}(N^3)$ to $\mathcal{O}(N\cdot m^2),$ where $m \ll N.$ Our approach is demonstrated in simulation and real data case studies where the physics are described by time-dependent ODEs describe (cardiovascular models) and space-time dependent PDEs (heat equation). In the studies, it is shown that our modelling framework can recover the true parameters of the physical models in cases where 1) the reality is more complex than our modelling choice and 2) the data acquisition process is biased while also producing accurate predictions. Furthermore, it is demonstrated that our approach is computationally faster than traditional Bayesian calibration methods.

stat.ML↗

arXiv2022

A spatial modeling framework for monitoring surveys with different sampling protocols with a case study for bird abundance in mid-Scandinavia

We present a new methodology to model total abundance by merging count data information from surveys with different sampling protocols. The proposed methods are used for data from national breeding bird monitoring programs in Norway and Sweden. Each census collects abundance data following two different sampling protocols in each country, i.e. these protocols provides data from four different sampling processes. The modeling framework assumes a common Gaussian Random Field shared by both the observed and true abundance with either a linear or a relaxed linear association between them. The models account for particularities of each sampling protocol by including terms that affect each observation process, i.e. accounting for differences in observation units and detectability. Bayesian inference is performed using the Integrated Nested Laplace Approximation (INLA) and the Stochastic Partial Differential Equation (SPDE) approach for spatial modeling. We also present the results of a simulation study based on the empirical census data from mid-Scandinavia to assess the performance of the models under model misspecification. Finally, maps of the total expected abundance of birds in our study region in mid-Scandinavia are presented with uncertainty estimates.

stat.ME↗

arXiv2022

A Shared Parameter Model for Systolic Blood Pressure Accounting for Data Missing Not at Random in the HUNT Study

In this work, blood pressure eleven years ahead is modeled using data from a longitudinal population-based health survey, the Trondelag Health (HUNT) Study, while accounting for missing data due to dropout between consecutive surveys (20-50 %). We propose and validate a shared parameter model (SPM) in the Bayesian framework with age, sex, body mass index, and initial blood pressure as explanatory variables. Further, we propose a novel evaluation scheme to assess data missing not at random (MNAR) by comparing the predictive performance of the fitted SPM with and without conditioning on the missing process. The results demonstrate that the SPM is suitable for inference for a dataset of this size (cohort of 64385 participants) and structure. The SPM indicates data MNAR and gives different parameter estimates than a naive model assuming data missing at random. The SPM and naive models are compared based on predictive performance in a validation dataset. The naive model performs slightly better than the SPM for the present participants. This is in accordance with results from a simulation study based on the SPM where we find that the naive model performs better for the present participants, while the SPM performs better for the dropouts.

stat.AP↗

arXiv2022

Quantile based modelling of diurnal temperature range with the five-parameter lambda distribution

Diurnal temperature range is an important variable in climate science that can provide information regarding climate variability and climate change. Changes in diurnal temperature range can have implications for hydrology, human health and ecology, among others. Yet, the statistical literature on modelling diurnal temperature range is lacking. In this paper we propose to model the distribution of diurnal temperature range using the five-parameter lambda (FPL) distribution. Additionally, in order to model diurnal temperature range with explanatory variables, we propose a distributional quantile regression model that combines quantile regression with marginal modelling using the FPL distribution. Inference is performed using the method of quantiles. The models are fitted to 30 years of daily observations of diurnal temperature range from 112 weather stations in the southern part of Norway. The flexible FPL distribution shows great promise as a model for diurnal temperature range, and performs well against competing models. The distributional quantile regression model is fitted to diurnal temperature range data using geographic, orographic and climatological explanatory variables. It performs well and captures much of the spatial variation in the distribution of diurnal temperature range in Norway.

stat.AP↗

arXiv2022

Bayesian calibration of Arterial Windkessel Model

This work is motivated by personalized digital twins based on observations and physical models for treatment and prevention of Hypertension. The models commonly used are simplification of the real process and the aim is to make inference about physically interpretable parameters. To account for model discrepancy we propose to set up the estimation problem in a Bayesian calibration framework. This naturally solves the inverse problem accounting for and quantifying the uncertainty in the model formulation, in the parameter estimates and predictions. We focus on the inverse problem, i.e. to estimate the physical parameters given observations. The models we consider are the two and three parameters Windkessel models (WK2 and WK3). These models simulate the blood pressure waveform given the blood inflow and a set of physically interpretable calibration parameters. The third parameter in WK3 function as a tuning parameter. The WK2 model offers physical interpretable parameters and therefore we adopt it as a computer model choice in a Bayesian calibration formulation. In a synthetic simulation study, we simulate noisy data from the WK3 model. We estimate the model parameters using conventional methods, i.e. least squares optimization and through the Bayesian calibration framework. It is demonstrated that our formulation can reconstruct the blood pressure waveform of the complex model, but most importantly can learn the parameters according to known mathematical connections between the two models. We also successfully apply this formulation to a real case study, where data was obtained from a pilot randomized controlled trial study. Our approach is successful for both the simulation study and the real cases.

stat.ME↗

arXiv2020

A geostatistical two field model that combines point observations and nested areal observations, and quantifies long-term spatial variability -- A case study of annual runoff predictions in the Voss area

In this study, annual runoff is estimated by using a Bayesian geostatistical model for interpolation of hydrological data of different spatial support. That is, streamflow observations from catchments (areal data), and precipitation and evaporation data (point data). The model contains one climatic spatial effect that is common for all years under study, and one year specific spatial effect. Hence, the framework enables a quantification of the spatial variability that is due to long-term weather patterns and processes. This can contribute to a better understanding of biases and uncertainties in environmental modeling. By using integrated nested Laplace approximations (INLA) and the stochastic partial differential equation approach (SPDE) to spatial modeling, the two field model is computationally feasible and fast. The suggested model is tested by predicting 10 years of annual runoff around Voss in Norway and through a simulation study. We find that on average we benefit from combining point and areal data compared to using only one of the data types, and that the interaction between nested areal data and point data gives a spatial model that takes us beyond smoothing. Another finding is that when climatic effects dominate over annual effects, systematic under- and overestimation of runoff over time can be expected. On the other hand, a dominating climatic spatial effect implies that short records of runoff from an otherwise ungauged catchment can lead to large improvements in the predictability of runoff.

stat.AP↗

arXiv2017

Benefits of spatio-temporal modelling for short term wind power forecasting at both individual and aggregated levels

The share of wind energy in total installed power capacity has grown rapidly in recent years around the world. Producing accurate and reliable forecasts of wind power production, together with a quantification of the uncertainty, is essential to optimally integrate wind energy into power systems. We build spatio-temporal models for wind power generation and obtain full probabilistic forecasts from 15 minutes to 5 hours ahead. Detailed analysis of the forecast performances on the individual wind farms and aggregated wind power are provided. We show that it is possible to improve the results of forecasting aggregated wind power by utilizing spatio-temporal correlations among individual wind farms. Furthermore, spatio-temporal models have the advantage of being able to produce spatially out-of-sample forecasts. We evaluate the predictions on a data set from wind farms in western Denmark and compare the spatio-temporal model with an autoregressive model containing a common autoregressive parameter for all wind farms, identifying the specific cases when it is important to have a spatio-temporal model instead of a temporal one. This case study demonstrates that it is possible to obtain fast and accurate forecasts of wind power generation at wind farms where data is available, but also at a larger portfolio including wind farms at new locations. The results and the methodologies are relevant for wind power forecasts across the globe as well as for spatial-temporal modelling in general.

stat.AP↗

arXiv2015

Spatial Modelling of Temperature and Humidity using Systems of Stochastic Partial Differential Equations

This work is motivated by constructing a weather simulator for precipitation. Temperature and humidity are two of the most important driving forces of precipitation, and the strategy is to have a stochastic model for temperature and humidity, and use a deterministic model to go from these variables to precipitation. Temperature and humidity are empirically positively correlated. Generally speaking, if variables are empirically dependent, then multivariate models should be considered. In this work we model humidity and temperature in southern Norway. We want to construct bivariate Gaussian random fields (GRFs) based on this dataset. The aim of our work is to use the bivariate GRFs to capture both the dependence structure between humidity and temperature as well as their spatial dependencies. One important feature for the dataset is that the humidity and temperature are not necessarily observed at the same locations. Both univariate and bivariate spatial models are fitted and compared. For modeling and inference the SPDE approach for univariate models and the systems of SPDEs approach for multivariate models have been used. To evaluate the performance of the difference between the univariate and bivariate models, we compare predictive performance using some commonly used scoring rules: mean absolute error, mean-square error and continuous ranked probability score. The results illustrate that we can capture strong positive correlation between the temperature and the humidity. Furthermore, the results also agree with the physical or empirical knowledge. At the end, we conclude that using the bivariate GRFs to model this dataset is superior to the approach with independent univariate GRFs both when evaluating point predictions and for quantifying prediction uncertainty.

stat.AP↗

arXiv2015

Estimation of a non-stationary model for annual precipitation in southern Norway using replicates of the spatial field

Estimation of stationary dependence structure parameters using only a single realisation of the spatial process, typically leads to inaccurate estimates and poorly identified parameters. A common way to handle this is to fix some of the parameters, or within the Bayesian framework, impose prior knowledge. In many applied settings, stationary models are not flexible enough to model the process of interest, thus non-stationary spatial models are used. However, more flexible models usually means more parameters, and the identifiability problem becomes even more challenging. We investigate aspects of estimation of a Bayesian non-stationary spatial model for annual precipitation using observations from multiple years. The model contains replicates of the spatial field, which increases precision of the estimates and makes them less prior sensitive. Using R-INLA, we analyse precipitation data from southern Norway, and investigate statistical properties of the replicate model in a simulation study. The non-stationary spatial model we explore belongs to a recently introduced class of stochastic partial differential equation (SPDE) based spatial models. This model class allows for non-stationary models with explanatory variables in the dependence structure. We derive conditions to facilitate prior specification for these types of non-stationary spatial models.

stat.ME↗