Spatial-Process Estimates as Smoothers

Author(s):  
Douglas W. Nychka
Keyword(s):  
2011 ◽  
Vol 2011 ◽  
pp. 1-35
Author(s):  
Sidi Ali Ould Abdi ◽  
Sophie Dabo-Niang ◽  
Aliou Diop ◽  
Ahmedoune Ould Abdi

Given a stationary multidimensional spatial process , we investigate a kernel estimate of the spatial conditional quantile function of the response variable given the explicative variable . Asymptotic normality of the kernel estimate is obtained when the sample considered is an -mixing sequence.


2020 ◽  
Vol 19 (4) ◽  
pp. 13-20
Author(s):  
A. A. Korneenkov ◽  
◽  
S. V. Ryazantsev ◽  
I. V. Fanta ◽  
E. E. Vyazemskaya ◽  
...  

The identification of risk factors, features and patterns of the emergence and spread of diseases in space requires a large array of diverse data and the use of a serious mathematical and statistical apparatus. The distribution of diseases in space is studied using spatial analysis tools, which are now widely used as information systems are introduced and data are accumulated that are relevant to public health. For most tasks of working with spatial data (data, events that have geographical, spatial coordinates), various geographic information systems are used. As a disease for spatial analysis, sensorineural hearing loss was chosen, with which patients were treated at the Saint-Petersburg Research of Ear, Throat, Nose and Speech during one year of the study. The main tasks of the spatial analysis of data on the incidence of sensorineural hearing loss (SNHL) for hospitalization were: visualization of a point pattern, which can form the geographical coordinates of the places of residence of inpatients with SNHL; assessment of the properties of the spatial process that generates this point image (assessment of the intensity of the process, its laws) using various statistical indicators; testing the hypothesis about the spatial randomness of this process and the influence of individual factors on it. R-code accompanied all calculations in the article. Calculations can be reproduced quite easily. The text of the article can be used as step-by-step instructions for their implementation.


1990 ◽  
Vol 20 (5) ◽  
pp. 536-546 ◽  
Author(s):  
Steen Magnussen

Tree height of jack pine full-sib families, originating from all possible combinations of three parental provenances and growing on three sites, was analyzed with 1 classical model and 11 nearest-neighbour spatial process models. Extension of the classical linear model with spatial interaction terms was deemed necessary in light of significant neighbourhood correlations among effect-free observations (residuals) on two of the three sites. The strength and extent of spatial and temporal correlations are demonstrated in both visual and tabular form. Only 4 of the 11 spatial models provided a substantial reduction (5–20%) in the significant difference between two estimates of full-sib family tree height. Spatial adjustments averaged 1–3% at the family level, with few families adjusted by more than 10%. The cumulative (temporal) effect of spatial covariance was demonstrated in rank correlations between adjusted and observed family means. No simple trends were obtained when adjusted variance components and heritabilities were compared with their unadjusted counter-parts, but most models tended to deflate genetic effects and reduce heritabilities. It is concluded that although spatial analyses provide an attractive tool for the experimenter, the lack of a cause and effect hypothesis in forest genetic trials necessitates model searching without the guarantee of true treatment effects. Spatial analysis provides good indicators of the need to collect additional site information for more powerful analyses. Careful planning and intensive site preparation may greatly reduce spatial covariances and the need for spatial analyses.


2014 ◽  
Vol 521 ◽  
pp. 485-489
Author(s):  
Hong Hao Fu ◽  
Guo Tian Cai ◽  
Dai Qing Zhao

This paper analyzes temporal and spatial process, and problems based on data between 1986 and 2010. Conclusions are as follows. Power supply of Guangdong relied more on distant outer-province power grids over time, not inner-province ones, close ones or independent power plants. This accelerating enlargement of power supply range could well satisfy its increasing power consumption. However, power production of western provinces couldnt simultaneously meet their own increasing demand and demand by Guangdong. Furthermore, total power transmission and electricity tariff were fixed by long-term framework agreements signed among governments, in which the transmission amount was too much while the tariff was too low, forcing the western provinces limiting their domestic demand without proper compensation. So the current enlarging trend of power supply range of Guangdong is unsustainable and its necessary to introduce power market mechanism through adjusting short-term total power transmission and power tariff according to the market situation.


SIMULATION ◽  
2021 ◽  
pp. 003754972110400
Author(s):  
Ozgur Ozmen ◽  
James Nutaro ◽  
Sassan Ostvar ◽  
Chin Hur ◽  
Chung Yin Kong

Barrett’s esophagus (BE) is a benign condition of the distal esophagus that initiates a multistage pathway to esophageal adenocarcinoma (EAC). Short of frequent intrusive (and costly) surveillance, effective screening for neoplasia in BE populations is yet to be established since progressors are rare and virtually undetectable without routine biopsies, which often sample only a small portion of the BE tissue. As a result, reliable estimation of the true prevalence of dysplasia in a BE population and evidence-based optimization of screening for at-risk individuals is challenging. Data-driven microsimulations, i.e., model-generated instances of disease history in a predefined virtual population, have found utility in the EAC screening literature as low-overhead alternatives to real-world hypothesis testing of optimal interventions for dysplasia. Despite the successes, computational limitations, paucity of knowledge and data on Barrett’s dysplasia, and the complexities of disease progression as a multiscale multiphysics process have hindered the treatment of disease progression in BE as a spatial process. Agent-based modeling of nucleation and proliferation processes in dysplasia warrants exploration in this context as an approximation that operates at a trade-off between computational tractability and precise representation of the composition and physics of the substrate (tissue). In this study, we describe spatially resolved simulations of premalignant progression toward EAC in a coarse-grained model of Barrett’s tissue that resolves the metaplastic tissue at a length scale of 0.42 mm (~3300 crypts/mm2). The model is calibrated to reproduce historical high-grade dysplasia prevalence when model-generated patients are screened using the Seattle protocol.


1997 ◽  
Vol 34 (03) ◽  
pp. 685-697
Author(s):  
Eric Renshaw ◽  
Yonglong Dai

A spatial process is considered in which two general birth-death processes are linked by migration of individuals. We examine conditions for weak symmetry and regularity, and develop necessary and sufficient conditions for recurrence. The results are easily extended to the k-process case.


Sensors ◽  
2020 ◽  
Vol 20 (13) ◽  
pp. 3663
Author(s):  
Valentina Karolj ◽  
Alberto Viseras ◽  
Luis Merino ◽  
Dmitriy Shutin

Exploration of spatial processes, such as radioactivity or temperature is a fundamental task in many robotic applications. In the literature, robotic exploration is mainly carried out for applications where the environment is a priori known. However, for most real life applications this assumption often does not hold, specifically for disaster scenarios. In this paper, we propose a novel integrated strategy that allows a robot to explore a spatial process of interest in an unknown environment. To this end, we build upon two major blocks. First, we propose the use of GP to model the spatial process of interest, and process entropy to drive the exploration. Second, we employ registration algorithms for robot mapping and localization, and frontier-based exploration to explore the environment. However, map and process exploration can be conflicting goals. Our integrated strategy fuses the two aforementioned blocks through a trade-off between process and map exploration. We carry out extensive evaluations of our algorithm in simulated environments with respect to different baselines and environment setups using simulated GP data as a process at hand. Additionally, we perform experimental verification with a mobile holonomic robot exploring a simulated process in an unknown labyrinth environment. Demonstrated results show that our integrated strategy outperforms both frontier-based and GP entropy-driven exploration strategies.


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