Change of support problemへの新たな空間統計モデルの開発

筑波大学 (University of Tsukuba)201

Variational approach for spatial point process intensity estimation

We introduce a new variational estimator for the intensity function of an inhomogeneous spatial point process with points in the $d$-dimensional Euclidean space and observed within a bounded region. The variational estimator applies in a simple and general setting when the intensity function is assumed to be of log-linear form $\beta+{\theta }^{\top}z(u)$ where $z$ is a spatial covariate function and the focus is on estimating ${\theta }$. The variational estimator is very simple to implement and quicker than alternative estimation procedures. We establish its strong consistency and asymptotic normality. We also discuss its finite-sample properties in comparison with the maximum first order composite likelihood estimator when considering various inhomogeneous spatial point process models and dimensions as well as settings were $z$ is completely or only partially known.Comment: Published in at http://dx.doi.org/10.3150/13-BEJ516 the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statistical Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm

Poisson intensity parameter estimation for stationary Gibbs point processes of finite interaction range

We introduce a semi-parametric estimator of the Poisson intensity parameter of a spatial stationary Gibbs point process. Under very mild assumptions satisfied by a large class of Gibbs models, we establish its strong consistency and asymptotic normality. We also consider its finite-sample properties in a simulation study

Drought effects on specific-cause mortality in Lisbon from 1983 to 2016: risks assessment by gender and age groups

Portugal (Southwestern Europe) experiences a high incidence of dry hazards such as drought, a phenomenon that entails a notable burden of morbidity and mortality worldwide. For the first time in the Lisbon district, a time-series study was conducted to evaluate the impact of drought measured by the Standardised Precipitation Index (SPI) and Standardised Precipitation-Evapotranspiration Index (SPEI) on the daily natural, circulatory, and respiratory mortality from 1983 to 2016. An assessment by gender and adult age population groups (45-64, 65-74, ≥75 years old) was included. To estimate the relative risks and attributable risks, generalised linear models with a Poisson link were used. Additionally, the influence of heatwaves and atmospheric pollution for the period from 2007 to 2016 (available period for pollution data) was considered. The main findings indicate statistically significant associations between drought conditions and all analysed causes of mortality. Moreover, SPEI shows an improved capability to reflect the different risks. People in the 45-64 year-old group did not indicate any significant influence in any of the cases, whereas the oldest groups had the highest risk. The drought effects on mortality among the population varied across the different study periods, and in general, the men population was affected more than the women population (except for the SPEI and circulatory mortality during the long study period). The short-term influence of droughts on mortality could be explained primarily by the effect of heatwaves and pollution; however, when both gender and age were considered in the Poisson models, the effect of drought also remained statistically significant when all climatic phenomena were included for specific groups of the total population and men. This type of study facilitates a better understanding of the population at risk and allows the development of more effective measures to mitigate the drought effects on the population.publishe

A hierarchically adaptable spatial regression model to link aggregated health data and environmental data

Health data and environmental data are commonly collected at different levels of aggregation. A persistent challenge of using a spatial regression model to link these data is that their associations can vary as a function of aggregation. This results into ecological fallacy if association at one aggregation level is used for inferencing at another level. We address this challenge by presenting a hierarchically adaptable spatial regression model. In essence, the model extends the spatially varying coefficient model to allow the response to be count data at larger aggregation levels than that of the covariates. A Bayesian hierarchical approach is used for inferencing the model parameters. Robust inference and optimal prediction over geographical space and at different spatial aggregation levels are studied by simulated data sets. The spatial associations at different spatial supports are largely different, but can be efficiently inferred when prior knowledge of the associations is available. The model is applied to study hand, foot and mouth disease (HFMD) in Da Nang city, Viet Nam. Decrease in vegetated areas corresponds with elevated HFMD risks. A study to the identifiability of the parameters shows a strong need for a highly informative prior distribution. We conclude that the model is robust to the underlying aggregation levels of the calibrating data for association inference and it is ready for application in health geography

Bandwidth selection for kernel estimators of the spatial intensity function

We discuss and compare various approaches to the problem of bandwidth selection for kernel estimators of intensity functions of spatial point processes. We also propose a new method based on the Campbell formula applied to the reciprocal intensity function. The new method is fully non-parametric, does not require knowledge of the product densities, and is not restricted to a specific class of point process models

Modified Linear Projection for Large Spatial Data Sets

Recent developments in engineering techniques for spatial data collection such as geographic information systems have resulted in an increasing need for methods to analyze large spatial data sets. These sorts of data sets can be found in various fields of the natural and social sciences. However, model fitting and spatial prediction using these large spatial data sets are impractically time-consuming, because of the necessary matrix inversions. Various methods have been developed to deal with this problem, including a reduced rank approach and a sparse matrix approximation. In this paper, we propose a modification to an existing reduced rank approach to capture both the large- and small-scale spatial variations effectively. We have used simulated examples and an empirical data analysis to demonstrate that our proposed approach consistently performs well when compared with other methods. In particular, the performance of our new method does not depend on the dependence properties of the spatial covariance functions.Comment: 29 pages, 5 figures, 4 table

Bandwidth selection for kernel estimators of the spatial intensity function

We discuss and compare various approaches to the problem of bandwidth selection for kernel estimators of intensity functions of spatial point processes. We also propose a new method based on the Campbell formula applied to the reciprocal intensity function. The new method is fully non-parametric, does not require knowledge of the product densities, and is not restricted to a specific class of point process models