Hierarchical Bayesian auto-regressive models for large space time data with applications to ozone concentration modelling

Increasingly large volumes of space-time data are collected everywhere by mobile computing applications, and in many of these cases temporal data are obtained by registering events, for example telecommunication or web traffic data. Having both the spatial and temporal dimensions adds substantial complexity to data analysis and inference tasks. The computational complexity increases rapidly for fitting Bayesian hierarchical models, as such a task involves repeated inversion of large matrices. The primary focus of this paper is on developing space-time auto-regressive models under the hierarchical Bayesian setup. To handle large data sets, a recently developed Gaussian predictive process approximation method (Banerjee et al. [1]) is extended to include auto-regressive terms of latent space-time processes. Specifically, a space-time auto-regressive process, supported on a set of a smaller number of knot locations, is spatially interpolated to approximate the original space-time process. The resulting model is specified within a hierarchical Bayesian framework and Markov chain Monte Carlo techniques are used to make inference. The proposed model is applied for analysing the daily maximum 8-hour average ground level ozone concentration data from 1997 to 2006 from a large study region in the eastern United States. The developed methods allow accurate spatial prediction of a temporally aggregated ozone summary, known as the primary ozone standard, along with its uncertainty, at any unmonitored location during the study period. Trends in spatial patterns of many features of the posterior predictive distribution of the primary standard, such as the probability of non-compliance with respect to the standard, are obtained and illustrated

Daily minimum and maximum temperature simulation over complex terrain

Spatiotemporal simulation of minimum and maximum temperature is a fundamental requirement for climate impact studies and hydrological or agricultural models. Particularly over regions with variable orography, these simulations are difficult to produce due to terrain driven nonstationarity. We develop a bivariate stochastic model for the spatiotemporal field of minimum and maximum temperature. The proposed framework splits the bivariate field into two components of "local climate" and "weather." The local climate component is a linear model with spatially varying process coefficients capturing the annual cycle and yielding local climate estimates at all locations, not only those within the observation network. The weather component spatially correlates the bivariate simulations, whose matrix-valued covariance function we estimate using a nonparametric kernel smoother that retains nonnegative definiteness and allows for substantial nonstationarity across the simulation domain. The statistical model is augmented with a spatially varying nugget effect to allow for locally varying small scale variability. Our model is applied to a daily temperature data set covering the complex terrain of Colorado, USA, and successfully accommodates substantial temporally varying nonstationarity in both the direct-covariance and cross-covariance functions.Comment: Published in at http://dx.doi.org/10.1214/12-AOAS602 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org

Pembangunan modul pembelajaran autocad dan kajian penerimaan pelajar. Satu kajian kes di Politeknik Kota Bharu

Modul Pengajaran dan Pembelajaran AutoCAD (MPP) merupakan satu media pengajaran yang mengandungi asas-asas mengenai komputer, perisian AutoCAD 2000 dan langkah-langkah berperingkat membuat lukisan teknikal menggunakan AutoCAD 2000. Kajian ini adalah bertujuan untuk menilai sejauh mana MPP ini boleh digunakan dalam proses pengajaran dan pembelajaran dalam aspek kesesuaian isi kandungan, sifat mesra pengguna dan kebolehlaksanaannya. Respondan untuk kajian ini ialah seramai 42 orang pelajar Diploma Kejuruteraan Elektrik Politeknik Kota Bharu. Untuk kajian ini instrumen yang digunakan ialah borang soal selidik di mana penilaian dilakukan berdasarkan persepsi responden terhadap MPP. Data-data yang dikumpulkan dianalisis menggunakan SPSS VI1.0 yang melibatkan skor min. Hasil kajian melaporkan dapatan yang diperolehi berkenaan penerimaan terhadap MPP. Hasil dapatan kajian menunjukkan penerimaan yang positif terhadap MPP oleh pelajar dan ianya mempimyai kebolehlaksanaan yang tinggi (skor min = 3.96) untuk diaplikasikan dalam proses pengajaran dan pembelajaran. Walaubagaimanapun pengkaji percaya MPP ini mempunyai ruang untuk penambahbaikan seperti saranan oleh penilai yang mengesahkan MPP ini agar ia lebih menarik dan sesuai digunakan pada masa depan

Air Pollution Related Asthma Inpatient Hospital Admission in the Las Vegas Valley

Asthma is a chronic respiratory condition characterized by inflammation in the lungs that causes airflow to be restricted. In Southern Nevada’s Las Vegas Valley, the natural basin geography causes air pollutants to accumulate. Research has linked air pollution with worsening asthma symptoms. The goal of this study was to determine the non-linear lagged relationship between Asthma Related Inpatient Hospital Admissions (ARIHA) and the Environmental Protection Agency’s (EPA) criteria air pollutants in the Las Vegas Valley using hospital and pollution monitoring station data. Overall, a statistically significant increased RR of ARIHA between 7 and 13 days after exposure to PM2.5 24-hour average levels from 0-35 μg/m3, and from 9-10 days after exposure to PM2.5 24-hour average 75 μg/m3 was found. Finally, 17 ZIP codes exhibited a statistically significant increased RR of ARIHA after adjusting for all variables, revealing a heterogeneous distribution of ZIP codes at a higher risk of ARIHA

A disposition of interpolation techniques

A large collection of interpolation techniques is available for application in environmental research. To help environmental scientists in choosing an appropriate technique a disposition is made, based on 1) applicability in space, time and space-time, 2) quantification of accuracy of interpolated values, 3) incorporation of ancillary information, and 4) incorporation of process knowledge. The described methods include inverse distance weighting, nearest neighbour methods, geostatistical interpolation methods, Kalman filter methods, Bayesian Maximum Entropy methods, etc. The applicability of methods in aggregation (upscaling) and disaggregation (downscaling) is discussed. Software for interpolation is described. The application of interpolation techniques is illustrated in two case studies: temporal interpolation of indicators for ecological water quality, and spatio-temporal interpolation and aggregation of pesticide concentrations in Dutch surface waters. A valuable next step will be to construct a decision tree or decision support system, that guides the environmental scientist to easy-to-use software implementations that are appropriate to solve their interpolation problem. Validation studies are needed to assess the quality of interpolated values, and the quality of information on uncertainty provided by the interpolation method