Turkiye Klinikleri Journal of Biostatistics

.: ORIGINAL RESEARCH
Adaptive Models for Nonstationary Spatial Covariance Structures
Durağan Olmayan Uzamsal Kovaryans Yapılar İçin Uyarlanabilir Modeller
Joseph Thomas EGHWERIDOa, Julian Ibezimako MBEGBUb
aFederal University of Petroleum Resources Effurun, Department of Mathematics and Computer Science, Delta State, NIGERIA
bUniversity of Benin, Department of Mathematics, Edo State, NIGERIA
Turkiye Klinikleri J Biostat. 2020;12(1):1-15
doi: 10.5336/biostatic.2019-66181
Article Language: EN
Full Text
ABSTRACT
 Objective: In modeling environment processes, multi- disciplinary methods are used to explain, explore and predict how the earth responds to natural human-induced environmental changes over time. Consequently, when analyzing spatial processes spatial domains, the spatial covariance of interest are always heterogeneous. However, this article proposed locally adaptive covariance for the spatial domain whose covariance is nonstationary in their spatial domain. The objectives of the study are to propose parametric, non-parametric and semi- parametric models for nonstationary spatial structure, continuous model for nonstationary spatial processes whose distance is far apart and to propose the adaptive weighting scheme approach that generates the optimal value for the nonparametric and semi-parametric models. Material and Methods: The spatial covariances are derived by applying the concept of adaptive weighting scheme approach on the covariance proposed in Nott and Dunsmuir (2002). Consequently, the local adaptive bandwidth for the nonstationary covariance was obtained for both the nonparametric and semi-parametric models. Simulations are conducted on the proposed model to examine the proposed model. Results and Conclusion: The results obtained are compared with existing models. The results indicate proposed spatial covariance are driven by the local bandwidths, penalty, weighted scheme, and tuning parameters. The adaptive models performed better in relation to existing covariances in terms of their mean square prediction errors (MSPE). The proposed models were further applied to real life Sulphate spatial data.

Keywords: Adaptive; locally, nonstationary; spatial covariance; variability
ÖZET
 Amaç: Çevresel süreçleri modellerken, dünyanın zaman içinde doğal insan kaynaklı çevresel değişikliklere nasıl tepki verdiğini açıklamak, araştırmak ve öngörmek için multi-disipliner yöntemler kullanılır. Sonuç olarak, uzamsal süreçleri incelerken uzamsal alanlar, ilgilenilen uzamsal kovaryans her zaman heterojendir. Bununla birlikte, bu makalede kovaryansı uzamsal alanlarında durağan olmayan uzamsal alan için yerel olarak uyarlanabilir kovaryans önerilmiştir. Makalenin amaçları durağan olmayan uzamsal yapılar, mesafesi çok uzak olan durağan olmayan uzamsal süreçler için sürekli model için parametrik, non-parametrik ve yarı-parametrik modeller önermek ve, non-parametrik ve yarı-parametrik modeller için optimal değeri yaratan adaptif uyarlamalı ağırlıklandırma şeması önermektir. Gereç ve Yöntemler: Uzamsal kovaryanslar, Nott ve Dunsmuir (2002)'de önerilen uyarlamalı ağırlıklandırma şeması yaklaşımı kovaryans üzerine uygulanarak türetilmiştir. Sonuç olarak, hem non-parametrik hem de yarı parametrik modeller için durağan olmayan kovaryans için yerel adaptif band genişliği elde edildi. Önerilen modeli değerlendirmek için önerilen model üzerine simulasyonlar yapıldı. Bulgular ve Sonuç: Elde edilen sonuçlar mevcut modellerle karşılaştırıldı. Bulgular önerilen uzamsal kovaryansın, yerel bant genişlikleri, ceza, ağırlıklı şema ve ayar parametreleri tarafından yönlendirildiğini göstermektedir. Uyarlanabilir modeller, ortalama karesel öngörü hataları (MSPE) açısından mevcut kovaryanslara göre daha iyi performans göstermiştir. Önerilen modeller ayrıca gerçek hayattaki sülfat uzamsal verilerine de uygulanmıştır.

Anahtar Kelimeler: Uyarlanabilir; yerel, durağan olmayan; uzamsal kovaryans; değişkenlik
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