Koşullu Otoregresif Bayes Model Yaklaşımı ile Türkiye Deprem Verilerinin Mekânsal Analizi

Abstract

Mekânsal veri türlerinden birisi olan alansal verilerde gözlem değerleri mekâna bağlı olarak değiştiği için gözlem değerleri arasında mekânsal otokorelasyon ortaya çıkar. Mekânsal modellerde mekân bilgisinin modele katılabilmesi için alanların ilişkilerini tanımlayan komşuluk matrisinin oluşturulması gerekir. Bu nedenle mekânsal otokorelasyonu dikkate alan modellerin kullanımı son yıllarda yaygınlaşmıştır. Genelleştirilmiş Doğrusal Modeller (GDM), mekânsal otokorelasyonun modellenmesinde yetersiz kalmaktadır. Koşullu Otoregresif Bayes (CARBayes) modeli ile daha önceden deprem verilerinin modellenmesi ile ilgili bir çalışma yapılmamıştır. Bu yüzden, bu çalışmada 2016 yılında Türkiye’de meydana gelen deprem sayıları kullanılarak CARBayes modelinin kullanımı önerilmiştir. CARBayes modeli Genelleştirilmiş Doğrusal Mekânsal Model (GDMM) formundadır. Verilerde alansal birim olarak “iller” alınmış ve komşuluk matrisleri oluşturulurken idari bölünüş sınırları dikkate alınmıştır. Oluşturulan komşuluk matrisi üzerinden kurulan permütasyon testi sonucunda deprem sayılarında mekânsal ilişki çıkmıştır. Bu yüzden, deprem sayıları ile ortalama deprem büyüklüğü arasındaki ilişki için GDMM’de mekân bilgisi komşuluk matrisi yardımı ile rastgele etki olarak modele eklenmiştir. Böylece artıklardaki otokorelasyon problemi çözülmüş ve tahmin değerleri elde edilmiştir. Tahmin değerlerinden yararlanılarak bir risk değeri hesaplanmış ve haritalandırma aracılığıyla riskli iller belirlenmiştir.

Keywords

• Mekânsal modeller
• Genelleştirilmiş Doğrusal Mekânsal Modeller
• CARBayes
• Türkiye deprem verileri

Spatial Analysis of Turkey Earthquake Data with Conditional Autoregressive Bayesian Model Approach

Abstract

Since the observation values in (spatial) areal data, which is one of the spatial data types, change depending on the space, spatial autocorrelation occurs between the observation values. In spatial models, in order for the spatial information to be included in the model, the neighborhood matrix, which defines the relations of the areas, must be created. For this reason, the use of models that take into account spatial autocorrelation has become widespread in recent years. Generalized Linear Models (GLM) are insufficient in modeling spatial autocorrelation. There is no previous study which has been done on modeling earthquake data with the Conditional Autoregressive Bayes (CARBayes) model. Therefore, in this study, the use of CARBayes model has been proposed by using the number of earthquakes occurred in Turkey in 2016. The CARBayes model is in the form of the Generalized Linear Spatial Model (GLSM). In the data set, “provinces” are taken as the spatial unit and administrative division boundaries are taken into account while creating neighborhood matrices. As a result of the permutation test established on the created neighborhood matrix, a spatial relationship is found in the earthquake numbers. Therefore, for the relationship between the number of earthquakes and the average earthquake size, the spatial information in GLSM is added to the model as a random effect with the help of the neighborhood matrix. Thus, the autocorrelation problem in residuals was solved and the predicted values were obtained. A risk value was calculated by using the estimated values and risky provinces were determined by mapping.

Keywords

• Spatial models
• Generalized Linear Spatial Models
• CARBayes
• Turkish earthquake data

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