In practice, data on the time of death of a living unit often have correlations due to the location of observations in the studied space.
One of the important issues in analyzing this type of survival data with spatial dependence is estimating parameters and predicting unknown values ​​at specific locations based on the observation vector. In this paper, to analyze this type of survival data, a Cox regression model with a piecewise exponential hazard function is used, and spatial dependence is added to the model as a Gaussian random field and a latent variable.
Due to the lack of an explicit form for the posterior distribution and complete conditional distributions and the length of calculations with Markov chain Monte Carlo algorithms, an approximate Bayesian approach is used to analyze this model. An applied example presents how to implement the approximate Bayesian approach.