Bayesian Methods In Spatial Statistics

In this essay, we present a discussion about Bayesian methods in Spatial Statistics. Bayesian methods are approaches to statistical inferences which have been around for several decades and are also used in Geographic Information Systems. The application of these methods in practical problems has increased significantly within the last few years due to recent advances in tools for computation and simulation [1]. At the heart of any Bayesian data analysis method are the likelihood function, which expresses information about the parameters in the data and the prior distribution, which quantifies the belief about the parameters before measurements. The prior distribution and likelihood function can be multiplied together to form a proportion to the posterior distribution which represents knowledge about the unknown parameters after the data has been observed [3]. We begin with an introduction to the basic steps in Bayesian analysis followed by defining the important terminologies in Bayesian methods which are “prior and posterior distributions” and “Markov-Chain Monte Carlo methods.” This is followed by explanation on how Bayesian perspective can be considered as a unified framework to view uncertainty. Finally, we present a comparison between Bayesian methods and the classical ' 'frequentist ' ' statistical methods. …show more content…
This uncertainty includes the quantities resulting from lack of sufficient information. Another important concept in Bayesian methods are the need to determine the prior probability distribution (probability distribution describing our beliefs about the uncertainty in the model before data becomes available) taking into account the available information. Generally, Bayesian methods involve the sequential application of the Bayes formula and the steps in these methods can be summarized as