Bayesian Methods Of Spatial Statistics Essay

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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.

Bayesian methods involve the use of random variables or more generally, unknown quantities to model all sources of uncertainty in statistical models. This…

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