Lecture #- Bayesian analysis of mapped data.ppt

Lecture #4: Bayesian analysis of mapped data
Spatial statistics in practice
Center for Tropical Ecology and Biodiversity, Tunghai University & Fushan Botanical Garden
Topics for today’s lecture
Frequentist versus Bayesian perspectives.
Implementing random effects models in GeoBUGS.
Spatially structured and unstructured random effects: the CAR, the ICAR, and the spatial filter specifications
LMM & GLMM move in the direction of Bayesian modeling
Fixed effects are in keeping with a frequentist viewpoint―individual unknown parameters
Random effects are distributions of parameters, and are in keeping with a Bayesian viewpoint
The model specifications tend to be the same, with estimation methods tending to differ
Sampling distribution-based inference: the reported p values
Frequentism: assigns probabilities to random events only according to their relative frequencies of occurrence, rejecting degree-of-belief interpretations of mathematical probability theory.
The frequentist approach considers  to be an unknown constant. Allowing for the possibility that  can take on a range of values, frequentist inference is based on a hypothetical repeated sampling principle that obtains desirable and (often) physically interpretable properties (., CIs).
Frequentist statistics typically is limited to posing questions in terms of a null hypothesis (., H0) that a parameter takes on a single value.
What is Bayesian analysis?
Bayesianism: contends that mathematical probability theory pertains to degree of plausibility/belief; when used with Bayes theorem (which casts analysis in conditional terms), it es Bayesian inference.
The Bayesian approach considers  as the realized value of a random variable Θ with a probability density (mass) function called the prior distribution (a marginal probability distribution that is interpreted as a description of what is known about a variable in the absence of empirical/theoretical evidence).
Bayesian statistics furnishes a generic