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Selected Geographic Resources in

Bayesian Analysis

(http://faculty.washington.edu/krumme/450/bayes.html)


Supporting & Related Pages:

Basic Introduction:

  • The "Bayesian method" is based on the Bayesian theorem which suggests that the degree to which one believes that a propositioon is true depends on on the a priori belief which one has in the truth of the proposition and in the evidence collected to to investigate the proposition.

  • Golledge & Stimson, Spatial Behavior, 1997, pp.51f..

Bayes' Theorem:


Posterior Probability = P (E1|F) = P(E1) P(F|E1)
---------------------
P(E1) P(F|E1) + P(E2) P(F|E2)

where:

P (E1|F) =

Posterior probability (The revised values of prior probabilities after receiving additional information)

P (E1) =

Prior probability (The probability which describes the decision maker's judgement about the states of the environment, future events, or hypotheses, before obtaining additional information)

P (F|E1) =

Likelihood or "conditional probability" (the probability of a given sample result, observation or new item of information, under the assumption that some particular hypothesis of state of the environment prevails)

Posterior Probability

 =

Joint Probability (of prior and conditional probabilities)
--------------------------------------------------------
Marginal Probability (= Sum of all Joint Probabilities)

Joint Probability

 =

Probability assigned to the joint occurence of each survey result F (=new information) and each of the underlying/possible events

Marginal (or unconditional) Probability

 =

Probability that a particular survey result occurs (are found by summing over the joint probabilities for each of the survey results (F)

Internet Sites

Clippings:

Literature:

Curry, Leslie, Seasonal Programming and Bayesian Assessment of Atmospheric Resources, in: W.R.Derrick Sewell, ed., Human Dimensions of Weather Modification. Research Paper No. 105, Chicago: Department of Geography, University of Chicago, 1966, pp.127-38.

Earman, John. Bayes or Bust: A critical Examination of Bayesian Confirmation Theory. Cambridge: MIT Press, 1992. [Review in JEL Sept.1993, pp.1441-2.]

Gregori, Tullio, University of Trieste, Trieste, Italy A Bayesian approach to analyze regional elasticities [Abstract]

This paper presents a bayesian approach to analyze regional elasticity distributions with a regular translog cost function. It is known that a proper statistical analysis concerning elasticities can be performed only with the bayesian approach..."

Grether, David M., "Testing Bayes Rule and the Representativeness Heuristic: Some Experimental Evidence," Journ.Econ.Behav.Organ. 17(1), Jan 1992, 31-57.

Hayter, Roger, Farmers' Crop Decisions and the Frost Hazard in East- Central Alberta: A Bayesian Approach, Tijdschrift voor Econ. en Sociale Geografie 66(2), 1975, 93-102.

Kahneman, Daniel, Paul Slovic and Amos Tversky, eds., Judgment under Uncertainty: Heuristics and Biases. Cambridge University Press, 1982.

Ch.25: Conservatism in human information processing: "Probabilities quantify uncertainty. A probability, according to Bayesians like ourselves, is simply a number between zero and one that represents the extent to which a somewhat idealized person believes a statement to be true.... Since such probabilities describe the person who holds the opinion more than the event the opnion is about, they are called personal probabilities." (p.359)
Bayesian statisticians argue that Bayes' s theorem is a formally optimal rule about how to revise opinions in the light of evidence...

King, L.J. and R.G.Golledge, "Bayesian Analysis and Models in Geographic Research," in Univ. of Iowa Geography Dept. Discussion Papers No.12, 1969, pp.15-45 [Geographical Essays Commemorating the Retirement of Harold H. McCarty]

"...assume it is known that a manufacturer is about to locate a new plant in the state. The question is raised, what is the probability that he will locate in a particular city? A frequentist would find this problem difficult to handle, indeed he likely would insist that it is not a proper research question! The Bayesian however, would tackle the question."

Krumme, Gunter (1977)

Puri, Anil, Gökçe Soydemir:
Forecasting industrial employment figures in Southern California: A Bayesian vector autoregressive model
Ann Reg Sci 34 (2000) 4, 503-514
Article in PDF format (125 KB)

Withers, Suzanne D. "Quantitative Methods: Bayesian Inference, Bayesian Thinking," Progress in Human Geography, 26(4), 2002, 553-66.

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