TITLE: Stochastic Modeling of Environmental Time Series

INSTRUCTOR: Richard W. Katz, Senior Scientist, Environmental and Societal Impacts Group, National Center for Atmospheric Research, Boulder, CO USA

SCHEDULE: 10 hours of class

DESCRIPTION: Stochastic modeling of environmental time series, with emphasis on scaling/aggregative properties. Environmental applications include precipitation.

PREREQUISITES: Probability and stochastic processes (e.g., Markov chains, central limit theorem), Statistical theory [e.g., maximum likelihood estimation, time series analysis (AR models)].

OUTLINE

I. Probabilistic Background

i. Scaling/aggregation

-- Variance of sums
-- Effect of temporal dependence

ii. Random sums

-- Variance & covariance decompositions
-- Central limit theorem

II. Statistical Background

i. Overdispersion phenomenon

ii. Mixtures of distributions

-- Observed
-- Hidden

III. EM Algorithm

i. Point estimation

ii. Model selection

iii. Standard errors

IV. Time Series Analysis

i. Mixtures of time series

-- Observed
-- Hidden

ii. Hidden Markov models

V. Spatio-Temporal Analysis

i. Extensions of temporal models

-- Conditional independence/Induced dependence
-- Observed and/or hidden covariates

REFERENCES

Guttorp, P., 1995: Stochastic Modeling of Scientific Data. Chapman & Hall, London.

McLachlan, G.J., and T. Krishnan, 1997: The EM Algorithm and Extensions. Wiley, New York.