A Hidden Markov Model for Space‐Time Precipitation

Abstract

A family of multivariate models for the occurrence/nonoccurrence of precipitation at N sites is constructed by assuming a different joint probability of events at the sites for each of a number of unobservable climate states. The climate process is assumed to follow a Markov chain. Simple formulae for first-and second-order parameter functions are derived, and used to find starting values for a numerical maximization of the likelihood. The method is illustrated by applying it to data for one site in Washington and to data for a network in the Great Plains. 558 BD Stem, R. D., and R. Coe, A model fitting analysis of rainfall data (with discussion), J. R. Star. Soc., $er. A., 147, 1-34, 1984.Waymire, E., V. K. Gupta, and I. Rodriguez-Iturbe, A spectral theory of rainfall intensity at the meso-/3 scale, Water Resour.

Prediction of earthquake hazard by hidden Markov model (around Bilecik, NW Turkey)

“…HMM has a powerful and flexible mathematical structure to make statistical inferences on partially observed stochastic processes. It has been successfully applied to many diverse areas, particularly speech recognition [14][15][16], finance/econometrics [6,[17][18][19], software reliability [20,21], traffic engineering [22], Biology [23], language modeling [24,25], metrology [26][27][28][29], bioinformatics [30][31][32][33], biophysics/biochemistry [34][35][36]. However, HMM has not as widely implemented as it should be in earthquake modeling.…”

A Non-Homogeneous Hidden Markov Model for the Analysis of Multi-Pollutant Exceedances Data

“…A Bayesian approach to inference for non-homogeneous hidden Markov model has been proposed by Filardo and Gordon (1998) and Meligkotsidou and Dellaportas (2010). In environmental studies, NHHM models have found widespread application in meteorology and hydrology, in studies of climate variability or climate change, and in statistical downscaling of daily precipitation from observed and numerical climate model simulations (see, e.g., Zucchini and Guttorp 1991;Hughes and Guttorp 1994;Hughes et al 1999;Charles et al 1999;Bellone et al 2000;Charles et al 2004;Robertson et al 2004;Betrò et al 2008). Fewer are the applications of homogeneous and non-homogeneous hidden Markov models in air quality studies, where this methodology has been mainly applied to study univariate pollutants concentrations under the assumption of normally-distributed data (Spezia, 2006;Dong et al, 2009) or to estimate exceedances probabilities (Lagona, 2005).…”

A non-parametric hidden Markov model for climate state identification

“…Hidden Markov models (HMMs) have become popular tools for modelling dependent random variables in such diverse areas as speech processing (Juang and Rabiner, 1991), DNA recognition (Churchill, 1989) and rainfall occurrence (Zucchini and Guttorp, 1991). HMMs are based on a doubly stochastic process (Rabiner, 1989), in which an underlying stochastic process that develops as a Markov chain produces an unobservable (hidden) state that can be inferred only through another set of stochastic processes.…”

“…Zucchini and Guttorp (1991) applied a hidden Markov model to describe patterns of precipitation in space and time. In the construction of this model, the authors introduced unobserved climate states, which had different rainfall distributions associated with them.…”