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Sansom J.,NIWA - National Institute of Water and Atmospheric Research | Thomson P.,Statistics Research Associates Ltd.
Water Resources Research | Year: 2010

A nonhomogeneous hidden semi-Markov model (NHSMM) for breakpoint rainfall data is proposed which extends the homogeneous hidden semi-Markov model (HSMM) of Sansom and Thomson (2001) to incorporate stochastic seasonality. The NHSMM model is able to switch seasons at times that are earlier or later than expected and, in this way, is able to explain additional seasonal variability due to varying length seasons. The model's hidden rainfall states align with precipitation mechanisms that are seasonally invariant, but the state dynamics are assumed to vary with season. Recursions for constructing the likelihood are developed and the EM algorithm used to fit the parameters of the model. An application of the model to breakpoint rainfall measurements from Invercargill, New Zealand, is discussed, and the results of fitting a number of different NHSMMs are compared to those from fitting the non-seasonal homogeneous HSMM. Copyright 2010 by the American Geophysical Union.

Pega F.,University of Otago | Pega F.,Huntington University | Gray A.,Statistics Research Associates Ltd. | Veale J.F.,University of British Columbia | And 2 more authors.
Journal of Environmental and Public Health | Year: 2013

Objective. Effectively addressing health disparities experienced by sexual minority populations requires high-quality official data on sexual orientation. We developed a conceptual framework of sexual orientation to improve the quality of sexual orientation data in New Zealand's Official Statistics System. Methods. We reviewed conceptual and methodological literature, culminating in a draft framework. To improve the framework, we held focus groups and key-informant interviews with sexual minority stakeholders and producers and consumers of official statistics. An advisory board of experts provided additional guidance. Results. The framework proposes working definitions of the sexual orientation topic and measurement concepts, describes dimensions of the measurement concepts, discusses variables framing the measurement concepts, and outlines conceptual grey areas. Conclusion. The framework proposes standard definitions and concepts for the collection of official sexual orientation data in New Zealand. It presents a model for producers of official statistics in other countries, who wish to improve the quality of health data on their citizens. © 2013 Frank Pega et al.

Ailliot P.,University of Western Brittany | Thompson C.,NIWA - National Institute of Water and Atmospheric Research | Thomson P.,Statistics Research Associates Ltd.
Water Resources Research | Year: 2011

The generalized extreme-value (GEV) distribution is widely used for modeling and characterizing extremes. It is a flexible three-parameter distribution that combines three extreme-value distributions within a single framework: the Gumbel, Frechet, and Weibull. Common methods used for estimating the GEV parameters are the method of maximum likelihood and the method of L-moments. This paper generalizes the mixed maximum likelihood and L-moments GEV estimation procedures proposed by Morrison and Smith (2002) and derives the asymptotic properties of the resulting estimators. Analytic expressions are given for the asymptotic covariance matrices in a number of important cases, including the estimators proposed by Morrison and Smith (2002). These expressions are verified by simulation and the efficiencies of the various estimators established. The asymptotic results are compared to those obtained for small to medium-size samples by simulation with the estimated parameters and quantiles assessed for accuracy and bias. Using simplified constraints for the support of the log likelihood, computational strategies and graphical tools are developed which lead to computationally efficient, numerically robust, estimation procedures suitable for automatic batch processing of many data sets. The methods are illustrated by application to annual maximum rainfall data at a large number of New Zealand locations. For Wellington, 24 h annual maximum rainfall over the period 1940-1999 is also considered within each phase of the Interdecadal Pacific Oscillation.© 2011 by the American Geophysical Union.

Carey-Smith T.,NIWA - National Institute of Water and Atmospheric Research | Sansom J.,NIWA - National Institute of Water and Atmospheric Research | Thomson P.,Statistics Research Associates Ltd.
Water Resources Research | Year: 2014

A hidden seasonal switching model for daily rainfall over a region is proposed where season onset times are stochastic and can vary from year to year. The model allows seasons to occur earlier or later than expected and have varying lengths. This stochastic seasonal variation accommodates considerably more of the observed intraannual rainfall variability than can be represented using seasonal models with standard fixed seasons. In essence, the model dynamically classifies daily rainfall time series into seasons whose onsets vary from year to year and within which the model parameters are assumed to be time homogeneous. A variety of nonseasonal models could have been used to describe daily rainfall within seasons. Here a generalization of the Richardson model is adopted which has rainfall states (dry, light rain, and heavy rain) some of which are hidden or unobserved. It is further assumed that the rainfall states generate rainfall that is independent of season (seasonally invariant), so it is only the dynamics of the rainfall states that vary from season to season. A suitable estimation strategy based on maximum likelihood and the EM algorithm is developed for fitting the model across a region. This strategy is validated on simulated data. Various forms of the model are fitted to daily rainfall measurements from 12 sites in southern New Zealand. These results are discussed and compared to those from fitting standard fixed season models. Key Points A hidden switching model for stochastic seasonality has been developed Stochastic seasons were modeled by a two-state nonhomogeneous Markov chain Stochastic seasonal models accommodate more observed rainfall variability ©2013. American Geophysical Union. All Rights Reserved.

Sansom J.,NIWA - National Institute of Water and Atmospheric Research | Thomson P.,Statistics Research Associates Ltd. | Carey-Smith T.,NIWA - National Institute of Water and Atmospheric Research
Journal of Geophysical Research: Atmospheres | Year: 2013

Seasonality is an important source of variation in many processes and needs to be incorporated into rainfall models. The stochastic seasonal rainfall models for high temporal resolution data [Sansom and Thomson, 2010] and daily data (T. Carey-Smith et al., A hidden seasonal switching model for multisite daily rainfall, manuscript in preparation 2012) both depend on the specification of one day of the year for each season being in the particular season. So, if the seasonality is to be represented by four seasons then it is necessary to provide four dates on each of which it can be said that, every year, the season is of the first, second, third or fourth type respectively on that day of the year. The model fitting can only proceed once these dates, the mid-seasons, have been provided.In a region of large seasonal rainfall variation the determination of these mid-seasons would not be difficult and the model fitting not sensitive to their choice. However, although it is clearly evident in the annual pattern of monthly accumulations, New Zealand's rainfall seasonality is not strong and careful assessment of the mid-season dates is necessary. They need to be estimated with a precision of days and the 55-year long rainfall records of daily data from 141 stations spread across New Zealand were analysed on a regional basis. The analysis found regionally coherent dates when the mean daily rain rate changed significantly and that over the years these dates could be modelled as a four component von Mises distribution with characteristics consistent with stochastic seasonality. Key Points NZ rainfall has seasonality but season change times vary from year-to-yearSignificance testing against randomly generated dates confirms this viewSeason change dates can be modeled as a 4 component Von Mises distribution ©2013. American Geophysical Union. All Rights Reserved.

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