Two new spatio-temporal hidden Markov models (HMM) are introduced in this thesis, with the purpose of capturing the persistent, spatially non-homogeneous nature of climate influence on annual rainfall series observed in Australia. The models extend the two-state HMM applied by Thyer (2001) by relaxing the assumption that all sites are under the same climate control. The Switch HMM (SHMM) allows at-site anomalous states, whilst still maintaining a regional control. The Regional HMM (RHMM), on the other hand, allows sites to be partitioned into different Markovian state regions. The analyses were conducted using a Bayesian framework to explicitly account for parameter uncertainty and select between competing hypotheses. Bayesian model averaging was used for comparison of the HMM and its generalisations. The HMM, SHMM and RHMM were applied to four groupings of four sites located on the Eastern coast of Australia, an area that has previously shown evidence of interannual persistence. In the majority of case studies, the RHMM variants showed greatest posterior weight, indicating that the data favoured the multiple region RHMM over the single region HMM or the SHMM variants. In no cases does the HMM produce the maximum marginal likelihood when compared to the SHMM and RHMM. The HMM state series and preferred model variants were sensitive to the parameterisation of the small-scale site-to-site correlation structure. Several parameterisations of the small-scale Gaussian correlation were trialled, namely Fitted Correlation, Exponential Decay Correlation, Empirical and Zero Correlation. Significantly, it was shown that annual rainfall data outliers can have a large effect on inference for a model that uses Gaussian distributions. The practical value of this modelling is demonstrated by the conditioning of the event based point rainfall model DRIP on the hidden state series of the HMM variants. Short timescale models typically underestimate annual variability because there is no explicit structure to incorporate long-term persistence. The two-state conditioned DRIP model was shown to reproduce the annual variability observed to a greater degree than the single state DRIP. / PhD Doctorate

Orientadores: Nancy Lopes Garcia, Alexsandro Giacomo Grimbert Gallo / Tese (doutorado) - Universidade Estadual de Campinas, Instituto de Matemática Estatística e Computação Científica / Made available in DSpace on 2018-08-24T12:54:22Z (GMT). No. of bitstreams: 1 Carvalho_WalterAugustoFonsecade_D.pdf: 1034671 bytes, checksum: 25dd72305f343655bedfde62a785a259 (MD5) Previous issue date: 2014 / Resumo: Esta tese é dedicada ao estudo dos processos de renovação binários obtidos como agregação de estados a partir de processos Markovianos com alfabeto finito. Na primeira parte, utilizamos uma abordagem matricial para obter condições sob as quais o processo agregado pertence a cada uma das seguintes classes: (1) Markoviano de ordem finita, (2) processo de ordem infinita com probabilidades de transição contínuas, (3) processo Gibbsiano. A segunda parte trata da distância d entre processos de renovação binários. Obtivemos condições sob as quais esta distância pode ser atingida entre tais processos / Abstract: This thesis is devoted to the study of binary renewal processes obtained as aggregation of states from Markov processes with finite alphabet. In the rst part, we use a matrix approach to obtain conditions under which the aggregated process belongs to each of the following classes: (1) Markov of finite order, (2) process of infinite order with continuous transition probabilities, (3) Gibbsian process. The second part deals with the distance d between binary renewal processes. We obtain conditions under which this distance can be achieved between these processes / Doutorado / Estatistica / Doutor em Estatística