Publicação
Contributions to spatial and temporal modelling
| Resumo: | Recent technological advances allow the collection of data in space and time in a wide range of contexts such as environmental and health sciences. Most of these data are generated by monitoring processes and present spatial and/or temporal structures. Traditionally spatial and temporal modelling assumes that the locations (in time or space) sampled are either fixed or stochastically independent of the spatial and temporally continuous phenomenon under study. However, it is well-known that, for example, in air pollution studies, typically the monitors are placed near the most likely pollution sources in areas of high population density. In context of medical studies, a patient is usually observed most frequently when he presents a worse clinical condition. In these examples neither are the observations obtained regularly in time/space nor are the observed locations (in time or space) stochastically independent of the phenomenon under study. Ignoring this dependence can lead to biased estimates and misleading inferences. In this work, we consider the problem of modelling time series with informative observation times. We introduce the concept of Preferential Sampling in the temporal dimension and we discuss alternative model-based approaches to make inference and prediction under stochastic sampling schemes. In the first approach, we present a model to deal with irregularly spaced time series in which the sampling design depends on the contemporaneous value of the underlying process, under the assumption of a Gaussian response variable. For this model, we present two estimation methods, one based on Monte Carlo simulations and the other based on a Laplace approximation. The second approach, proposes a model for irregularly spaced time series in which the sampling design depends on all past history of the observed processes. All discussed model-based approaches are illustrated with numerical studies. |
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| Autores principais: | Monteiro, Andreia Alves Forte Oliveira |
| Assunto: | Preferential Sampling time series continuous time autoregressive process SPDE evolutionary processes Amostragem Preferencial séries temporais processos autorregressivos contínuos no tempo equações diferenciais parciais estocásticas processos Evolucionários |
| Ano: | 2019 |
| País: | Portugal |
| Tipo de documento: | tese de doutoramento |
| Tipo de acesso: | acesso aberto |
| Instituição associada: | Universidade do Minho |
| Idioma: | inglês |
| Origem: | RepositóriUM - Universidade do Minho |
| Resumo: | Recent technological advances allow the collection of data in space and time in a wide range of contexts such as environmental and health sciences. Most of these data are generated by monitoring processes and present spatial and/or temporal structures. Traditionally spatial and temporal modelling assumes that the locations (in time or space) sampled are either fixed or stochastically independent of the spatial and temporally continuous phenomenon under study. However, it is well-known that, for example, in air pollution studies, typically the monitors are placed near the most likely pollution sources in areas of high population density. In context of medical studies, a patient is usually observed most frequently when he presents a worse clinical condition. In these examples neither are the observations obtained regularly in time/space nor are the observed locations (in time or space) stochastically independent of the phenomenon under study. Ignoring this dependence can lead to biased estimates and misleading inferences. In this work, we consider the problem of modelling time series with informative observation times. We introduce the concept of Preferential Sampling in the temporal dimension and we discuss alternative model-based approaches to make inference and prediction under stochastic sampling schemes. In the first approach, we present a model to deal with irregularly spaced time series in which the sampling design depends on the contemporaneous value of the underlying process, under the assumption of a Gaussian response variable. For this model, we present two estimation methods, one based on Monte Carlo simulations and the other based on a Laplace approximation. The second approach, proposes a model for irregularly spaced time series in which the sampling design depends on all past history of the observed processes. All discussed model-based approaches are illustrated with numerical studies. |
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