Research output: Thesis › Doctoral Thesis

Unpublished

**State space modelling of extreme values with particle filters.** / Wyncoll, David P.

Research output: Thesis › Doctoral Thesis

Wyncoll, DP 2009, 'State space modelling of extreme values with particle filters', PhD, Lancaster University.

Wyncoll, D. P. (2009). *State space modelling of extreme values with particle filters*. Lancaster University.

Wyncoll DP. State space modelling of extreme values with particle filters. Lancaster University, 2009. 208 p.

@phdthesis{0aaefd1959854024989503440a8b8b06,

title = "State space modelling of extreme values with particle filters",

abstract = "State space models are a flexible class of Bayesian model that can be used to smoothly capture non-stationarity. Observations are assumed independent given a latent state process so that their distribution can change gradually over time. Sequential Monte Carlo methods known as particle filters provide an approach to inference for such models whereby observations are added to the fit sequentially. Though originally developed for on-line inference, particle filters, along with related particle smoothers, often provide the best approach for off-line inference. This thesis develops new results for particle filtering and in particular develops a new particle smoother that has a computational complexity that is linear in the number of Monte Carlo samples. This compares favourably with the quadratic complexity of most of its competitors resulting in greater accuracy within a given time frame. The statistical analysis of extremes is important in many fields where the largest or smallest values have the biggest effect. Accurate assessments of the likelihood of extreme events are crucial to judging how severe they could be. While the extreme values of a stationary time series are well understood, datasets of extremes often contain varying degrees of non-stationarity. How best to extend standard extreme value models to account for non-stationary series is a topic of ongoing research. The thesis develops inference methods for extreme values of univariate and multivariate non-stationary processes using state space models fitted using particle methods. Though this approach has been considered previously in the univariate case, we identify problems with the existing method and provide solutions and extensions to it. The application of the methodology is illustrated through the analysis of a series of world class athletics running times, extreme temperatures at a site in the Antarctic, and sea-level extremes on the east coast of England.",

keywords = "Particle filtering and smoothing, extreme value theory, state space models, Monte Carlo methods, EM algorithm, time series modelling, athletics records, Antarctic temperatures, sea-levels",

author = "Wyncoll, {David P.}",

year = "2009",

month = jun

language = "English",

publisher = "Lancaster University",

school = "Lancaster University",

}

TY - THES

T1 - State space modelling of extreme values with particle filters

AU - Wyncoll, David P.

PY - 2009/6

Y1 - 2009/6

N2 - State space models are a flexible class of Bayesian model that can be used to smoothly capture non-stationarity. Observations are assumed independent given a latent state process so that their distribution can change gradually over time. Sequential Monte Carlo methods known as particle filters provide an approach to inference for such models whereby observations are added to the fit sequentially. Though originally developed for on-line inference, particle filters, along with related particle smoothers, often provide the best approach for off-line inference. This thesis develops new results for particle filtering and in particular develops a new particle smoother that has a computational complexity that is linear in the number of Monte Carlo samples. This compares favourably with the quadratic complexity of most of its competitors resulting in greater accuracy within a given time frame. The statistical analysis of extremes is important in many fields where the largest or smallest values have the biggest effect. Accurate assessments of the likelihood of extreme events are crucial to judging how severe they could be. While the extreme values of a stationary time series are well understood, datasets of extremes often contain varying degrees of non-stationarity. How best to extend standard extreme value models to account for non-stationary series is a topic of ongoing research. The thesis develops inference methods for extreme values of univariate and multivariate non-stationary processes using state space models fitted using particle methods. Though this approach has been considered previously in the univariate case, we identify problems with the existing method and provide solutions and extensions to it. The application of the methodology is illustrated through the analysis of a series of world class athletics running times, extreme temperatures at a site in the Antarctic, and sea-level extremes on the east coast of England.

AB - State space models are a flexible class of Bayesian model that can be used to smoothly capture non-stationarity. Observations are assumed independent given a latent state process so that their distribution can change gradually over time. Sequential Monte Carlo methods known as particle filters provide an approach to inference for such models whereby observations are added to the fit sequentially. Though originally developed for on-line inference, particle filters, along with related particle smoothers, often provide the best approach for off-line inference. This thesis develops new results for particle filtering and in particular develops a new particle smoother that has a computational complexity that is linear in the number of Monte Carlo samples. This compares favourably with the quadratic complexity of most of its competitors resulting in greater accuracy within a given time frame. The statistical analysis of extremes is important in many fields where the largest or smallest values have the biggest effect. Accurate assessments of the likelihood of extreme events are crucial to judging how severe they could be. While the extreme values of a stationary time series are well understood, datasets of extremes often contain varying degrees of non-stationarity. How best to extend standard extreme value models to account for non-stationary series is a topic of ongoing research. The thesis develops inference methods for extreme values of univariate and multivariate non-stationary processes using state space models fitted using particle methods. Though this approach has been considered previously in the univariate case, we identify problems with the existing method and provide solutions and extensions to it. The application of the methodology is illustrated through the analysis of a series of world class athletics running times, extreme temperatures at a site in the Antarctic, and sea-level extremes on the east coast of England.

KW - Particle filtering and smoothing

KW - extreme value theory

KW - state space models

KW - Monte Carlo methods

KW - EM algorithm

KW - time series modelling

KW - athletics records

KW - Antarctic temperatures

KW - sea-levels

M3 - Doctoral Thesis

PB - Lancaster University

ER -