title: Computational Bayesian inference using low discrepancy sequences

authors: Brown, Paul Tamataatoi

subjects: Bayesian Inference

abstract: The Integrated Nested Laplace Approximation (INLA) provides fast and accurate Bayesian inference for complex hierarchical models. For INLA, and other deterministic methods, the hyperparameter space is explored and points are laid out in a grid structure. These points are used in some numerical integration scheme for which marginal posterior distributions are computed. The main drawback is that the number of points increase exponentially with the number of hyperparameters. The grid is a type of quasi-Monte Carlo (QMC) point set. Low discrepancy sequences (LDS) are QMC point sets that are well known to have significant advantages over grids in terms of convergence and accuracy, and suffer less from the so-called curse of dimensionality.

This work makes several important contributions. We introduce a new method using LDS to compute marginal posterior distributions for hyperparameters, discuss the convergence properties of the approximations and show that they converge to the true posterior. We also show how these methods can be incorporated into the INLA inference framework, and we outline important extensions that improve the accuracy of our approximations with little extra computational effort needed. Lastly, we build a unique spatio-temporal model of residential crime in Hamilton, using INLA’s stochastic partial differential equation approach to a Log-Gaussian Cox Process, and use an LDS to approximate the latent parameters of the model.

Our results show that for a fixed number of points or computational time, LDS methods can outperform general grid-based methods, leading to better marginal posterior approximations. Modifying the method for the purposes of incorporation to INLA, we show that we can outperform INLA’s grid with respect to computational speed, and obtain accurate and flexible approximations to the model hyperparameters.

text: Computational Bayesian inference using low discrepancy sequences The Integrated Nested Laplace Approximation (INLA) provides fast and accurate Bayesian inference for complex hierarchical models. For INLA, and other deterministic methods, the hyperparameter space is explored and points are laid out in a grid structure. These points are used in some numerical integration scheme for which marginal posterior distributions are computed. The main drawback is that the number of points increase exponentially with the number of hyperparameters. The grid is a type of quasi-Monte Carlo (QMC) point set. Low discrepancy sequences (LDS) are QMC point sets that are well known to have significant advantages over grids in terms of convergence and accuracy, and suffer less from the so-called curse of dimensionality.

This work makes several important contributions. We introduce a new method using LDS to compute marginal posterior distributions for hyperparameters, discuss the convergence properties of the approximations and show that they converge to the true posterior. We also show how these methods can be incorporated into the INLA inference framework, and we outline important extensions that improve the accuracy of our approximations with little extra computational effort needed. Lastly, we build a unique spatio-temporal model of residential crime in Hamilton, using INLA’s stochastic partial differential equation approach to a Log-Gaussian Cox Process, and use an LDS to approximate the latent parameters of the model.

Our results show that for a fixed number of points or computational time, LDS methods can outperform general grid-based methods, leading to better marginal posterior approximations. Modifying the method for the purposes of incorporation to INLA, we show that we can outperform INLA’s grid with respect to computational speed, and obtain accurate and flexible approximations to the model hyperparameters.

year: 2019

title: Historical tsunami database for New Zealand

authors: Fraser, Rodger James

subjects: Tsunamis

abstract: New Zealand has suffered relatively few tsunamis compared to many countries around or within the Pacific rim, but has experienced over 30 tsunamis during the last 177 years. The larger events occurred prior to the time when coastal settlements became highly
populated. The New Zealand Ministry of Civil Defence is responsible for managing such extreme events, and for this function it is advantageous to have a comprehensive database for rapid appraisal of tsunami warnings. This project therefor aims to extend the existing tsunami events data and to present it in an operational database for The New Zealand Ministry of Civil Defence. In addition from the tsunami database, tsunami runup risk and expected tsunami runup heights for several New Zealand coastal sectors were calculated.

Using existing dates of tsunami events, new reports of tsunami waves were researched from South Island newspaper archives. Additional extra information about the tsunami waves, for example wave height and wave period, was also obtained from the newspapers for existing reports.

The tsunami data, including source mechanism data, was entered into a database spreadsheet in the form of a lookup table using Microsoft Excel. Event sources are divided into key regions as defined by The National Geophysical Data Centre of the National Oceanic and Atmospheric Administration. Tsunami events are divided up into key regions defined by Regional Council authorities. The database will enable The Ministry of Civil Defence to predict tsunami heights around New Zealand by interpolating data from past events. 

Tsunami return periods and expected runup calculations were made for various sites around New Zealand. It was found that destructive tsunami waves are most likely to originate from local sources. The most common and largest far-field tsunami waves are from the West Coast of South America

text: Historical tsunami database for New Zealand New Zealand has suffered relatively few tsunamis compared to many countries around or within the Pacific rim, but has experienced over 30 tsunamis during the last 177 years. The larger events occurred prior to the time when coastal settlements became highly
populated. The New Zealand Ministry of Civil Defence is responsible for managing such extreme events, and for this function it is advantageous to have a comprehensive database for rapid appraisal of tsunami warnings. This project therefor aims to extend the existing tsunami events data and to present it in an operational database for The New Zealand Ministry of Civil Defence. In addition from the tsunami database, tsunami runup risk and expected tsunami runup heights for several New Zealand coastal sectors were calculated.

Using existing dates of tsunami events, new reports of tsunami waves were researched from South Island newspaper archives. Additional extra information about the tsunami waves, for example wave height and wave period, was also obtained from the newspapers for existing reports.

The tsunami data, including source mechanism data, was entered into a database spreadsheet in the form of a lookup table using Microsoft Excel. Event sources are divided into key regions as defined by The National Geophysical Data Centre of the National Oceanic and Atmospheric Administration. Tsunami events are divided up into key regions defined by Regional Council authorities. The database will enable The Ministry of Civil Defence to predict tsunami heights around New Zealand by interpolating data from past events. 

Tsunami return periods and expected runup calculations were made for various sites around New Zealand. It was found that destructive tsunami waves are most likely to originate from local sources. The most common and largest far-field tsunami waves are from the West Coast of South America

year: 1998

title: Homeless Māori Men: Re-connection, Re-joining, and Re-membering Ways of Being

authors: King, Pita Richard Wiremu

subjects: Māori psychology

abstract: There are a range of interventions and programmes to address the on-going issue of Māori homelessness. This thesis explores a gardening project hosted by a Ngāti Whātua marae (communal complex used for everyday Māori life) in Auckland for homeless Māori men. The garden project facilitates a sense of belonging, dignity, purpose, meaning and connectedness with other Māori people. It provides insights into how culturally-patterned relationships are centrally important to resolving the overrepresentation of indigenous peoples’ in homelessness populations. I employ the use of semi-structured interviews, reflective journaling, and photography as techniques to record and document the daily interactions in the marae gardens. Participants came from three distinct groups, which include: homeless Māori men, the Auckland City Mission, and Ngāti Whātua o Orakei. A total of eight participants were formally interviewed, along with another six who engaged in casual conversations, in this research, with ages ranged from 30 to 70 years of age. Key findings from this research relate to the construction and preservation of Māori identity while in a state of homelessness, the functioning of marae as spaces of care that foster the wellbeing of Māori, and the role of food in the reproduction of Māori cultural values in everyday life. The broader significance of my work is to use indigenous concepts to build an understanding of the activities, needs and relationships of homeless Māori men that they can recognise themselves from.

text: Homeless Māori Men: Re-connection, Re-joining, and Re-membering Ways of Being There are a range of interventions and programmes to address the on-going issue of Māori homelessness. This thesis explores a gardening project hosted by a Ngāti Whātua marae (communal complex used for everyday Māori life) in Auckland for homeless Māori men. The garden project facilitates a sense of belonging, dignity, purpose, meaning and connectedness with other Māori people. It provides insights into how culturally-patterned relationships are centrally important to resolving the overrepresentation of indigenous peoples’ in homelessness populations. I employ the use of semi-structured interviews, reflective journaling, and photography as techniques to record and document the daily interactions in the marae gardens. Participants came from three distinct groups, which include: homeless Māori men, the Auckland City Mission, and Ngāti Whātua o Orakei. A total of eight participants were formally interviewed, along with another six who engaged in casual conversations, in this research, with ages ranged from 30 to 70 years of age. Key findings from this research relate to the construction and preservation of Māori identity while in a state of homelessness, the functioning of marae as spaces of care that foster the wellbeing of Māori, and the role of food in the reproduction of Māori cultural values in everyday life. The broader significance of my work is to use indigenous concepts to build an understanding of the activities, needs and relationships of homeless Māori men that they can recognise themselves from.

year: 2014