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: Assessment of demand for food under concurrent PR and FR schedules in the brushtail possum (Trichosurus Vulpecula)

authors: Cameron, Kristie Elizabeth

abstract: The aim of this study was to compare the demand by possums for foods under different arrangements of concurrent progressive-ratio and fixed-ratio schedules of reinforcement. In Experiment 1, every possible food pair made up of berries, chicken, egg, foliage, insects, and mushroom was presented (30 pairs in total). The requirement on the progressive-ratio schedule increased within a session and the fixed-ratio was kept constant at 30. In Experiment 2, a subset of the foods from Experiment 1 were used (chicken, mushroom, egg, and berries) and in separate conditions the fixed-ratio was either 30 or 10 responses. In Experiment 3, the foods were the same as used in Experiment 2 and the progressive-ratio schedule increased every five sessions and the fixed-ratio was kept constant at 30. Exponential models of demand were applied to consumption rates to compare the parameters of initial demand, essential value and Pmax, and break point and cross point across foods. The models described the data well and consumption rates were similar when the incrementing schedules increased within- and across sessions. Demand was highest for berries, egg, and locust in Experiment 1 and egg and chicken in Experiments 2 and 3. This finding has practical implications for understanding possum food preferences in the wild as a function of other available food sources and for informing pest control strategies of potential lures.

text: Assessment of demand for food under concurrent PR and FR schedules in the brushtail possum (Trichosurus Vulpecula) The aim of this study was to compare the demand by possums for foods under different arrangements of concurrent progressive-ratio and fixed-ratio schedules of reinforcement. In Experiment 1, every possible food pair made up of berries, chicken, egg, foliage, insects, and mushroom was presented (30 pairs in total). The requirement on the progressive-ratio schedule increased within a session and the fixed-ratio was kept constant at 30. In Experiment 2, a subset of the foods from Experiment 1 were used (chicken, mushroom, egg, and berries) and in separate conditions the fixed-ratio was either 30 or 10 responses. In Experiment 3, the foods were the same as used in Experiment 2 and the progressive-ratio schedule increased every five sessions and the fixed-ratio was kept constant at 30. Exponential models of demand were applied to consumption rates to compare the parameters of initial demand, essential value and Pmax, and break point and cross point across foods. The models described the data well and consumption rates were similar when the incrementing schedules increased within- and across sessions. Demand was highest for berries, egg, and locust in Experiment 1 and egg and chicken in Experiments 2 and 3. This finding has practical implications for understanding possum food preferences in the wild as a function of other available food sources and for informing pest control strategies of potential lures.

year: 2015

title: Kaitiakitanga - Active guardianship, responsibilities and relationships with the world: Towards a bio-cultural future In early childhood education

authors: Paul-Burke, Kura

abstract: The world is a vast family, and humans are children of the earth and sky, and cousins to all living things. Such unity means that nature is the ultimate teacher about life (Royal 2010, p. 9).
For Māori (indigenous peoples of Aotearoa New Zealand) the term kaitiakitanga (pronounced, kye-tee-ah-key-tar-ngah) is often used to refer to the active guardianship and management of natural organisms and their environments. Mātauranga Māori or Māori knowledge positions humans within nature and focuses on ways in which cultural understandings and intergenerational connections between people and their biophysical contexts assist in the retention and protection of biodiversity and ecologically sustainable ecosystems. This entry critically reflects notions of kaitiakitanga and bio-cultural connectivity as important and meaningful contributors for young children and their relationships with and for the world.

text: Kaitiakitanga - Active guardianship, responsibilities and relationships with the world: Towards a bio-cultural future In early childhood education The world is a vast family, and humans are children of the earth and sky, and cousins to all living things. Such unity means that nature is the ultimate teacher about life (Royal 2010, p. 9).
For Māori (indigenous peoples of Aotearoa New Zealand) the term kaitiakitanga (pronounced, kye-tee-ah-key-tar-ngah) is often used to refer to the active guardianship and management of natural organisms and their environments. Mātauranga Māori or Māori knowledge positions humans within nature and focuses on ways in which cultural understandings and intergenerational connections between people and their biophysical contexts assist in the retention and protection of biodiversity and ecologically sustainable ecosystems. This entry critically reflects notions of kaitiakitanga and bio-cultural connectivity as important and meaningful contributors for young children and their relationships with and for the world.

year: 2015