Weibull model selection for reliability modelling

A large number of models have been derived from the two-parameter Weibull distribution and are referred to as Weibull models. They exhibit a wide range of shapes for the density and hazard functions, which makes them suitable for modelling complex failure data sets. The WPP and IWPP plot allows one to determine in a systematic manner if one or more of these models are suitable for modelling a given data set. This paper deals with this topic.

Forecasting stock returns using model-selection criteria

This paper examines the economic significance of return predictability in Australian equities. In light of considerable model uncertainty, formal model-selection criteria are used to choose a specification for the predictive model. A portfolio-switching strategy is implemented according to model predictions. Relative to a buy-and-hold market investment, the returns to the portfolio-switching strategy are impressive under several model-selection criteria, even after accounting for transaction costs. However, as these findings are not robust across other model-selection criteria examined, it is difficult to conclude that the degree of return predictability is economically significant.

Analysis of Melanoma Onset: Assessing Familial Aggregation by Using Estimating Equations and Fitting Variance Components via Bayesian Random Effects Models

We investigate whether relative contributions of genetic and shared environmental factors are associated with an increased risk in melanoma. Data from the Queensland Familial Melanoma Project comprising 15,907 subjects arising from 1912 families were analyzed to estimate the additive genetic, common and unique environmental contributions to variation in the age at onset of melanoma. Two complementary approaches for analyzing correlated time-to-onset family data were considered: the generalized estimating equations (GEE) method in which one can estimate relationship-specific dependence simultaneously with regression coefficients that describe the average population response to changing covariates; and a subject-specific Bayesian mixed model in which heterogeneity in regression parameters is explicitly modeled and the different components of variation may be estimated directly. The proportional hazards and Weibull models were utilized, as both produce natural frameworks for estimating relative risks while adjusting for simultaneous effects of other covariates. A simple Markov Chain Monte Carlo method for covariate imputation of missing data was used and the actual implementation of the Bayesian model was based on Gibbs sampling using the free ware package BUGS. In addition, we also used a Bayesian model to investigate the relative contribution of genetic and environmental effects on the expression of naevi and freckles, which are known risk factors for melanoma.

An empirical study of Hoelfding Racing for model selction in K-nearest neighbor classification

Racing algorithms have recently been proposed as a general-purpose method for performing model selection in machine teaming algorithms. In this paper, we present an empirical study of the Hoeffding racing algorithm for selecting the k parameter in a simple k-nearest neighbor classifier. Fifteen widely-used classification datasets from UCI are used and experiments conducted across different confidence levels for racing. The results reveal a significant amount of sensitivity of the k-nn classifier to its model parameter value. The Hoeffding racing algorithm also varies widely in its performance, in terms of the computational savings gained over an exhaustive evaluation. While in some cases the savings gained are quite small, the racing algorithm proved to be highly robust to the possibility of erroneously eliminating the optimal models. All results were strongly dependent on the datasets used.

Mechanisms of drought-induced population decline in an endangered wallaby

The bridled nailtail wallaby is restricted to one locality in central Queensland, Australia. The population declined severely during a major drought between 1991 and 1995. We investigated age-specific covariates of survival and proximate causes of mortality from 1994 to 1997, using mark-recapture and radio-tagging techniques at two study sites. Using a matrix population model, we also modelled the effect of drought on age-specific survival and the intrinsic rate of population increase,;,. The only significant covariate of survival for adults was a measure of health unrelated to drought. Rainfall, food, predator activity, year, sex and habitat were not associated with variation in adult survival. Juvenile survival was negatively affected by drought, and predation was the proximate cause of most juvenile deaths. The matrix projection model showed that the observed juvenile survivorship during the drought was low enough to have produced a population decline, although fecundity and survival of other age classes was high throughout the study. (C) 2001 Elsevier Science Ltd. All rights reserved.

A generalized Markov sampler

A recent development of the Markov chain Monte Carlo (MCMC) technique is the emergence of MCMC samplers that allow transitions between different models. Such samplers make possible a range of computational tasks involving models, including model selection, model evaluation, model averaging and hypothesis testing. An example of this type of sampler is the reversible jump MCMC sampler, which is a generalization of the Metropolis-Hastings algorithm. Here, we present a new MCMC sampler of this type. The new sampler is a generalization of the Gibbs sampler, but somewhat surprisingly, it also turns out to encompass as particular cases all of the well-known MCMC samplers, including those of Metropolis, Barker, and Hastings. Moreover, the new sampler generalizes the reversible jump MCMC. It therefore appears to be a very general framework for MCMC sampling. This paper describes the new sampler and illustrates its use in three applications in Computational Biology, specifically determination of consensus sequences, phylogenetic inference and delineation of isochores via multiple change-point analysis.

Genetic diversity and population structure of Tasmanian devils, the largest marsupial carnivore

Genetic diversity and population structure were investigated across the core range of Tasmanian devils (Sarcophilus laniarius; Dasyuridae), a wide-ranging marsupial carnivore restricted to the island of Tasmania. Heterozygosity (0.386-0.467) and allelic diversity (2.7-3.3) were low in all subpopulations and allelic size ranges were small and almost continuous, consistent with a founder effect. Island effects and repeated periods of low population density may also have contributed to the low variation. Within continuous habitat, gene flow appears extensive up to 50 km (high assignment rates to source or close neighbour populations; nonsignificant values of pairwise F-ST), in agreement with movement data. At larger scales (150-250 km), gene flow is reduced (significant pairwise F-ST) but there is no evidence for isolation by distance. The most substantial genetic structuring was observed for comparisons spanning unsuitable habitat, implying limited dispersal of devils between the well-connected, eastern populations and a smaller northwestern population. The genetic distinctiveness of the northwestern population was reflected in all analyses: unique alleles; multivariate analyses of gene frequency (multidimensional scaling, minimum spanning tree, nearest neighbour); high self-assignment (95%); two distinct populations for Tasmania were detected in isolation by distance and in Bayesian model-based clustering analyses. Marsupial carnivores appear to have stronger population subdivisions than their placental counterparts.

A genetic estimation algorithm for parameters of stochastic ordinary differential equations

A generic method for the estimation of parameters for Stochastic Ordinary Differential Equations (SODEs) is introduced and developed. This algorithm, called the GePERs method, utilises a genetic optimisation algorithm to minimise a stochastic objective function based on the Kolmogorov-Smirnov statistic. Numerical simulations are utilised to form the KS statistic. Further, the examination of some of the factors that improve the precision of the estimates is conducted. This method is used to estimate parameters of diffusion equations and jump-diffusion equations. It is also applied to the problem of model selection for the Queensland electricity market. (C) 2003 Elsevier B.V. All rights reserved.

The effects of habitat fragmentation due to forestry plantation establishment on the demography and genetic variation of a marsupial carnivore, Antechinus agilis

We conducted a demographic and genetic study to investigate the effects of fragmentation due to the establishment of an exotic softwood plantation on populations of a small marsupial carnivore, the agile antechinus (Antechinus agilis), and the factors influencing the persistence of those populations in the fragmented habitat. The first aspect of the study was a descriptive analysis of patch occupancy and population size, in which we found a patch occupancy rate of 70% among 23 sites in the fragmented habitat compared to 100% among 48 sites with the same habitat characteristics in unfragmented habitat. Mark-recapture analyses yielded most-likely population size estimates of between 3 and 85 among the 16 occupied patches in the fragmented habitat. Hierarchical partitioning and model selection were used to identify geographic and habitat-related characteristics that influence patch occupancy and population size. Patch occupancy was primarily influenced by geographic isolation and habitat quality (vegetation basal area). The variance in population size among occupied sites was influenced primarily by forest type (dominant Eucalyptus species) and, to a lesser extent, by patch area and topographic context (gully sites had larger populations). A comparison of the sex ratios between the samples from the two habitat contexts revealed a significant deficiency of males in the fragmented habitat. We hypothesise that this is due to male-biased dispersal in an environment with increased dispersal-associated mortality. The population size and sex ratio data were incorporated into a simulation study to estimate the proportion of genetic diversity that would have been lost over the known timescale since fragmentation if the patch populations had been totally isolated. The observed difference in genetic diversity (gene diversity and allelic richness at microsatellite and mitochondrial markers) between 16 fragmented and 12 unfragmented sites was extremely low and inconsistent with the isolation of the patch populations. Our results show that although the remnant habitat patches comprise approximately 2% of the study area, they can support non-isolated populations. However, the distribution of agile antechinus populations in the fragmented system is dependent on habitat quality and patch connectivity. (C) 2004 Elsevier Ltd. All rights reserved.

Evaluating trends in abundance of immature green turtles, Chelonia mydas, in the Greater Caribbean

Many long-lived marine species exhibit life history traits. that make them more vulnerable to overexploitation. Accurate population trend analysis is essential for development and assessment of management plans for these species. However, because many of these species disperse over large geographic areas, have life stages inaccessible to human surveyors, and/or undergo complex developmental migrations, data on trends in abundance are often available for only one stage of the population, usually breeding adults. The green turtle (Chelonia mydas) is one of these long-lived species for which population trends are based almost exclusively on either numbers of females that emerge to nest or numbers of nests deposited each year on geographically restricted beaches. In this study, we generated estimates of annual abundance for juvenile green turtles at two foraging grounds in the Bahamas based on long-term capture-mark-recapture (CMR) studies at Union Creek (24 years) and Conception Creek (13 years), using a two-stage approach. First, we estimated recapture probabilities from CMR data using the Cormack-Jolly-Seber models in the software program MARK; second, we estimated annual abundance of green turtles. at both study sites using the recapture probabilities in a Horvitz-Thompson type estimation procedure. Green turtle abundance did not change significantly in Conception Creek, but, in Union Creek, green turtle abundance had successive phases of significant increase, significant decrease, and stability. These changes in abundance resulted from changes in immigration, not survival or emigration. The trends in abundance on the foraging grounds did not conform to the significantly increasing trend for the major nesting population at Tortuguero, Costa Rica. This disparity highlights the challenges of assessing population-wide trends of green turtles and other long-lived species. The best approach for monitoring population trends may be a combination of (1) extensive surveys to provide data for large-scale trends in relative population abundance, and (2) intensive surveys, using CMR techniques, to estimate absolute abundance and evaluate the demographic processes' driving the trends.

Modelling pre-clearing vegetation distribution using GIS-integrated statistical, ecological and data models: A case study from the wet tropics of Northeastern Australia

Traditional vegetation mapping methods use high cost, labour-intensive aerial photography interpretation. This approach can be subjective and is limited by factors such as the extent of remnant vegetation, and the differing scale and quality of aerial photography over time. An alternative approach is proposed which integrates a data model, a statistical model and an ecological model using sophisticated Geographic Information Systems (GIS) techniques and rule-based systems to support fine-scale vegetation community modelling. This approach is based on a more realistic representation of vegetation patterns with transitional gradients from one vegetation community to another. Arbitrary, though often unrealistic, sharp boundaries can be imposed on the model by the application of statistical methods. This GIS-integrated multivariate approach is applied to the problem of vegetation mapping in the complex vegetation communities of the Innisfail Lowlands in the Wet Tropics bioregion of Northeastern Australia. The paper presents the full cycle of this vegetation modelling approach including sampling sites, variable selection, model selection, model implementation, internal model assessment, model prediction assessments, models integration of discrete vegetation community models to generate a composite pre-clearing vegetation map, independent data set model validation and model prediction's scale assessments. An accurate pre-clearing vegetation map of the Innisfail Lowlands was generated (0.83r(2)) through GIS integration of 28 separate statistical models. This modelling approach has good potential for wider application, including provision of. vital information for conservation planning and management; a scientific basis for rehabilitation of disturbed and cleared areas; a viable method for the production of adequate vegetation maps for conservation and forestry planning of poorly-studied areas. (c) 2006 Elsevier B.V. All rights reserved.

Bayesian analysis of the error correction model

This paper presents a method for estimating the posterior probability density of the cointegrating rank of a multivariate error correction model. A second contribution is the careful elicitation of the prior for the cointegrating vectors derived from a prior on the cointegrating space. This prior obtains naturally from treating the cointegrating space as the parameter of interest in inference and overcomes problems previously encountered in Bayesian cointegration analysis. Using this new prior and Laplace approximation, an estimator for the posterior probability of the rank is given. The approach performs well compared with information criteria in Monte Carlo experiments. (C) 2003 Elsevier B.V. All rights reserved.

A Comparison of Bayesian and Sampling Theory Inferences in a Probit Model

HE PROBIT MODEL IS A POPULAR DEVICE for explaining binary choice decisions in econometrics. It has been used to describe choices such as labor force participation, travel mode, home ownership, and type of education. These and many more examples can be found in papers by Amemiya (1981) and Maddala (1983). Given the contribution of economics towards explaining such choices, and given the nature of data that are collected, prior information on the relationship between a choice probability and several explanatory variables frequently exists. Bayesian inference is a convenient vehicle for including such prior information. Given the increasing popularity of Bayesian inference it is useful to ask whether inferences from a probit model are sensitive to a choice between Bayesian and sampling theory techniques. Of interest is the sensitivity of inference on coefficients, probabilities, and elasticities. We consider these issues in a model designed to explain choice between fixed and variable interest rate mortgages. Two Bayesian priors are employed: a uniform prior on the coefficients, designed to be noninformative for the coefficients, and an inequality restricted prior on the signs of the coefficients. We often know, a priori, whether increasing the value of a particular explanatory variable will have a positive or negative effect on a choice probability. This knowledge can be captured by using a prior probability density function (pdf) that is truncated to be positive or negative. Thus, three sets of results are compared:those from maximum likelihood (ML) estimation, those from Bayesian estimation with an unrestricted uniform prior on the coefficients, and those from Bayesian estimation with a uniform prior truncated to accommodate inequality restrictions on the coefficients.

International market selection: Developing a model from Australian case studies

This paper develops a theory that firms seek out new country markets on the basis of expected commercial returns. These expectations depend on judgements about the attractiveness of the market and the firm's competitive position in it, which in turn are influenced by informants. It is the number and strengths of these informants that will underlie the probability of a country being identified and assessed as a new market by any firm.

A general model for host plant selection in phytophagous insects

We develop a general theoretical framework for exploring the host plant selection behaviour of herbivorous insects. This model can be used to address a number of questions, including the evolution of specialists, generalists, preference hierarchies, and learning. We use our model to: (i) demonstrate the consequences of the extent to which the reproductive success of a foraging female is limited by the rate at which they find host plants (host limitation) or the number of eggs they carry (egg limitation); (ii) emphasize the different consequences of variation in behaviour before and after landing on (locating) a host (termed pre- and post-alighting, respectively); (iii) show that, in contrast to previous predictions, learning can be favoured in post-alighting behaviour-in particular, individuals can be selected to concentrate oviposition on an abundant low-quality host, whilst ignoring a rare higher-quality host; (iv) emphasize the importance of interactions between mechanisms in favouring specialization or learning. (C) 2002 Elsevier Science Ltd.