Generalised growth models for aquatic species with an application to blacklip abalone (Haliotis rubra)

This paper presents a maximum likelihood method for estimating growth parameters for an aquatic species that incorporates growth covariates, and takes into consideration multiple tag-recapture data. Individual variability in asymptotic length, age-at-tagging, and measurement error are also considered in the model structure. Using distribution theory, the log-likelihood function is derived under a generalised framework for the von Bertalanffy and Gompertz growth models. Due to the generality of the derivation, covariate effects can be included for both models with seasonality and tagging effects investigated. Method robustness is established via comparison with the Fabens, improved Fabens, James and a non-linear mixed-effects growth models, with the maximum likelihood method performing the best. The method is illustrated further with an application to blacklip abalone (Haliotis rubra) for which a strong growth-retarding tagging effect that persisted for several months was detected. (C) 2013 Elsevier B.V. All rights reserved.

A new family of multivariate heavy-tailed distributions with variable marginal amounts of tailweight: Application to robust clustering

We propose a family of multivariate heavy-tailed distributions that allow variable marginal amounts of tailweight. The originality comes from introducing multidimensional instead of univariate scale variables for the mixture of scaled Gaussian family of distributions. In contrast to most existing approaches, the derived distributions can account for a variety of shapes and have a simple tractable form with a closed-form probability density function whatever the dimension. We examine a number of properties of these distributions and illustrate them in the particular case of Pearson type VII and t tails. For these latter cases, we provide maximum likelihood estimation of the parameters and illustrate their modelling flexibility on simulated and real data clustering examples.

Nineteenth century narratives reveal historic catch rates for Australian snapper (Pagrus auratus)

Snapper (Pagrus auratus) is widely distributed throughout subtropical and temperate southern oceans and forms a significant recreational and commercial fishery in Queensland, Australia. Using data from government reports, media sources, popular publications and a government fisheries survey carried out in 1910, we compiled information on individual snapper fishing trips that took place prior to the commencement of fisherywide organized data collection, from 1871 to 1939. In addition to extracting all available quantitative data, we translated qualitative information into bounded estimates and used multiple imputation to handle missing values, forming 287 records for which catch rate (snapper fisher−1 h−1) could be derived. Uncertainty was handled through a parametric maximum likelihood framework (a transformed trivariate Gaussian), which facilitated statistical comparisons between data sources. No statistically significant differences in catch rates were found among media sources and the government fisheries survey. Catch rates remained stable throughout the time series, averaging 3.75 snapper fisher−1 h−1 (95% confidence interval, 3.42–4.09) as the fishery expanded into new grounds. In comparison, a contemporary (1993–2002) south-east Queensland charter fishery produced an average catch rate of 0.4 snapper fisher−1 h−1 (95% confidence interval, 0.31–0.58). These data illustrate the productivity of a fishery during its earliest years of development and represent the earliest catch rate data globally for this species. By adopting a formalized approach to address issues common to many historical records – missing data, a lack of quantitative information and reporting bias – our analysis demonstrates the potential for historical narratives to contribute to contemporary fisheries management.

Enhanced processing of SPOT multispectral satellite imagery for environmental monitoring and modelling

The Taita Hills in southeastern Kenya form the northernmost part of Africa’s Eastern Arc Mountains, which have been identified by Conservation International as one of the top ten biodiversity hotspots on Earth. As with many areas of the developing world, over recent decades the Taita Hills have experienced significant population growth leading to associated major changes in land use and land cover (LULC), as well as escalating land degradation, particularly soil erosion. Multi-temporal medium resolution multispectral optical satellite data, such as imagery from the SPOT HRV, HRVIR, and HRG sensors, provides a valuable source of information for environmental monitoring and modelling at a landscape level at local and regional scales. However, utilization of multi-temporal SPOT data in quantitative remote sensing studies requires the removal of atmospheric effects and the derivation of surface reflectance factor. Furthermore, for areas of rugged terrain, such as the Taita Hills, topographic correction is necessary to derive comparable reflectance throughout a SPOT scene. Reliable monitoring of LULC change over time and modelling of land degradation and human population distribution and abundance are of crucial importance to sustainable development, natural resource management, biodiversity conservation, and understanding and mitigating climate change and its impacts. The main purpose of this thesis was to develop and validate enhanced processing of SPOT satellite imagery for use in environmental monitoring and modelling at a landscape level, in regions of the developing world with limited ancillary data availability. The Taita Hills formed the application study site, whilst the Helsinki metropolitan region was used as a control site for validation and assessment of the applied atmospheric correction techniques, where multiangular reflectance field measurements were taken and where horizontal visibility meteorological data concurrent with image acquisition were available. The proposed historical empirical line method (HELM) for absolute atmospheric correction was found to be the only applied technique that could derive surface reflectance factor within an RMSE of < 0.02 ps in the SPOT visible and near-infrared bands; an accuracy level identified as a benchmark for successful atmospheric correction. A multi-scale segmentation/object relationship modelling (MSS/ORM) approach was applied to map LULC in the Taita Hills from the multi-temporal SPOT imagery. This object-based procedure was shown to derive significant improvements over a uni-scale maximum-likelihood technique. The derived LULC data was used in combination with low cost GIS geospatial layers describing elevation, rainfall and soil type, to model degradation in the Taita Hills in the form of potential soil loss, utilizing the simple universal soil loss equation (USLE). Furthermore, human population distribution and abundance were modelled with satisfactory results using only SPOT and GIS derived data and non-Gaussian predictive modelling techniques. The SPOT derived LULC data was found to be unnecessary as a predictor because the first and second order image texture measurements had greater power to explain variation in dwelling unit occurrence and abundance. The ability of the procedures to be implemented locally in the developing world using low-cost or freely available data and software was considered. The techniques discussed in this thesis are considered equally applicable to other medium- and high-resolution optical satellite imagery, as well the utilized SPOT data.

On probability-based inference under data missing by design

Whether a statistician wants to complement a probability model for observed data with a prior distribution and carry out fully probabilistic inference, or base the inference only on the likelihood function, may be a fundamental question in theory, but in practice it may well be of less importance if the likelihood contains much more information than the prior. Maximum likelihood inference can be justified as a Gaussian approximation at the posterior mode, using flat priors. However, in situations where parametric assumptions in standard statistical models would be too rigid, more flexible model formulation, combined with fully probabilistic inference, can be achieved using hierarchical Bayesian parametrization. This work includes five articles, all of which apply probability modeling under various problems involving incomplete observation. Three of the papers apply maximum likelihood estimation and two of them hierarchical Bayesian modeling. Because maximum likelihood may be presented as a special case of Bayesian inference, but not the other way round, in the introductory part of this work we present a framework for probability-based inference using only Bayesian concepts. We also re-derive some results presented in the original articles using the toolbox equipped herein, to show that they are also justifiable under this more general framework. Here the assumption of exchangeability and de Finetti's representation theorem are applied repeatedly for justifying the use of standard parametric probability models with conditionally independent likelihood contributions. It is argued that this same reasoning can be applied also under sampling from a finite population. The main emphasis here is in probability-based inference under incomplete observation due to study design. This is illustrated using a generic two-phase cohort sampling design as an example. The alternative approaches presented for analysis of such a design are full likelihood, which utilizes all observed information, and conditional likelihood, which is restricted to a completely observed set, conditioning on the rule that generated that set. Conditional likelihood inference is also applied for a joint analysis of prevalence and incidence data, a situation subject to both left censoring and left truncation. Other topics covered are model uncertainty and causal inference using posterior predictive distributions. We formulate a non-parametric monotonic regression model for one or more covariates and a Bayesian estimation procedure, and apply the model in the context of optimal sequential treatment regimes, demonstrating that inference based on posterior predictive distributions is feasible also in this case.

Joint Regression and Association Models for Repeated Categorical Responses

The focus of this study is on statistical analysis of categorical responses, where the response values are dependent of each other. The most typical example of this kind of dependence is when repeated responses have been obtained from the same study unit. For example, in Paper I, the response of interest is the pneumococcal nasopharengyal carriage (yes/no) on 329 children. For each child, the carriage is measured nine times during the first 18 months of life, and thus repeated respones on each child cannot be assumed independent of each other. In the case of the above example, the interest typically lies in the carriage prevalence, and whether different risk factors affect the prevalence. Regression analysis is the established method for studying the effects of risk factors. In order to make correct inferences from the regression model, the associations between repeated responses need to be taken into account. The analysis of repeated categorical responses typically focus on regression modelling. However, further insights can also be gained by investigating the structure of the association. The central theme in this study is on the development of joint regression and association models. The analysis of repeated, or otherwise clustered, categorical responses is computationally difficult. Likelihood-based inference is often feasible only when the number of repeated responses for each study unit is small. In Paper IV, an algorithm is presented, which substantially facilitates maximum likelihood fitting, especially when the number of repeated responses increase. In addition, a notable result arising from this work is the freely available software for likelihood-based estimation of clustered categorical responses.

Flying-Fox Roost Disturbance and Hendra Virus Spillover Risk

Bats of the genus Pteropus (flying-foxes) are the natural host of Hendra virus (HeV) which periodically causes fatal disease in horses and humans in Australia. The increased urban presence of flying-foxes often provokes negative community sentiments because of reduced social amenity and concerns of HeV exposure risk, and has resulted in calls for the dispersal of urban flying-fox roosts. However, it has been hypothesised that disturbance of urban roosts may result in a stress-mediated increase in HeV infection in flying-foxes, and an increased spillover risk. We sought to examine the impact of roost modification and dispersal on HeV infection dynamics and cortisol concentration dynamics in flying-foxes. The data were analysed in generalised linear mixed models using restricted maximum likelihood (REML). The difference in mean HeV prevalence in samples collected before (4.9%), during (4.7%) and after (3.4%) roost disturbance was small and non-significant (P = 0.440). Similarly, the difference in mean urine specific gravity-corrected urinary cortisol concentrations was small and non-significant (before = 22.71 ng/mL, during = 27.17, after = 18.39) (P= 0.550). We did find an underlying association between cortisol concentration and season, and cortisol concentration and region, suggesting that other (plausibly biological or environmental) variables play a role in cortisol concentration dynamics. The effect of roost disturbance on cortisol concentration approached statistical significance for region, suggesting that the relationship is not fixed, and plausibly reflecting the nature and timing of disturbance. We also found a small positive statistical association between HeV excretion status and urinary cortisol concentration. Finally, we found that the level of flying-fox distress associated with roost disturbance reflected the nature and timing of the activity, highlighting the need for a ‘best practice’ approach to dispersal or roost modification activities. The findings usefully inform public discussion and policy development in relation to Hendra virus and flying-fox management.

Hazard Function Models to Estimate Mortality Rates Affecting Fish Populations with Application to the Sea Mullet (Mugil cephalus) Fishery on the Queensland Coast (Australia)

Fisheries management agencies around the world collect age data for the purpose of assessing the status of natural resources in their jurisdiction. Estimates of mortality rates represent a key information to assess the sustainability of fish stocks exploitation. Contrary to medical research or manufacturing where survival analysis is routinely applied to estimate failure rates, survival analysis has seldom been applied in fisheries stock assessment despite similar purposes between these fields of applied statistics. In this paper, we developed hazard functions to model the dynamic of an exploited fish population. These functions were used to estimate all parameters necessary for stock assessment (including natural and fishing mortality rates as well as gear selectivity) by maximum likelihood using age data from a sample of catch. This novel application of survival analysis to fisheries stock assessment was tested by Monte Carlo simulations to assert that it provided unbiased estimations of relevant quantities. The method was applied to the data from the Queensland (Australia) sea mullet (Mugil cephalus) commercial fishery collected between 2007 and 2014. It provided, for the first time, an estimate of natural mortality affecting this stock: 0.22±0.08 year −1 .

Computing the Stochastic Complexity of Simple Probabilistic Graphical Models

Minimum Description Length (MDL) is an information-theoretic principle that can be used for model selection and other statistical inference tasks. There are various ways to use the principle in practice. One theoretically valid way is to use the normalized maximum likelihood (NML) criterion. Due to computational difficulties, this approach has not been used very often. This thesis presents efficient floating-point algorithms that make it possible to compute the NML for multinomial, Naive Bayes and Bayesian forest models. None of the presented algorithms rely on asymptotic analysis and with the first two model classes we also discuss how to compute exact rational number solutions.

Computationally Efficient Methods for MDL-Optimal Density Estimation and Data Clustering

The Minimum Description Length (MDL) principle is a general, well-founded theoretical formalization of statistical modeling. The most important notion of MDL is the stochastic complexity, which can be interpreted as the shortest description length of a given sample of data relative to a model class. The exact definition of the stochastic complexity has gone through several evolutionary steps. The latest instantation is based on the so-called Normalized Maximum Likelihood (NML) distribution which has been shown to possess several important theoretical properties. However, the applications of this modern version of the MDL have been quite rare because of computational complexity problems, i.e., for discrete data, the definition of NML involves an exponential sum, and in the case of continuous data, a multi-dimensional integral usually infeasible to evaluate or even approximate accurately. In this doctoral dissertation, we present mathematical techniques for computing NML efficiently for some model families involving discrete data. We also show how these techniques can be used to apply MDL in two practical applications: histogram density estimation and clustering of multi-dimensional data.

Co2 emissions and income trajectory in Australia: The role of technological change

This study investigates the relationship between per capita carbon dioxide (CO2) emissions and per capita GDP in Australia, while controlling for technological state as measured by multifactor productivity and export of black coal. Although technological progress seems to play a critical role in achieving long term goals of CO2 reduction and economic growth, empirical studies have often considered time trend to proxy technological change. However, as discoveries and diffusion of new technologies may not progress smoothly with time, the assumption of a deterministic technological progress may be incorrect in the long run. The use of multifactor productivity as a measure of technological state, therefore, overcomes the limitations and provides practical policy directions. This study uses recently developed bound-testing approach, which is complemented by Johansen- Juselius maximum likelihood approach and a reasonably large sample size to investigate the cointegration relationship. Both of the techniques suggest that cointegration relationship exists among the variables. The long-run and short-run coefficients of CO2 emissions function is estimated using ARDL approach. The empirical findings in the study show evidence of the existence of Environmental Kuznets Curve type relationship for per capita CO2 emissions in the Australian context. The technology as measured by the multifactor productivity, however, is not found as an influencing variable in emissionsincome trajectory.

A conditional random field-based downscaling method for assessment of climate change impact on multisite daily precipitation in the Mahanadi basin

Downscaling to station-scale hydrologic variables from large-scale atmospheric variables simulated by general circulation models (GCMs) is usually necessary to assess the hydrologic impact of climate change. This work presents CRF-downscaling, a new probabilistic downscaling method that represents the daily precipitation sequence as a conditional random field (CRF). The conditional distribution of the precipitation sequence at a site, given the daily atmospheric (large-scale) variable sequence, is modeled as a linear chain CRF. CRFs do not make assumptions on independence of observations, which gives them flexibility in using high-dimensional feature vectors. Maximum likelihood parameter estimation for the model is performed using limited memory Broyden-Fletcher-Goldfarb-Shanno (L-BFGS) optimization. Maximum a posteriori estimation is used to determine the most likely precipitation sequence for a given set of atmospheric input variables using the Viterbi algorithm. Direct classification of dry/wet days as well as precipitation amount is achieved within a single modeling framework. The model is used to project the future cumulative distribution function of precipitation. Uncertainty in precipitation prediction is addressed through a modified Viterbi algorithm that predicts the n most likely sequences. The model is applied for downscaling monsoon (June-September) daily precipitation at eight sites in the Mahanadi basin in Orissa, India, using the MIROC3.2 medium-resolution GCM. The predicted distributions at all sites show an increase in the number of wet days, and also an increase in wet day precipitation amounts. A comparison of current and future predicted probability density functions for daily precipitation shows a change in shape of the density function with decreasing probability of lower precipitation and increasing probability of higher precipitation.

Low ML-Decoding Complexity, Large Coding Gain, Full-Rate, Full-Diversity STBCs for 2 x 2 and 4 x 2 MIMO Systems

This paper deals with low maximum-likelihood (ML)-decoding complexity, full-rate and full-diversity space-time block codes (STBCs), which also offer large coding gain, for the 2 transmit antenna, 2 receive antenna (2 x 2) and the 4 transmit antenna, 2 receive antenna (4 x 2) MIMO systems. Presently, the best known STBC for the 2 2 system is the Golden code and that for the 4 x 2 system is the DjABBA code. Following the approach by Biglieri, Hong, and Viterbo, a new STBC is presented in this paper for the 2 x 2 system. This code matches the Golden code in performance and ML-decoding complexity for square QAM constellations while it has lower ML-decoding complexity with the same performance for non-rectangular QAM constellations. This code is also shown to be information-lossless and diversity-multiplexing gain (DMG) tradeoff optimal. This design procedure is then extended to the 4 x 2 system and a code, which outperforms the DjABBA code for QAM constellations with lower ML-decoding complexity, is presented. So far, the Golden code has been reported to have an ML-decoding complexity of the order of for square QAM of size. In this paper, a scheme that reduces its ML-decoding complexity to M-2 root M is presented.

A Low-Complexity Near-ML Performance Achieving Algorithm for Large MIMO Detection

In this paper, we present a low-complexity, near maximum-likelihood (ML) performance achieving detector for large MIMO systems having tens of transmit and receive antennas. Such large MIMO systems are of interest because of the high spectral efficiencies possible in such systems. The proposed detection algorithm, termed as multistage likelihood-ascent search (M-LAS) algorithm, is rooted in Hopfield neural networks, and is shown to possess excellent performance as well as complexity attributes. In terms of performance, in a 64 x 64 V-BLAST system with 4-QAM, the proposed algorithm achieves an uncoded BER of 10(-3) at an SNR of just about 1 dB away from AWGN-only SISO performance given by Q(root SNR). In terms of coded BER, with a rate-3/4 turbo code at a spectral efficiency of 96 bps/Hz the algorithm performs close to within about 4.5 dB from theoretical capacity, which is remarkable in terms of both high spectral efficiency as well as nearness to theoretical capacity. Our simulation results show that the above performance is achieved with a complexity of just O(NtNt) per symbol, where N-t and N-tau denote the number of transmit and receive antennas.

Algebraic distributed space-time codes with low ML decoding complexity

"Extended Clifford algebras" are introduced as a means to obtain low ML decoding complexity space-time block codes. Using left regular matrix representations of two specific classes of extended Clifford algebras, two systematic algebraic constructions of full diversity Distributed Space-Time Codes (DSTCs) are provided for any power of two number of relays. The left regular matrix representation has been shown to naturally result in space-time codes meeting the additional constraints required for DSTCs. The DSTCs so constructed have the salient feature of reduced Maximum Likelihood (ML) decoding complexity. In particular, the ML decoding of these codes can be performed by applying the lattice decoder algorithm on a lattice of four times lesser dimension than what is required in general. Moreover these codes have a uniform distribution of power among the relays and in time, thus leading to a low Peak to Average Power Ratio at the relays.