Improved estimation of size-transition matrices using tag-recapture data

We derive a new method for determining size-transition matrices (STMs) that eliminates probabilities of negative growth and accounts for individual variability. STMs are an important part of size-structured models, which are used in the stock assessment of aquatic species. The elements of STMs represent the probability of growth from one size class to another, given a time step. The growth increment over this time step can be modelled with a variety of methods, but when a population construct is assumed for the underlying growth model, the resulting STM may contain entries that predict negative growth. To solve this problem, we use a maximum likelihood method that incorporates individual variability in the asymptotic length, relative age at tagging, and measurement error to obtain von Bertalanffy growth model parameter estimates. The statistical moments for the future length given an individual's previous length measurement and time at liberty are then derived. We moment match the true conditional distributions with skewed-normal distributions and use these to accurately estimate the elements of the STMs. The method is investigated with simulated tag-recapture data and tag-recapture data gathered from the Australian eastern king prawn (Melicertus plebejus).

Bayesian designs with frequentist and Bayesian error rate considerations

So far, most Phase II trials have been designed and analysed under a frequentist framework. Under this framework, a trial is designed so that the overall Type I and Type II errors of the trial are controlled at some desired levels. Recently, a number of articles have advocated the use of Bavesian designs in practice. Under a Bayesian framework, a trial is designed so that the trial stops when the posterior probability of treatment is within certain prespecified thresholds. In this article, we argue that trials under a Bayesian framework can also be designed to control frequentist error rates. We introduce a Bayesian version of Simon's well-known two-stage design to achieve this goal. We also consider two other errors, which are called Bayesian errors in this article because of their similarities to posterior probabilities. We show that our method can also control these Bayesian-type errors. We compare our method with other recent Bayesian designs in a numerical study and discuss implications of different designs on error rates. An example of a clinical trial for patients with nasopharyngeal carcinoma is used to illustrate differences of the different designs.

An optimal design for screening trials

Yao, Begg, and Livingston (1996, Biometrics 52, 992-1001) considered the optimal group size for testing a series of potentially therapeutic agents to identify a promising one as soon as possible for given error rates. The number of patients to be tested with each agent was fixed as the group size. We consider a sequential design that allows early acceptance and rejection, and we provide an optimal strategy to minimize the sample sizes (patients) required using Markov decision processes. The minimization is under the constraints of the two types (false positive and false negative) of error probabilities, with the Lagrangian multipliers corresponding to the cost parameters for the two types of errors. Numerical studies indicate that there can be a substantial reduction in the number of patients required.

Asymptotic behavior of a hierarchical system of learning automata

Learning automata arranged in a two-level hierarchy are considered. The automata operate in a stationary random environment and update their action probabilities according to the linear-reward- -penalty algorithm at each level. Unlike some hierarchical systems previously proposed, no information transfer exists from one level to another, and yet the hierarchy possesses good convergence properties. Using weak-convergence concepts it is shown that for large time and small values of parameters in the algorithm, the evolution of the optimal path probability can be represented by a diffusion whose parameters can be computed explicitly.

Overfitting Bayesian mixture models with an unknown number of components

This paper proposes solutions to three issues pertaining to the estimation of finite mixture models with an unknown number of components: the non-identifiability induced by overfitting the number of components, the mixing limitations of standard Markov Chain Monte Carlo (MCMC) sampling techniques, and the related label switching problem. An overfitting approach is used to estimate the number of components in a finite mixture model via a Zmix algorithm. Zmix provides a bridge between multidimensional samplers and test based estimation methods, whereby priors are chosen to encourage extra groups to have weights approaching zero. MCMC sampling is made possible by the implementation of prior parallel tempering, an extension of parallel tempering. Zmix can accurately estimate the number of components, posterior parameter estimates and allocation probabilities given a sufficiently large sample size. The results will reflect uncertainty in the final model and will report the range of possible candidate models and their respective estimated probabilities from a single run. Label switching is resolved with a computationally light-weight method, Zswitch, developed for overfitted mixtures by exploiting the intuitiveness of allocation-based relabelling algorithms and the precision of label-invariant loss functions. Four simulation studies are included to illustrate Zmix and Zswitch, as well as three case studies from the literature. All methods are available as part of the R package Zmix, which can currently be applied to univariate Gaussian mixture models.

Constructive Perspectives on Inductive Logic

Constructive (intuitionist, anti-realist) semantics has thus far been lacking an adequate concept of truth in infinity concerning factual (i.e., empirical, non-mathematical) sentences. One consequence of this problem is the difficulty of incorporating inductive reasoning in constructive semantics. It is not possible to formulate a notion for probable truth in infinity if there is no adequate notion of what truth in infinity is. One needs a notion of a constructive possible world based on sensory experience. Moreover, a constructive probability measure must be defined over these constructively possible empirical worlds. This study defines a particular kind of approach to the concept of truth in infinity for Rudolf Carnap's inductive logic. The new approach is based on truth in the consecutive finite domains of individuals. This concept will be given a constructive interpretation. What can be verifiably said about an empirical statement with respect to this concept of truth, will be explained, for which purpose a constructive notion of epistemic probability will be introduced. The aim of this study is also to improve Carnap's inductive logic. The study addresses the problem of justifying the use of an "inductivist" method in Carnap's lambda-continuum. A correction rule for adjusting the inductive method itself in the course of obtaining evidence will be introduced. Together with the constructive interpretation of probability, the correction rule yields positive prior probabilities for universal generalizations in infinite domains.

Leibniz on Rational Decision-Making

In this study I discuss G. W. Leibniz's (1646-1716) views on rational decision-making from the standpoint of both God and man. The Divine decision takes place within creation, as God freely chooses the best from an infinite number of possible worlds. While God's choice is based on absolutely certain knowledge, human decisions on practical matters are mostly based on uncertain knowledge. However, in many respects they could be regarded as analogous in more complicated situations. In addition to giving an overview of the divine decision-making and discussing critically the criteria God favours in his choice, I provide an account of Leibniz's views on human deliberation, which includes some new ideas. One of these concerns is the importance of estimating probabilities in making decisions one estimates both the goodness of the act itself and its consequences as far as the desired good is concerned. Another idea is related to the plurality of goods in complicated decisions and the competition this may provoke. Thirdly, heuristic models are used to sketch situations under deliberation in order to help in making the decision. Combining the views of Marcelo Dascal, Jaakko Hintikka and Simo Knuuttila, I argue that Leibniz applied two kinds of models of rational decision-making to practical controversies, often without explicating the details. The more simple, traditional pair of scales model is best suited to cases in which one has to decide for or against some option, or to distribute goods among parties and strive for a compromise. What may be of more help in more complicated deliberations is the novel vectorial model, which is an instance of the general mathematical doctrine of the calculus of variations. To illustrate this distinction, I discuss some cases in which he apparently applied these models in different kinds of situation. These examples support the view that the models had a systematic value in his theory of practical rationality.

Climate information needs of Gascoyne-Murchison pastoralists: a representative study of the Western Australian grazing industry

The Gascoyne-Murchison region of Western Australia experiences an arid to semi-arid climate with a highly variable temporal and spatial rainfall distribution. The region has around 39.2 million hectares available for pastoral lease and supports predominantly catle and sheep grazing leases. In recent years a number of climate forecasting systems have been available offering rainfall probabilities with different lead times and a forecast period; however, the extent to which these systems are capable of fulfilling the requirements of the local pastoralists is still ambiguous. Issues can range from ensuring forecasts are issued with sufficient lead time to enable key planning or decisions to be revoked or altered, to ensuring forecast language is simple and clear, to negate possible misunderstandings in interpretation. A climate research project sought to provide an objective method to determine which available forecasting systems had the greatest forecasting skill at times of the year relevant to local property management. To aid this climate research project, the study reported here was undertaken with an overall objective of exploring local pastoralists' climate information needs. We also explored how well they understand common climate forecast terms such as 'mean', median' and 'probability', and how they interpret and apply forecast information to decisions. A stratified, proportional random sampling was used for the purpose of deriving the representative sample based on rainfall-enterprise combinations. In order to provide more time for decision-making than existing operational forecasts that are issued with zero lead time, pastoralists requested that forecasts be issued for May-July and January-March with lead times counting down from 4 to 0 months. We found forecasts of between 20 and 50 mm break-of-season or follow-up rainfall were likely to influence decisions. Eighty percent of pastoralists demonstrated in a test question that they had a poor technical understanding of how to interpret the standard wording of a probabilistic median rainfall forecast. this is worthy of further research to investigate whether inappropriate management decisions are being made because the forecasts are being misunderstood. We found more than half the respondents regularly access and use weather and climate forecasts or outlook information from a range of sources and almost three-quarters considered climate information or tools useful, with preferred methods for accessing this information by email, faxback service, internet and the Department of Agriculture Western Australia's Pastoral Memo. Despite differences in enterprise types and rainfall seasonality across the region we found seasonal climate forecasting needs were relatively consistent. It became clear that providing basic training and working with pastoralists to help them understand regional climatic drivers, climate terminology and jargon, and the best ways to apply the forecasts to enhance decision-making are important to improve their use of information. Consideration could also be given to engaging a range of producers to write the climate forecasts themselves in the language they use and understand, in consultation with the scientists who prepare the forecasts.

Rainfall and streamflow response to El Niño Southern Oscillation: a case study in a semiarid catchment, Australia.

This paper aims to compare the shift in frequency distribution and skill of seasonal climate forecasting of both streamflow and rainfall in eastern Australia based on the Southern Oscillation Index (SOI) Phase system. Recent advances in seasonal forecasting of climate variables have highlighted opportunities for improving decision making in natural resources management. Forecasting of rainfall probabilities for different regions in Australia is available, but the use of similar forecasts for water resource supply has not been developed. The use of streamflow forecasts may provide better information for decision-making in irrigation supply and flow management for improved ecological outcomes. To examine the relative efficacy of seasonal forecasting of streamflow and rainfall, the shift in probability distributions and the forecast skill were evaluated using the Wilcoxon rank-sum test and the linear error in probability space (LEPS) skill score, respectively, at three river gauging stations in the Border Rivers Catchment of the Murray-Darling Basin in eastern Australia. A comparison of rainfall and streamflow distributions confirms higher statistical significance in the shift of streamflow distribution than that in rainfall distribution. Moreover, streamflow distribution showed greater skill of forecasting with 0-3 month lead time, compared to rainfall distribution.

The impact of inter-fraction set-up errors on the probability of pulmonary and cardiac complication in left-sided breast cancer patients

Purpose This study evaluated the impact of patient set-up errors on the probability of pulmonary and cardiac complications in the irradiation of left-sided breast cancer. Methods and Materials Using the CMS XiO Version 4.6 (CMS Inc., St Louis, MO) radiotherapy planning system's NTCP algorithm and the Lyman -Kutcher-Burman (LKB) model, we calculated the DVH indices for the ipsilateral lung and heart and the resultant normal tissue complication probabilities (NTCP) for radiation-induced pneumonitis and excess cardiac mortality in 12 left-sided breast cancer patients. Results Isocenter shifts in the posterior direction had the greatest effect on the lung V20, heart V25, mean and maximum doses to the lung and the heart. Dose volume histograms (DVH) results show that the ipsilateral lung V20 tolerance was exceeded in 58% of the patients after 1cm posterior shifts. Similarly, the heart V25 tolerance was exceeded after 1cm antero-posterior and left-right isocentric shifts in 70% of the patients. The baseline NTCPs for radiation-induced pneumonitis ranged from 0.73% - 3.4% with a mean value of 1.7%. The maximum reported NTCP for radiation-induced pneumonitis was 5.8% (mean 2.6%) after 1cm posterior isocentric shift. The NTCP for excess cardiac mortality were 0 % in 100% of the patients (n=12) before and after setup error simulations. Conclusions Set-up errors in left sided breast cancer patients have a statistically significant impact on the Lung NTCPs and DVH indices. However, with a central lung distance of 3cm or less (CLD <3cm), and a maximum heart distance of 1.5cm or less (MHD<1.5cm), the treatment plans could tolerate set-up errors of up to 1cm without any change in the NTCP to the heart.

A comparison of mark-recapture distance-sampling methods applied to aerial surveys of eastern grey kangaroos

Aerial surveys of kangaroos (Macropus spp.) in Queensland are used to make economically important judgements on the levels of viable commercial harvest. Previous analysis methods for aerial kangaroo surveys have used both mark-recapture methodologies and conventional distance-sampling analyses. Conventional distance sampling has the disadvantage that detection is assumed to be perfect on the transect line, while mark-recapture methods are notoriously sensitive to problems with unmodelled heterogeneity in capture probabilities. We introduce three methodologies for combining together mark-recapture and distance-sampling data, aimed at exploiting the strengths of both methodologies and overcoming the weaknesses. Of these methods, two are based on the assumption of full independence between observers in the mark-recapture component, and this appears to introduce more bias in density estimation than it resolves through allowing uncertain trackline detection. Both of these methods give lower density estimates than conventional distance sampling, indicating a clear failure of the independence assumption. The third method, termed point independence, appears to perform very well, giving credible density estimates and good properties in terms of goodness-of-fit and percentage coefficient of variation. Estimated densities of eastern grey kangaroos range from 21 to 36 individuals km-2, with estimated coefficients of variation between 11% and 14% and estimated trackline detection probabilities primarily between 0.7 and 0.9.

Modelling climatic risks of aflatoxin contamination in maize

Aflatoxins are highly carcinogenic mycotoxins produced by two fungi, Aspergillus flavus and A. parasiticus, under specific moisture and temperature conditions before harvest and/or during storage of a wide range of crops including maize. Modelling of interactions between host plant and environment during the season can enable quantification of preharvest aflatoxin risk and its potential management. A model was developed to quantify climatic risks of aflatoxin contamination in maize using principles previously used for peanuts. The model outputs an aflatoxin risk index in response to seasonal temperature and soil moisture during the maize grain filling period using the APSIM's maize module. The model performed well in simulating climatic risk of aflatoxin contamination in maize as indicated by a significant R2 (P ≤ 0.01) between aflatoxin risk index and the measured aflatoxin B1 in crop samples, which was 0.69 for a range of rainfed Australian locations and 0.62 when irrigated locations were also included in the analysis. The model was further applied to determine probabilities of exceeding a given aflatoxin risk in four non-irrigated maize growing locations of Queensland using 106 years of historical climatic data. Locations with both dry and hot climates had a much higher probability of higher aflatoxin risk compared with locations having either dry or hot conditions alone. Scenario analysis suggested that under non-irrigated conditions the risk of aflatoxin contamination could be minimised by adjusting sowing time or selecting an appropriate hybrid to better match the grain filling period to coincide with lower temperature and water stress conditions.

Summative evaluation of climate application activities with pastoralists in western Queensland

Survey methods were engaged to measure the change in use and knowledge of climate information by pastoralists in western Queensland. The initial mail survey was undertaken in 2000-01 (n=43) and provided a useful benchmark of pastoralists climate knowledge. Two years of climate applications activities were completed and clients were re-surveyed in 2003 (n=49) to measure the change in knowledge and assess the effectiveness of the climate applications activities. Two methods were used to assess changes in client knowledge, viz., self-assessment and test questions. We found that the use of seasonal climate forecasts in decision making increased from 36% in 2001 (n=42) to 51% in 2003 (n=49) (P=0.07). The self-assessment technique was unsatisfactory as a measure of changing knowledge over short periods (1-3 years), but the test question technique was successful and indicated an improvement in climate knowledge among respondents. The increased levels of use of seasonal climate forecasts in management and improved knowledge was partly attributed to the climate applications activities of the project. Further, those who used seasonal forecasting (n=25) didn't understand key components of forecasts (e.g. probability, median) better than those who didn't use seasonal forecasts (n=24) (P>0.05). This identifies the potential for misunderstanding and misinterpretation of forecasts among users and highlights the need for providers of forecasts to understand the difficulties and prepare simply written descriptions of forecasts and disseminate these with the maps showing probabilities. The most preferred means of accessing climate information were internet, email, 'The Season Ahead' newsletter and newspaper. The least preferred were direct contact with extension officers and attending field days and group meetings. Eighty-six percent of respondents used the internet and 67% used ADSL broadband internet (April 2003). Despite these findings, extension officers play a key role in preparing and publishing the information on the web, in emails and newsletters. We also believe that direct contact with extension officers trained in climate applications is desirable in workshop-like events to improve knowledge of the difficult concepts underpinning climate forecasts, which may then stimulate further adoption.

Probabilistic forecasts of the onset of the north Australian wet season

The amount and timing of early wet-season rainfall are important for the management of many agricultural industries in north Australia. With this in mind, a wet-season onset date is defined based on the accumulation of rainfall to a predefined threshold, starting from 1 September, for each square of a 1° gridded analysis of daily rainfall across the region. Consistent with earlier studies, the interannual variability of the onset dates is shown to be well related to the immediately preceding July-August Southern Oscillation index (SOI). Based on this relationship, a forecast method using logistic regression is developed to predict the probability that onset will occur later than the climatological mean date. This method is expanded to also predict the probabilities that onset will be later than any of a range of threshold dates around the climatological mean. When assessed using cross-validated hindcasts, the skill of the predictions exceeds that of climatological forecasts in the majority of locations in north Australia, especially in the Top End region, Cape York, and central Queensland. At times of strong anomalies in the July-August SOI, the forecasts are reliably emphatic. Furthermore, predictions using tropical Pacific sea surface temperatures (SSTs) as the predictor are also tested. While short-lead (July-August predictor) forecasts are more skillful using the SOI, long-lead (May-June predictor) forecasts are more skillful using Pacific SSTs, indicative of the longer-term memory present in the ocean.

Self-rating scales in the assessment of current and childhood symptoms of attention deficit hyperactivity disorder in adults

Objective: Attention deficit hyperactivity disorder (ADHD) is a life-long condition, but because of its historical status as a self-remitting disorder of childhood, empirically validated and reliable methods for the assessment of adults are scarce. In this study, the validity and reliability of the Wender Utah Rating Scale (WURS) and the Adult Problem Questionnaire (APQ), which survey childhood and current symptoms of ADHD, respectively, were studied in a Finnish sample. Methods: The self-rating scales were administered to adults with an ADHD diagnosis (n = 38), healthy control participants (n = 41), and adults diagnosed with dyslexia (n = 37). Items of the self-rating scales were subjected to factor analyses, after which the reliability and discriminatory power of the subscales, derived from the factors, were examined. The effects of group and gender on the subscales of both rating scales were studied. Additionally, the effect of age on the subscales of the WURS was investigated. Finally, the diagnostic accuracy of the total scores was studied. Results: On the basis of the factor analyses, a four-factor structure for the WURS and five-factor structure for the APQ had the best fit to the data. All of the subscales of the APQ and three of the WURS achieved sufficient reliability. The ADHD group had the highest scores on all of the subscales of the APQ, whereas two of the subscales of the WURS did not statistically differ between the ADHD and the Dyslexia group. None of the subscales of the WURS or the APQ was associated with the participant's gender. However, one subscale of the WURS describing dysthymia was positively correlated with the participant's age. With the WURS, the probability of a correct positive classification was .59 in the current sample and .21 when the relatively low prevalence of adult ADHD was taken into account. The probabilities of correct positive classifications with the APQ were .71 and .23, respectively. Conclusions: The WURS and the APQ can provide accurate and reliable information of childhood and adult ADHD symptoms, given some important constraints. Classifications made on the basis of the total scores are reliable predictors of ADHD diagnosis only in populations with a high proportion of ADHD and a low proportion of other similar disorders. The subscale scores can provide detailed information of an individual's symptoms if the characteristics and limitations of each domain are taken into account. Improvements are suggested for two subscales of the WURS.