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The problem of statistical calibration of a measuring instrument can be framed both in a statistical context as well as in an engineering context. In the first, the problem is dealt with by distinguishing between the ‘classical’ approach and the ‘inverse’ regression approach. Both of these models are static models and are used to estimate exact measurements from measurements that are affected by error. In the engineering context, the variables of interest are considered to be taken at the time at which you observe it. The Bayesian time series analysis method of Dynamic Linear Models can be used to monitor the evolution of the measures, thus introducing adynamicapproach to statistical calibration. The research presented employs a new approach to performing statistical calibration. A simulation study in the context of microwave radiometry is conducted that compares the dynamic model to traditional static frequentist and Bayesian approaches. The focus of the study is to understand how well thedynamic statistical calibrationmethod performs under various signal-to-noise ratios,r. [ABSTRACT FROM PUBLISHER]

Bayesian analysis often requires the researcher to employ Markov Chain Monte Carlo (MCMC) techniques to draw samples from a posterior distribution which in turn is used to make inferences. Currently, several approaches to determine convergence of the chain as well as sensitivities of the resulting inferences have been developed. This work develops a Hellinger distance approach to MCMC diagnostics. An approximation to the Hellinger distance between two distributionsfandgbased on sampling is introduced. This approximation is studied via simulation to determine the accuracy. A criterion for using this Hellinger distance for determining chain convergence is proposed as well as a criterion for sensitivity studies. These criteria are illustrated using a dataset concerning theAnguilla australis, an eel native to New Zealand. [ABSTRACT FROM PUBLISHER]

This paper introduces a framework for incorporating uncertainty in water supply system models that uses Bayesian statistics and mixed-integer programming. The output of the framework includes the most probable least cost solution, the probability of feasibility for a given solution, component probabilities for each decision, and a distribution of the optimal objective function value. The method is applied to the problem of developing a water supply system design for Israel, Jordan, and the Palestinian territories. The method allows decision makers to evaluate various alternatives for a water supply plan that incorporates uncertainties in future demand and costs. The design of a water supply plan is a concern with properties that are distinct from traditional approaches to the design of water distribution systems; namely, local engineering decisions concerning pipe diameters and water pressure are not explicitly modeled, but large-scale decisions concerning the construction of water conveyances (pipes, canals, and tunnels) and sources (desalination plants) are the focus in the model. [ABSTRACT FROM AUTHOR]

Understanding the determinants of species' distributions and abundances is a central theme in ecology. The development of statistical models to achieve this has a long history and the notion that the model should closely reflect underlying scientific understanding has encouraged ecologists to adopt complex statistical methods as they arise. In this paper we describe a Bayesian hierarchical model that reflects a conceptual ecological model of multi-scaled environmental determinants of riverine fish species' distributions and abundances. We illustrate this with distribution and abundance data of a small-bodied fish species, the Empire gudgeon Hypseleotris galii, in the Mary and Albert Rivers, Queensland, Australia. Specifically, the model sought to address; 1) the extent that landscape-scale abiotic variables can explain the species' distribution compared to local-scale variables, 2) how local-scale abiotic variables can explain species' abundances, and 3) how are these local-scale relationships mediated by landscape-scale variables. Overall, the model accounted for around 60% of variation in the distribution and abundance of H. galii. The findings show that the landscape-scale variables explain much of the distribution of the species; however, there was considerable improvement in estimating the species' distribution with the addition of local-scale variables. There were many strong relationships between abundance and local-scale abiotic variables; however, several of these relationships were mediated by some of the landscape-scale variables. The extent of spatial autocorrelation in the data was relatively low compared to the distances among sampling reaches. Our findings exemplify that Bayesian statistical modelling provides a robust framework for statistical modelling that reflects our ecological understanding. This allows ecologists to address a range of ecological questions with a single unified probability model rather than a series of disconnected analyses. [ABSTRACT FROM AUTHOR]

Bayesian inclusion probabilities have become a popular tool for variable assessment. From a frequentist perspective, it is often difficult to evaluate these probabilities as typically no Type I error rates are considered, neither are any explorations of power of the methods given. This paper considers how a frequentist may evaluate Bayesian inclusion probabilities for screening predictors. This evaluation looks at both unrestricted and restricted model spaces and develops a framework which a frequentist can utilize inclusion probabilities that preserve Type I error rates. Furthermore, this framework is applied to an analysis of the Arabidopsis thaliana with respect to determining quantitative trait loci associated with cotelydon opening angle. [ABSTRACT FROM AUTHOR]

Abstract: Diameter distributions of loblolly pine trees (Pinus taeda L.) were derived using Bayesian methods. The Bayesian derived distributions were compared to traditional maximum likelihood techniques for estimating diameter distributions. The data for this study come from a planting density study established in 1983 at four locations in Virginia and North Carolina. Results of the Bayesian analysis show that different distributional forms had the highest posterior probability at different ages for the diameter distributions. Standard goodness-of-fit statistics for the maximum likelihood estimates did not consistently recommend a distribution for the empirical data. Further, there were cases where no distribution was chosen from the candidate distributions based on the goodness-of-fit statistics. The lack of a clear distribution that fits over the range of ages for the diameter data suggests that a Bayesian model averaging technique would be beneficial for deriving tree diameter distributions with probability proportional to the posterior distribution. A simulation study was conducted to compare the goodness-of-fit statistics from the averaged distributional model and other candidate distributions. Results indicated that the averaged distribution had superior goodness-of-fit values over the candidate models; the exception being when the candidate distribution was an exact fit to the data. [Copyright &y& Elsevier]