A Bayesian A-optimal and model robust design criterion

Summary . Suppose that the true model underlying a set of data is one of a finite set of candidate models, and that parameter estimation for this model is of primary interest. With this goal, optimal design must depend on a loss function across all possible models. A common method that accounts for model uncertainty is to average the loss over all models; this is the basis of what is known as Läuter's criterion. We generalize Läuter's criterion and show that it can be placed in a Bayesian decision theoretic framework, by extending the definition of Bayesian A‐optimality. We use this generalized A‐optimality to find optimal design points in an environmental safety setting. In estimating the smallest detectable trace limit in a water contamination problem, we obtain optimal designs that are quite different from those suggested by standard A‐optimality.     

A generalized discriminant rule when training population and test population differ on their descriptive parameters

Standard discriminant analysis methods make the assumption that both the labeled sample used to estimate the discriminant rule and the nonlabeled sample on which this rule is applied arise from the same population. In this work, we consider the case where the two populations are slightly different. In the multinormal context, we establish that both populations are linked through linear mapping. Estimation of the nonlabeled sample discriminant rule is then obtained by estimating parameters of this linear relationship. Several models describing this relationship are proposed and associated estimated parameters are given. An experimental illustration is also provided in which sex of birds that differ morphometrically over their geographical range is to be deterrmined and a comparison with the standard allocation rule is performed. Extension to a partially labeled sample is also discussed.     

Latent class model diagnosis

In many areas of medical research, such as psychiatry and gerontology, latent class variables are used to classify individuals into disease categories, often with the intention of hierarchical modeling. Problems arise when it is not clear how many disease classes are appropriate, creating a need for model selection and diagnostic techniques. Previous work has shown that the Pearson chi 2 statistic and the log-likelihood ratio G2 statistic are not valid test statistics for evaluating latent class models. Other methods, such as information criteria, provide decision rules without providing explicit information about where discrepancies occur between a model and the data. Identifiability issues further complicate these problems. This paper develops procedures for assessing Markov chain Monte Carlo convergence and model diagnosis and for selecting the number of categories for the latent variable based on evidence in the data using Markov chain Monte Carlo techniques. Simulations and a psychiatric example are presented to demonstrate the effective use of these methods.     

A generic model of electron transport in mitochondria

In this paper, a simplified, generic model of mitochondrial metabolism is explored. In particular the following question is addressed: To what extent are phenomena observed in experiments and simulations of mitochondrial metabolism generic, in the sense that they must occur in all models with this basic structure? Of particular interest are the electron transport chain and oxidative phosphorylation, and how flux through the system and the redox states of intermediates respond to physiologically important stimuli. These stimuli include changes in substrate supply (NADH/FADH(2)), in oxygenation, and in membrane proton gradient/ATP demand. Analytical techniques are used to show that certain experimentally observed effects must occur in the generic model. These include the responses of both flux and redox states to changed substrate and oxygen concentrations. At the same time other effects, such as the responses of redox states to changes in proton gradient, are dependent on the details of the model, and are not common to every model with the same basic structure. The phenomenon of saturation in response to large inputs is also discussed.     

The structure and phase behaviour of alpha-tocopherol-rich domains in 1-palmitoyl-2-oleoyl-phosphatidylethanolamine

The effect of alpha-tocopherol on the structure and thermotropic phase behaviour of 1-palmitoyl-2-oleoyl-phosphatidylethanolamine dispersed in excess water was examined by synchrotron X-ray diffraction and differential scanning calorimetry. Small- and wide-angle X-ray scattering intensity profiles were recorded from mixed dispersions containing up to 20 mol% alpha-tocopherol during temperature scans over the range 10-75 degrees C. These showed that a domain enriched in alpha-tocopherol phase separated from pure phospholipid in the mixture. This domain tends to have inverted hexagonal structure which coexists with phospholipid bilayers depleted of alpha-tocopherol. The scattering intensity and dimensions of the phase are dependent on the temperature and proportion of alpha-tocopherol in the mixture. Phase separations were also manifest in calorimetric scans of the mixed dispersions evidenced from the appearance of multiple peaks at temperatures corresponding to transitions observed in the X-ray scattering experiments. The effect of alpha-tocopherol in the range 0-20 mol% on the phase behaviour and structure of the phospholipid as observed from the X-ray scattering and calorimetric results have been used to construct a partial phase diagram of the mixture in the temperature range 10-75 degrees C. This shows that alpha-tocopherol has a marked tendency to partition from bilayers of the phospholipid to form an enriched domain in which the phospholipid assumes a hexagonal-II structure.     

Homogeneity/Heterogeneity Hypotheses for Standardized Mortality Ratios Based on Minimum Power‐divergence Estimators

This paper analyzes the power divergence estimators when homogeneity/heterogeneity hypotheses among standardized mortality ratios (SMRs) are taken into account. A Monte Carlo study shows that when the standard mortality rate is not external, that is it is estimated from the sample data, these estimators have a good performance even for small sample sets and in particular the minimum chi‐square estimators have a better behavior compared to the classical maximum likelihood estimators. In order to make decisions under homogeneity/heterogeneity hypotheses of SMRs we propose some test‐statistics which consider the minimum power divergence estimators. Through a numerical example focused on SMRs of melanoma mortality ratios in different regions of the US, a homogeneity/heterogeneity study is illustrated.