On the relationship between connections and the asymptotic properties of predictive distributions

In a recent paper, Komaki studied the second-order asymptotic properties of predictive distributions, using the Kullback-Leibler divergence as a loss function. He showed that estimative distributions with asymptotically efficient estimators can be improved by predictive distributions that do not belong to the model. The model is assumed to be a multidimensional curved exponential family. In this paper we generalize the result assuming as a loss function any f divergence. A relationship arises between alpha connections and optimal predictive distributions. In particular, using an alpha divergence to measure the goodness of a predictive distribution, the optimal shift of the estimate distribution is related to alpha-covariant derivatives. The expression that we obtain for the asymptotic risk is also useful to study the higher-order asymptotic properties of an estimator, in the mentioned class of loss functions.

Making better biogeographical predictions of species' distributions

1. Biogeographical models of species' distributions are essential tools for assessing impacts of changing environmental conditions on natural communities and ecosystems. Practitioners need more reliable predictions to integrate into conservation planning (e.g. reserve design and management). 2. Most models still largely ignore or inappropriately take into account important features of species' distributions, such as spatial autocorrelation, dispersal and migration, biotic and environmental interactions. Whether distributions of natural communities or ecosystems are better modelled by assembling individual species' predictions in a bottom-up approach or modelled as collective entities is another important issue. An international workshop was organized to address these issues. 3. We discuss more specifically six issues in a methodological framework for generalized regression: (i) links with ecological theory; (ii) optimal use of existing data and artificially generated data; (iii) incorporating spatial context; (iv) integrating ecological and environmental interactions; (v) assessing prediction errors and uncertainties; and (vi) predicting distributions of communities or collective properties of biodiversity. 4. Synthesis and applications. Better predictions of the effects of impacts on biological communities and ecosystems can emerge only from more robust species' distribution models and better documentation of the uncertainty associated with these models. An improved understanding of causes of species' distributions, especially at their range limits, as well as of ecological assembly rules and ecosystem functioning, is necessary if further progress is to be made. A better collaborative effort between theoretical and functional ecologists, ecological modellers and statisticians is required to reach these goals.

Mood disorders in eating disorder patients: Prevalence and chronology of ONSET.

OBJECTIVES: In a clinical population, we estimated the frequency of mood disorders among 271 patients suffering from Anorexia Nervosa (AN) and Bulimia Nervosa (BN) in comparison to a control group matched for age and gender. METHOD: The frequency of mood disorders was measured using the Mini International Neuropsychiatric Interview (MINI), DSM-IV version. RESULTS: Mood disorders were more frequent among eating disorder (ED) patients than among controls, with a global prevalence of the order of 80% for each ED group. The majority of the mood disorders comorbid with ED were depressive disorders (MDD and dysthymia). The relative chronology of onset of these disorders was equivocal, because mood disorders in some cases preceded and in others followed the onset of the eating disorders. LIMITATIONS: Our sample was characterized by patients with severe ED and high comorbidities, and thus do not represent the entire population of AN or BN. This also may have resulted in an overestimation of prevalence. CONCLUSION: Mood disorders appear significantly more frequently in patients seeking care for ED than in controls. These results have implications for the assessment and treatment of ED patients, and for the aetio-pathogenesis of these disorders.

Characterization of Probability Distributions Using the Residual Entropy Function

The present study on the characterization of probability distributions using the residual entropy function. The concept of entropy is extensively used in literature as a quantitative measure of uncertainty associated with a random phenomenon. The commonly used life time models in reliability Theory are exponential distribution, Pareto distribution, Beta distribution, Weibull distribution and gamma distribution. Several characterization theorems are obtained for the above models using reliability concepts such as failure rate, mean residual life function, vitality function, variance residual life function etc. Most of the works on characterization of distributions in the reliability context centers around the failure rate or the residual life function. The important aspect of interest in the study of entropy is that of locating distributions for which the shannon’s entropy is maximum subject to certain restrictions on the underlying random variable. The geometric vitality function and examine its properties. It is established that the geometric vitality function determines the distribution uniquely. The problem of averaging the residual entropy function is examined, and also the truncated form version of entropies of higher order are defined. In this study it is established that the residual entropy function determines the distribution uniquely and that the constancy of the same is characteristics to the geometric distribution

Invariant density for a class of initial distributions under quadratic mapping

For the discrete-time quadratic map xt+1=4xt(1-xt) the evolution equation for a class of non-uniform initial densities is obtained. It is shown that in the t to infinity limit all of them approach the invariant density for the map.

Characterization of Probability Distributions by Variance Bounds and its Applications

Department of Statistics, Cochin University of Science and Technology

Some Properties of Weighted Distributions for Truncated Random Variables

The present study gave emphasis on characterizing continuous probability distributions and its weighted versions in univariate set up. Therefore a possible work in this direction is to study the properties of weighted distributions for truncated random variables in discrete set up. The problem of extending the measures into higher dimensions as well as its weighted versions is yet to be examined. As the present study focused attention to length-biased models, the problem of studying the properties of weighted models with various other weight functions and their functional relationships is yet to be examined.

Characterizations of Life Distributions Using Conditional Expectations of Doubly (Interval) Truncated Random Variables

In this article, we study reliability measures such as geometric vitality function and conditional Shannon’s measures of uncertainty proposed by Ebrahimi (1996) and Sankaran and Gupta (1999), respectively, for the doubly (interval) truncated random variables. In survival analysis and reliability engineering, these measures play a significant role in studying the various characteristics of a system/component when it fails between two time points. The interrelationships among these uncertainty measures for various distributions are derived and proved characterization theorems arising out of them

Some Properties of Weighted Distributions in the Context of Repairable Systems

In this article we introduce some structural relationships between weighted and original variables in the context of maintainability function and reversed repair rate. Furthermore, we prove some characterization theorems for specific models such as power, exponential, Pareto II, beta, and Pearson system of distributions using the relationships between the original and weighted random variables

Properties of Equilibrium Distributions of Order n

The present work is intended to discuss various properties and reliability aspects of higher order equilibrium distributions in continuous, discrete and multivariate cases, which contribute to the study on equilibrium distributions. At first, we have to study and consolidate the existing literature on equilibrium distributions. For this we need some basic concepts in reliability. These are being discussed in the 2nd chapter, In Chapter 3, some identities connecting the failure rate functions and moments of residual life of the univariate, non-negative continuous equilibrium distributions of higher order and that of the baseline distribution are derived. These identities are then used to characterize the generalized Pareto model, mixture of exponentials and gamma distribution. An approach using the characteristic functions is also discussed with illustrations. Moreover, characterizations of ageing classes using stochastic orders has been discussed. Part of the results of this chapter has been reported in Nair and Preeth (2009). Various properties of equilibrium distributions of non-negative discrete univariate random variables are discussed in Chapter 4. Then some characterizations of the geo- metric, Waring and negative hyper-geometric distributions are presented. Moreover, the ageing properties of the original distribution and nth order equilibrium distribu- tions are compared. Part of the results of this chapter have been reported in Nair, Sankaran and Preeth (2012). Chapter 5 is a continuation of Chapter 4. Here, several conditions, in terms of stochastic orders connecting the baseline and its equilibrium distributions are derived. These conditions can be used to rede_ne certain ageing notions. Then equilibrium distributions of two random variables are compared in terms of various stochastic orders that have implications in reliability applications. In Chapter 6, we make two approaches to de_ne multivariate equilibrium distribu- tions of order n. Then various properties including characterizations of higher order equilibrium distributions are presented. Part of the results of this chapter have been reported in Nair and Preeth (2008). The Thesis is concluded in Chapter 7. A discussion on further studies on equilib- rium distributions is also made in this chapter.

A comparative analysis by means of quantum molecular similarity measures of density distributions derived from conventional ab initio and density functional methods

A procedure based on quantum molecular similarity measures (QMSM) has been used to compare electron densities obtained from conventional ab initio and density functional methodologies at their respective optimized geometries. This method has been applied to a series of small molecules which have experimentally known properties and molecular bonds of diverse degrees of ionicity and covalency. Results show that in most cases the electron densities obtained from density functional methodologies are of a similar quality than post-Hartree-Fock generalized densities. For molecules where Hartree-Fock methodology yields erroneous results, the density functional methodology is shown to yield usually more accurate densities than those provided by the second order Møller-Plesset perturbation theory

Pollen-based reconstructions of biome distributions for Australia, Southeast Asia and the Pacific (SEAPAC region) at 0,6000 and 18,000 14C yr B.P.

Aim  This paper documents reconstructions of the vegetation patterns in Australia, Southeast Asia and the Pacific (SEAPAC region) in the mid-Holocene and at the last glacial maximum (LGM). Methods  Vegetation patterns were reconstructed from pollen data using an objective biomization scheme based on plant functional types. The biomization scheme was first tested using 535 modern pollen samples from 377 sites, and then applied unchanged to fossil pollen samples dating to 6000 ± 500 or 18,000 ± 1000 14C yr bp. Results  1. Tests using surface pollen sample sites showed that the biomization scheme is capable of reproducing the modern broad-scale patterns of vegetation distribution. The north–south gradient in temperature, reflected in transitions from cool evergreen needleleaf forest in the extreme south through temperate rain forest or wet sclerophyll forest (WSFW) and into tropical forests, is well reconstructed. The transitions from xerophytic through sclerophyll woodlands and open forests to closed-canopy forests, which reflect the gradient in plant available moisture from the continental interior towards the coast, are reconstructed with less geographical precision but nevertheless the broad-scale pattern emerges. 2. Differences between the modern and mid-Holocene vegetation patterns in mainland Australia are comparatively small and reflect changes in moisture availability rather than temperature. In south-eastern Australia some sites show a shift towards more moisture-stressed vegetation in the mid-Holocene with xerophytic woods/scrub and temperate sclerophyll woodland and shrubland at sites characterized today by WSFW or warm-temperate rain forest (WTRF). However, sites in the Snowy Mountains, on the Southern Tablelands and east of the Great Dividing Range have more moisture-demanding vegetation in the mid-Holocene than today. South-western Australia was slightly drier than today. The single site in north-western Australia also shows conditions drier than today in the mid-Holocene. Changes in the tropics are also comparatively small, but the presence of WTRF and tropical deciduous broadleaf forest and woodland in the mid-Holocene, in sites occupied today by cool-temperate rain forest, indicate warmer conditions. 3. Expansion of xerophytic vegetation in the south and tropical deciduous broadleaf forest and woodland in the north indicate drier conditions across mainland Australia at the LGM. None of these changes are informative about the degree of cooling. However the evidence from the tropics, showing lowering of the treeline and forest belts, indicates that conditions were between 1 and 9 °C (depending on elevation) colder. The encroachment of tropical deciduous broadleaf forest and woodland into lowland evergreen broadleaf forest implies greater aridity. Main conclusions  This study provides the first continental-scale reconstruction of mid-Holocene and LGM vegetation patterns from Australia, Southeast Asia and the Pacific (SEAPAC region) using an objective biomization scheme. These data will provide a benchmark for evaluation of palaeoclimate simulations within the framework of the Palaeoclimate Modelling Intercomparison Project.

Predictors of onset of depression and anxiety in the year after diagnosis of breast cancer

Background Depression and anxiety are common after diagnosis of breast cancer. We examined to what extent these are recurrences of previous disorder and, controlling for this, whether shame, self-blame and low social support after diagnosis predicted onset of depression and anxiety subsequently. Method Women with primary breast cancer who had been treated surgically self-reported shame, self-blame, social support and emotional distress post-operatively. Psychiatric interview 12 months later identified those with adult lifetime episodes of major depression (MD) or generalized anxiety disorder (GAD) before diagnosis and onset over the subsequent year. Statistical analysis examined predictors of each disorder in that year. Results Of the patients, two-thirds with episodes of MD and 40% with episodes of GAD during the year after diagnosis were experiencing recurrence of previous disorder. Although low social support, self-blame and shame were each associated with both MD and GAD after diagnosis, they did not mediate the relationship of disorder after diagnosis with previous disorder. Low social support, but not shame or self-blame, predicted recurrence after controlling for previous disorder. Conclusions Anxiety and depression during the first year after diagnosis of breast cancer are often the recurrence of previous disorder. In predicting disorder following diagnosis, self-blame and shame are merely markers of previous disorder. Low social support is an independent predictor and therefore may have a causal role.

Older age of onset in child L2 acquisition can be facilitative: evidence from the acquisition of English passives by Spanish natives

We report a longitudinal comprehension study of (long) passive constructions in two native-Spanish child groups differing by age of initial exposure to L2 English (young group: 3;0-4;0 years; older group: 6;0-7;0 years); where amount of input, L2 exposure environment, and socio-economic status are controlled. Data from a forced-choice task show that both groups comprehend active sentences, not passives, initially (after 3.6 years of exposure). One year later, both groups improve, but only the older group reaches ceiling on both actives and passives. Two years from initial testing, the younger group catches up. Input alone cannot explain why the younger group takes 5 years to accomplish what the older group does in 4. We claim that some properties take longer to acquire at certain ages because language development is partially constrained by general cognitive and linguistic development (e.g. de Villiers, 2007; Long & Rothman, 2014; Paradis, 2008, 2010, 2011; Tsimpli, 2014).