Approximating Probability Densities by Iterated Laplace Approximations

The Laplace approximation is an old, but frequently used method to approximate integrals for Bayesian calculations. In this paper we develop an extension of the Laplace approximation, by applying it iteratively to the residual, i.e., the difference between the current approximation and the true function. The final approximation is thus a linear combination of multivariate normal densities, where the coefficients are chosen to achieve a good fit to the target distribution. We illustrate on real and artificial examples that the proposed procedure is a computationally efficient alternative to current approaches for approximation of multivariate probability densities. The R-package iterLap implementing the methods described in this article is available from the CRAN servers.Comment: to appear in Journal of Computational and Graphical Statistics, http://pubs.amstat.org/loi/jcg

The AdMit Package

This short note presents the R package AdMit which provides flexible functions to approximate a certain target distribution and it provides an efficient sample of random draws from it, given only a kernel of the target density function. The estimation procedure is fully automatic and thus avoids the time-consuming anddifficult task of tuning a sampling algorithm. To illustrate the use of the package, we apply the AdMit methodology to a bivariate bimodal distribution. We describe the use of the functions provided by the package and document the ability and relevance of the methodology to reproduce the shape of non-elliptical distributions.importance sampling;R software;Bayesian;adaptive mixture;student-t distribution;independence chain Metropolis-Hasting algorithm

Adaptive mixture of Student-t distributions as a flexible candidate distribution for efficient simulation: the R package AdMit

textabstractThis paper presents the R package AdMit which provides flexible functions to approximate a certain target distribution and to efficiently generate a sample of random draws from it, given only a kernel of the target density function. The core algorithm consists of the function AdMit which fits an adaptive mixture of Student-t distributions to the density of interest. Then, importance sampling or the independence chain Metropolis-Hastings algorithm is used to obtain quantities of interest for the target density, using the fitted mixture as the importance or candidate density. The estimation procedure is fully automatic and thus avoids the time-consuming and difficult task of tuning a sampling algorithm. The relevance of the package is shown in two examples. The first aims at illustrating in detail the use of the functions provided by the package in a bivariate bimodal distribution. The second shows the relevance of the adaptive mixture procedure through the Bayesian estimation of a mixture of ARCH model fitted to foreign exchange log-returns data. The methodology is compared to standard cases of importance sampling and the Metropolis-Hastings algorithm using a naive candidate and with the Griddy-Gibbs approach

Evolutionary approaches to signal decomposition in an application service management system

The increased demand for autonomous control in enterprise information systems has generated interest on efficient global search methods for multivariate datasets in order to search for original elements in time-series patterns, and build causal models of systems interactions, utilization dependencies, and performance characteristics. In this context, activity signals deconvolution is a necessary step to achieve effective adaptive control in Application Service Management. The paper investigates the potential of population-based metaheuristic algorithms, particularly variants of particle swarm, genetic algorithms and differential evolution methods, for activity signals deconvolution when the application performance model is unknown a priori. In our approach, the Application Service Management System is treated as a black- or grey-box, and the activity signals deconvolution is formulated as a search problem, decomposing time-series that outline relations between action signals and utilization-execution time of resources. Experiments are conducted using a queue-based computing system model as a test-bed under different load conditions and search configurations. Special attention was put on high-dimensional scenarios, testing effectiveness for large-scale multivariate data analyses that can obtain a near-optimal signal decomposition solution in a short time. The experimental results reveal benefits, qualities and drawbacks of the various metaheuristic strategies selected for a given signal deconvolution problem, and confirm the potential of evolutionary-type search to effectively explore the search space even in high-dimensional cases. The approach and the algorithms investigated can be useful in support of human administrators, or in enhancing the effectiveness of feature extraction schemes that feed decision blocks of autonomous controllers

Environmental and Parental Influences on Offspring Health and Growth in Great Tits (Parus major)

PMCID: PMC3728352This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited

The design and function of birds’ nests

All birds construct nests in which to lay eggs and/or raise offspring. Traditionally, it was thought that natural selection and the requirement to minimize the risk of predation determined the design of completed nests. However, it is becoming increasingly apparent that sexual selection also influences nest design. This is an important development as while species such as bowerbirds build structures that are extended phenotypic signals whose sole purpose is to attract a mate, nests contain eggs and/or offspring, thereby suggesting a direct tradeoff between the conflicting requirements of natural and sexual selection. Nest design also varies adaptively in order to both minimize the detrimental effects of parasites and to create a suitable microclimate for parents and developing offspring in relation to predictable variation in environmental conditions. Our understanding of the design and function of birds’ nests has increased considerably in recent years, and the evidence suggests that nests have four nonmutually exclusive functions. Consequently, we conclude that the design of birds’ nests is far more sophisticated than previously realized and that nests are multifunctional structures that have important fitness consequences for the builder/s

No Evidence for a Trade-Off between Reproductive Investment and Immunity in a Rodent

Life history theory assumes there are trade-offs between competing functions such as reproduction and immunity. Although well studied in birds, studies of the trade-offs between reproduction and immunity in small mammals are scarce. Here we examined whether reduced immunity is a consequence of reproductive effort in lactating Brandt's voles (Lasiopodomys brandtii). Specifically, we tested the effects of lactation on immune function (Experiment I). The results showed that food intake and resting metabolic rate (RMR) were higher in lactating voles (6≤ litter size ≤8) than that in non-reproductive voles. Contrary to our expectation, lactating voles also had higher levels of serum total Immunoglobulin G (IgG) and anti-keyhole limpet hemocyanin (KLH) IgG and no change in phytohemagglutinin (PHA) response and anti-KLH Immunoglobulin M (IgM) compared with non-reproductive voles, suggesting improved rather than reduced immune function. To further test the effect of differences in reproductive investment on immunity, we compared the responses between natural large (n≥8) and small litter size (n≤6) (Experiment II) and manipulated large (11–13) and small litter size (2–3) (Experiment III). During peak lactation, acquired immunity (PHA response, anti-KLH IgG and anti-KLH IgM) was not significantly different between voles raising large or small litters in both experiments, despite the measured difference in reproductive investment (greater litter size, litter mass, RMR and food intake in the voles raising larger litters). Total IgG was higher in voles with natural large litter size than those with natural small litter size, but decreased in the enlarged litter size group compared with control and reduced group. Our results showed that immune function is not suppressed to compensate the high energy demands during lactation in Brandt's voles and contrasting the situation in birds, is unlikely to be an important aspect mediating the trade-off between reproduction and survival

The impact of personality, morphotype and shore height on temperature-mediated behavioural responses in the beadlet anemone<i>Actinia equina</i>

Between-individual variation in behavioural phenotype, termed personality, is an important determinant of how populations cope with acute environmental fluctuation related to climate change. Personality in the beadlet sea anemone Actinia equina is linked to genetically distinct morphotypes, which are associated with different heights on the shore. In the intertidal zone, high-shore environments experience more environmental fluctuation due to longer periods of exposure, and animals adapted to live in these environments are predicted to deal more effectively with environmental perturbation than their low-shore counterparts. We collected beadlet anemones of two different morphotypes from three different shore heights. We investigated variation in two behaviours at three different temperatures and in a temporal control treatment where the temperature was not changed: startle response time, the time it took an anemone to re-extend its tentacles after a threatening stimulus, and immersion response time, the time to re-extend tentacles after simulated tidal immersion. These behaviours reflect risk-taking and allow individuals to be categorized as bold, shy or intermediate based upon response times. Both behaviours showed significant changes as the temperature increased. For immersion response, the morphotype associated with the low-shore-lengthened response times at high temperatures. For startle response, all animals lengthened their response times at high temperatures but animals collected from the low-shore lengthened theirs to the greatest degree. At the individual level, although control individuals exhibited temporal changes in their response times, a clear effect of temperature was present in both behaviours. Shy and bold individuals became more intermediate at higher temperatures in immersion response (this effect was present to a lesser degree in control individuals), while intermediate individuals raised their response times at higher temperatures for startle response. Given that prolonged tentacle retraction reduces foraging opportunities and can negatively impact respiratory efficiency, our data suggest that some individuals within a single population of A. equina, particularly those associated with the lower shore, may exhibit less effective behavioural responses to temperature shifts than others. These findings demonstrate that acute temperature changes influence risk-taking, and could have profound short and long-term implications for survival in the face of climate change