Phenotypic evolution studied by layered stochastic differential equations

Time series of cell size evolution in unicellular marine algae (division Haptophyta; Coccolithus lineage), covering 57 million years, are studied by a system of linear stochastic differential equations of hierarchical structure. The data consists of size measurements of fossilized calcite platelets (coccoliths) that cover the living cell, found in deep-sea sediment cores from six sites in the world oceans and dated to irregular points in time. To accommodate biological theory of populations tracking their fitness optima, and to allow potentially interpretable correlations in time and space, the model framework allows for an upper layer of partially observed site-specific population means, a layer of site-specific theoretical fitness optima and a bottom layer representing environmental and ecological processes. While the modeled process has many components, it is Gaussian and analytically tractable. A total of 710 model specifications within this framework are compared and inference is drawn with respect to model structure, evolutionary speed and the effect of global temperature.Comment: Published in at http://dx.doi.org/10.1214/12-AOAS559 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org

Likelihood-based inference for clustered line transect data

Abstract The uncertainty in estimation of spatial animal density from line transect surveys depends on the degree of spatial clustering in the animal population. To quantify the clustering we model line transect data as independent thinnings of spatial shot-noise Cox processes. Likelihood-based inference is implemented using Markov chain Monte Carlo (MCMC) methods to obtain efficient estimates of spatial clustering parameters. Uncertainty is addressed using parametric bootstrap or by consideration of posterior distributions in a Bayesian setting. 1 Maximum likelihood estimation and Bayesian inference are compared in an example concerning minke whales in the northeast Atlantic

The engine of fertility influencedby interbirth employment?

The decline in fertility is often related to the increased labor force participation among married women. This article discusses the relationship between fertility and employment by using a dynamic methodology of life-course analysis based on time series data. An important question in the article is whether the probability of having a child is influenced by employment. We emphasize the probability of a second birth, however we also give some attention to the third birth

Confidence is epistemic probability for empirical science

In its orthodoxy standard frequentist statistics deals only with aleatory probability, suppressing the intuitive epistemic probability representing inferential uncertainty. Confidence distributions, which are posterior distributions not based on any Bayesian priors, are discussed in nontechnical terms, with emphasis on the confidence curve. The correspondence between confidence curves and likelihoods allows independent confidence curves and confidence intervals to be integrated. Confidence and (serious) p-values are interpreted as epistemic probabilities, which do not fully follow ordinary probability calculus. Dimension reduction and other operations might be done on the likelihood related to the confidence curve. Confidence distributions and objective Bayes have much in common

Integrative fish stock assessment by frequentist methods: confidence distributions and likelihoods for bowhead whales

Frequentist concepts of confidence distribution, reduced likelihood and likelihood synthesis are presented as tools for integrative statistical analysis, leading to distributional inference. Bias correction, often achieved by simulations, is emphasised. The methods are illustrated on data concerning bowhead whales off Alaska, and they are briefly compared with Bayesian methods.No disponibl

AALBORG UNIVERSITY

Likelihood-based inference for clustered line transect data b