On two conjectures about perturbations of the stochastic growth rate

The stochastic growth rate describes long-run growth of a population that lives in a fluctuating environment. Perturbation analysis of the stochastic growth rate provides crucial information for population managers, ecologists and evolutionary biologists. This analysis quantifies the response of the stochastic growth rate to changes in demographic parameters. A form of this analysis deals with changes that only occur in some environmental states. Caswell put forth two conjectures about environment-specific perturbations of the stochastic growth rate. The conjectures link the stationary distribution of the stochastic environmental process with the magnitude of some environment-specific perturbations. This note disproves one conjecture and proves the other.     

Discrimination of AR,MA and ARMA time series models

The problem of discrimination between two stationary ARMA time series models is considered, and in particular AR(p), MA(p), ARMA(1,1) models. The discriminant based on the likelihood ration leads to a quadratic form that is generally too complicated to evaluated explicitly. The discriminant can be expressed approximately as a linear combination of independent chi–squared random varianles each with one degree of freedom, the coefficients, of which are eigenvalues of cumbersome matrices. An analytical solution which gives the coefficients approximately is suggested.     

Nonparametric Estimation of the Number of Drug Users in Hong Kong Using Repeated Multiple Lists

We update a previous approach to the estimation of the size of an open population when there are multiple lists at each time point. Our motivation is 35 years of longitudinal data on the detection of drug users by the Central Registry of Drug Abuse in Hong Kong. We develop a two‐stage smoothing spline approach. This gives a flexible and easily implemented alternative to the previous method which was based on kernel smoothing. The new method retains the property of reducing the variability of the individual estimates at each time point. We evaluate the new method by means of a simulation study that includes an examination of the effects of variable selection. The new method is then applied to data collected by the Central Registry of Drug Abuse. The parameter estimates obtained are compared with the well known Jolly–Seber estimates based on single capture methods.     

Some applications,properties and conjectures for higher order cumulants of a markovian stepping-stone model

This paper investigates certain tridiagonal coefficient matrices from linear differential equations for the joint cumulants of a Markovian stepping-stone model. The model is used to describe the dynamics of insect population growth, and is illustrated with an application to the spread of Africanized honey bees. The coefficient matrices are shown to have certain structure. A conjecture concerning their eigenvalues is proven for a special case of interest, and is also investigated numerically and by symbolic mathematical analysis.     

Variance estimation for measures of change in probability sampling

Variance estimation of changes requires estimates of variances and covariances that would be relatively straightforward to make if the sample remained the same from one wave to the next, but this is rarely the case in practice as successive waves are usually different overlapping samples. The author proposes a design‐based estimator for covariance matrices that is adapted to this situation. Under certain conditions, he shows that his approach yields non‐negative definite estimates for covariance matrices and therefore positive variance estimates for a large class of measures of change.     

NONPARAMETRIC METHOD FOR ESTIMATING THE SIZE OF AN OPEN POPULATION USING MARGINAL DATA FROM REPEATED MULTIPLE LISTS

Kernel smoothing methods are used to extend the Poisson log‐linear approach to the estimation of the size of population using multiple lists to an open population when the multiple lists are recorded at each time point. The data is marginal as only the lists at each time point are available and the transitions of individuals between lists at different time points are not observable. Our analysis is motivated by and applied to data on the number of drug addicts in the Hong Kong Special Administrative Region.     

中国经济增长路径中稳定状态推移的政策模拟 ——基于拉姆齐模型的实证研究

 本文基于拉姆齐模型的动态分析框架，借助于对其中若干重要参数的分析，对中国经济增长中的稳定状态及其推移问题进行了实证研究；并利用研究结论对中国经济增长的最优路径进行了模拟。初步结论为：①中国经济增长路径中存在稳定状态且随其参变量的变化而移动；②此稳定状态可以通过政策优化参数而向后推移；③可调控参数分别为消费跨期替代弹性、人均消费增长率、资本份额、技术进步速率、社会平均折旧率、人口自然增长率。     

A UNIFIED FRAMEWORK FOR MODELLING WILDLIFE POPULATION DYNAMICS†

This paper proposes a unified framework for defining and fitting stochastic, discrete‐time, discrete‐stage population dynamics models. The biological system is described by a state‐space model, where the true but unknown state of the population is modelled by a state process, and this is linked to survey data by an observation process. All sources of uncertainty in the inputs, including uncertainty about model specification, are readily incorporated. The paper shows how the state process can be represented as a generalization of the standard Leslie or Lefkovitch matrix. By dividing the state process into subprocesses, complex models can be constructed from manageable building blocks. The paper illustrates the approach with a model of the British grey seal metapopulation, using sequential importance sampling with kernel smoothing to fit the model.     

ULM,a software for conservation and evolutionary biologists

Matrix models for population dynamics have recently been studied intensively and have many applications to theoretical and applied problems (conservation, management). The computer program ULM (Unified Life Models) collects a good part of the actual knowledge on the subject. It is a powerful tool to study the life cycle of species and meta-populations. In the general framework of discrete dynamical systems and symbolic computation, simple commands and convenient graphics are provided to assist the biologist. The main features of the program are shown through detailed examples: a simple model of a starling population life cycle is first presented leading to basic concepts (growth rates, stable age distribution, sensitivities); the same model is used to study competing strategies in a varying environment (extinction probabilities, stochastic sensitivities); a meta-population model with migrations is then presented; some results on migration strategies and evolutionary stable strategies are eventually proposed.     

All Invariant Moments of the Wishart Distribution

Abstract.  In this paper, we compute moments of a Wishart matrix variate U of the form E ( Q ( U )) where Q ( u ) is a polynomial with respect to the entries of the symmetric matrix u , invariant in the sense that it depends only on the eigenvalues of the matrix u . This gives us in particular the expected value of any power of the Wishart matrix U or its inverse U ^{− 1}. For our proofs, we do not rely on traditional combinatorial methods but rather on the interplay between two bases of the space of invariant polynomials in U . This means that all moments can be obtained through the multiplication of three matrices with known entries. Practically, the moments are obtained by computer with an extremely simple Maple program.     

Inference of Seasonal Long‐memory Time Series with Measurement Error

We consider the Whittle likelihood estimation of seasonal autoregressive fractionally integrated moving‐average models in the presence of an additional measurement error and show that the spectral maximum Whittle likelihood estimator is asymptotically normal. We illustrate by simulation that ignoring measurement errors may result in incorrect inference. Hence, it is pertinent to test for the presence of measurement errors, which we do by developing a likelihood ratio (LR) test within the framework of Whittle likelihood. We derive the non‐standard asymptotic null distribution of this LR test and the limiting distribution of LR test under a sequence of local alternatives. Because in practice, we do not know the order of the seasonal autoregressive fractionally integrated moving‐average model, we consider three modifications of the LR test that takes model uncertainty into account. We study the finite sample properties of the size and the power of the LR test and its modifications. The efficacy of the proposed approach is illustrated by a real‐life example.     

Design optimisation for pharmacokinetic modeling of a cocktail of phenotyping drugs

Our paper proposes a methodological strategy to select optimal sampling designs for phenotyping studies including a cocktail of drugs. A cocktail approach is of high interest to determine the simultaneous activity of enzymes responsible for drug metabolism and pharmacokinetics, therefore useful in anticipating drug–drug interactions and in personalized medicine. Phenotyping indexes, which are area under the concentration‐time curves, can be derived from a few samples using nonlinear mixed effect models and maximum a posteriori estimation. Because of clinical constraints in phenotyping studies, the number of samples that can be collected in individuals is limited and the sampling times must be as flexible as possible. Therefore to optimize joint design for several drugs (i.e., to determine a compromise between informative times that best characterize each drug's kinetics), we proposed to use a compound optimality criterion based on the expected population Fisher information matrix in nonlinear mixed effect models. This criterion allows weighting different models, which might be useful to take into account the importance accorded to each target in a phenotyping test. We also computed windows around the optimal times based on recursive random sampling and Monte‐Carlo simulation while maintaining a reasonable level of efficiency for parameter estimation. We illustrated this strategy for two drugs often included in phenotyping cocktails, midazolam (probe for CYP3A) and digoxin (P‐glycoprotein), based on the data of a previous study, and were able to find a sparse and flexible design. The obtained design was evaluated by clinical trial simulations and shown to be efficient for the estimation of population and individual parameters. Copyright © 2015 John Wiley & Sons, Ltd.     

Shrinkage tuning parameter selection in precision matrices estimation

Recent literature provides many computational and modeling approaches for covariance matrices estimation in a penalized Gaussian graphical models but relatively little study has been carried out on the choice of the tuning parameter. This paper tries to fill this gap by focusing on the problem of shrinkage parameter selection when estimating sparse precision matrices using the penalized likelihood approach. Previous approaches typically used K-fold cross-validation in this regard. In this paper, we first derived the generalized approximate cross-validation for tuning parameter selection which is not only a more computationally efficient alternative, but also achieves smaller error rate for model fitting compared to leave-one-out cross-validation. For consistency in the selection of nonzero entries in the precision matrix, we employ a Bayesian information criterion which provably can identify the nonzero conditional correlations in the Gaussian model. Our simulations demonstrate the general superiority of the two proposed selectors in comparison with leave-one-out cross-validation, 10-fold cross-validation and Akaike information criterion.     

Estimating common parameters of growth curve models under a quadratic loss

Consider the problem of estimating the common matrix of several growth curve models with possibly different unknown covariance matrices under the quadratic loss. The paper gives a combined estimator with a smaller risk than MLE of each growth curve model.     

Bayesian inference and data cloning in the calibration of population projection matrices

Discrete time models are used in Ecology for describing the dynamics of an age-structured population. They can be introduced from a deterministic or from a stochastic viewpoint. We analyze a stochastic model for the case in which the dynamics of the population is described by means of a projection matrix. In this statistical model, fertility rates and survival rates are unknown parameters which are estimated by using a Bayesian approach and also data cloning, which is a simulation-based method especially useful with complex hierarchical models.

Both methodologies are applied to real data from the population of Steller sea lions located in the Alaska coast since 1978–2004. The estimates obtained from these methods show a good behavior when they are compared to the nonmissing actual values.     

HEAVY-TAILED-DISTRIBUTED THRESHOLD STOCHASTIC VOLATILITY MODELS IN FINANCIAL TIME SERIES

To capture mean and variance asymmetries and time‐varying volatility in financial time series, we generalize the threshold stochastic volatility (THSV) model and incorporate a heavy‐tailed error distribution. Unlike existing stochastic volatility models, this model simultaneously accounts for uncertainty in the unobserved threshold value and in the time‐delay parameter. Self‐exciting and exogenous threshold variables are considered to investigate the impact of a number of market news variables on volatility changes. Adopting a Bayesian approach, we use Markov chain Monte Carlo methods to estimate all unknown parameters and latent variables. A simulation experiment demonstrates good estimation performance for reasonable sample sizes. In a study of two international financial market indices, we consider two variants of the generalized THSV model, with US market news as the threshold variable. Finally, we compare models using Bayesian forecasting in a value‐at‐risk (VaR) study. The results show that our proposed model can generate more accurate VaR forecasts than can standard models.     

A Population Approach to Analysis of Variance Models

Several authors have contributed to what can now be considered a rather complete theory for analysis of variance in cases with orthogonal factors. By using this theory on an assumed basic reference population, the orthogonality concept gives a natural definition of independence between factors in the population. By looking upon the treated units in designed experiments as a formal sample from a future population about which we want to make inference, a natural parametrization of expectations and variances connected to such experiments arises. This approach seems to throw light upon several controversial questions in the theory of mixed models. Also, it gives a framework for discussing the choice of conditioning in models     

Maximum likelihood from spatial random effects models via the stochastic approximation expectation maximization algorithm

We introduce a class of spatial random effects models that have Markov random fields (MRF) as latent processes. Calculating the maximum likelihood estimates of unknown parameters in SREs is extremely difficult, because the normalizing factors of MRFs and additional integrations from unobserved random effects are computationally prohibitive. We propose a stochastic approximation expectation-maximization (SAEM) algorithm to maximize the likelihood functions of spatial random effects models. The SAEM algorithm integrates recent improvements in stochastic approximation algorithms; it also includes components of the Newton-Raphson algorithm and the expectation-maximization (EM) gradient algorithm. The convergence of the SAEM algorithm is guaranteed under some mild conditions. We apply the SAEM algorithm to three examples that are representative of real-world applications: a state space model, a noisy Ising model, and segmenting magnetic resonance images (MRI) of the human brain. The SAEM algorithm gives satisfactory results in finding the maximum likelihood estimate of spatial random effects models in each of these instances.     

Fast Inference for Network Models of Infectious Disease Spread

Models of infectious disease over contact networks offer a versatile means of capturing heterogeneity in populations during an epidemic. Highly connected individuals tend to be infected at a higher rate early during an outbreak than those with fewer connections. A powerful approach based on the probability generating function of the individual degree distribution exists for modelling the mean field dynamics of outbreaks in such a population. We develop the same idea in a stochastic context, by proposing a comprehensive model for 1‐week‐ahead incidence counts. Our focus is inferring contact network (and other epidemic) parameters for some common degree distributions, in the case when the network is non‐homogeneous ‘at random’. Our model is initially set within a susceptible–infectious–removed framework, then extended to the susceptible–infectious–removed–susceptible scenario, and we apply this methodology to influenza A data.     

Bilinear modulation models for seasonal tables of counts

We propose generalized linear models for time or age-time tables of seasonal counts, with the goal of better understanding seasonal patterns in the data. The linear predictor contains a smooth component for the trend and the product of a smooth component (the modulation) and a periodic time series of arbitrary shape (the carrier wave). To model rates, a population offset is added. Two-dimensional trends and modulation are estimated using a tensor product B-spline basis of moderate dimension. Further smoothness is ensured using difference penalties on the rows and columns of the tensor product coefficients. The optimal penalty tuning parameters are chosen based on minimization of a quasi-information criterion. Computationally efficient estimation is achieved using array regression techniques, avoiding excessively large matrices. The model is applied to female death rate in the US due to cerebrovascular diseases and respiratory diseases.