Efficient methods for fitting nonlinear non-Gaussian state-space models of wildlife population dynamics

近年来，人们对野生动物种群动态的机械模型进行拟合以调查动物数量、存活率和出生率的兴趣和方法有了巨大的增长。基于最大似然法和贝叶斯方法的各种统计方法已经被提出。例如用于最大似然估计的卡尔曼滤波(及其扩展)和用于贝叶斯模型的马尔可夫链蒙特卡罗(MCMC)或粒子滤波。每种方法都有优缺点--例如，卡尔曼滤波是为线性高斯模型设计的(但在其他情况下似乎表现得非常好)；MCMC是一种优秀的综合方法，但它可能很难得出有效的采样器(即，那些在合理的计算机时间范围内产生可靠答案的采样器)；粒子滤波很容易编程，但对于一些模型(例如，具有随机影响的模型)来说效率非常低。在这个项目中，我们的目标是融合这些方法的各个方面，以提高估计的效率。例如，我们将研究在粒子滤波算法中使用卡尔曼滤波估计作为重要性采样的开始，并使用粒子滤波在MCMC算法中提供建议。

Recent years have seen an enormous growth in interest in and methods for fitting mechanisticmodels of wildlife population dynamics to survey data on animal numbers, survival and birth rates.Various statistical methods have been proposed, based both on maximum likelihood and Bayesianapproaches. Examples include the Kalman filter (and extensions) for maximum likelihood estimationand Markov chain Monte Carlo (MCMC) or particle filtering for Bayesian models. Each hasadvantages and disadvantages - for example the Kalman filter is designed for linear Gaussian models(but seems to do remarkably well in other circumstances); MCMC is an excellent omnibus methodbut it can be difficult to derive efficient samplers (i.e., those that produce reliable answers in areasonable amount of computer time); particle filtering is easy to program but very inefficient forsome models (e.g., those with random effects). In this project, we aim to blend aspects of theseapproaches to increase the efficiency of the estimation. For example, we will investigate usingKalman filter estimates as importance sampling starts in a particle filter algorithm, and using theparticle filter to provide proposals in an MCMC algorithm.