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Observation Process (observation + process)

Distribution by Scientific Domains
Mathematics and Statistics60%

Selected Abstracts

Analysis of particulate matter air pollution using Markov random field models of spatial dependence

ENVIRONMETRICS, Issue 5-6 2002
Mark S. Kaiser
Abstract Researchers are beginning to realize the need to take spatial structure into account when modeling data on air pollutants. We develop several models for particulate matter in an urban region that allow spatial dependence to be represented in different manners over a time period of one year. The models are based on a Markov random field approach, and a conceptualization of observed data as arising from two random processes, a conditionally independent observation process and a spatially dependent latent pollution process. Optimal predictors are developed for both of these processes, and predictions of the observation process are used for model assessment. Copyright © 2002 John Wiley & Sons, Ltd. [source]

INVESTIGATING EVOLUTIONARY TRADE-OFFS IN WILD POPULATIONS OF ATLANTIC SALMON (SALMO SALAR): INCORPORATING DETECTION PROBABILITIES AND INDIVIDUAL HETEROGENEITY

EVOLUTION, Issue 9 2010
Mathieu Buoro
Evolutionary trade-offs among demographic parameters are important determinants of life-history evolution. Investigating such trade-offs under natural conditions has been limited by inappropriate analytical methods that fail to address the bias in demographic estimates that can result when issues of detection (uncertain detection of individual) are ignored. We propose a new statistical approach to quantify evolutionary trade-offs in wild populations. Our method is based on a state-space modeling framework that focuses on both the demographic process of interest as well as the observation process. As a case study, we used individual mark,recapture data for stream-dwelling Atlantic salmon juveniles in the Scorff River (Southern Brittany, France). In freshwater, juveniles face two life-history choices: migration to the ocean and sexual maturation (for males). Trade-offs may appear with these life-history choices and survival, because all are energy dependent. We found a cost of reproduction on survival for fish staying in freshwater and a survival advantage associated with the "decision" to migrate. Our modeling framework opens up promising prospects for the study of evolutionary trade-offs when some life-history traits are not, or only partially, observable. [source]

Moment based regression algorithms for drift and volatility estimation in continuous-time Markov switching models

THE ECONOMETRICS JOURNAL, Issue 2 2008
Robert J. Elliott
Summary, We consider a continuous time Markov switching model (MSM) which is widely used in mathematical finance. The aim is to estimate the parameters given observations in discrete time. Since there is no finite dimensional filter for estimating the underlying state of the MSM, it is not possible to compute numerically the maximum likelihood parameter estimate via the well known expectation maximization (EM) algorithm. Therefore in this paper, we propose a method of moments based parameter estimator. The moments of the observed process are computed explicitly as a function of the time discretization interval of the discrete time observation process. We then propose two algorithms for parameter estimation of the MSM. The first algorithm is based on a least-squares fit to the exact moments over different time lags, while the second algorithm is based on estimating the coefficients of the expansion (with respect to time) of the moments. Extensive numerical results comparing the algorithm with the EM algorithm for the discretized model are presented. [source]

On Smoothing Trends in Population Index Modeling

BIOMETRICS, Issue 4 2007
Chiara Mazzetta
Summary In this article, we consider the U.K. Common Birds Census counts and their use in monitoring bird abundance. We use a state,space modeling approach within a Bayesian framework to describe population level trends over time and contribute to the alert system used by the British Trust for Ornithology. We account for potential overdispersion and excess zero counts by modeling the observation process with a zero-inflated negative binomial, while the system process is described by second-order polynomial growth models. In order to provide a biological motivation for the amount of smoothing applied to the observed series the system variance is related to the demographic characteristics of the species, so as to help the specification of its prior distribution. In particular, the available information on productivity and survival is used to formulate prior expectations on annual percentage changes in the population level and then used to constrain the variance of the system process. We discuss an example of how to interpret alternative choices for the degree of smoothing and how these relate to the classification of species, over time, into conservation lists. [source]