Home  About us  Contact
 

True Model (true + model)

Distribution by Scientific Domains
Mathematics and Statistics40%

Selected Abstracts

Model uncertainty in the ecosystem approach to fisheries

FISH AND FISHERIES, Issue 4 2007
Simeon L. Hill
Abstract Fisheries scientists habitually consider uncertainty in parameter values, but often neglect uncertainty about model structure, an issue of increasing importance as ecosystem models are devised to support the move to an ecosystem approach to fisheries (EAF). This paper sets out pragmatic approaches with which to account for uncertainties in model structure and we review current ways of dealing with this issue in fisheries and other disciplines. All involve considering a set of alternative models representing different structural assumptions, but differ in how those models are used. The models can be asked to identify bounds on possible outcomes, find management actions that will perform adequately irrespective of the true model, find management actions that best achieve one or more objectives given weights assigned to each model, or formalize hypotheses for evaluation through experimentation. Data availability is likely to limit the use of approaches that involve weighting alternative models in an ecosystem setting, and the cost of experimentation is likely to limit its use. Practical implementation of an EAF should therefore be based on management approaches that acknowledge the uncertainty inherent in model predictions and are robust to it. Model results must be presented in ways that represent the risks and trade-offs associated with alternative actions and the degree of uncertainty in predictions. This presentation should not disguise the fact that, in many cases, estimates of model uncertainty may be based on subjective criteria. The problem of model uncertainty is far from unique to fisheries, and a dialogue among fisheries modellers and modellers from other scientific communities will therefore be helpful. [source]

Estimation Optimality of Corrected AIC and Modified Cp in Linear Regression

INTERNATIONAL STATISTICAL REVIEW, Issue 2 2006
Simon L. Davies
Summary Model selection criteria often arise by constructing unbiased or approximately unbiased estimators of measures known as expected overall discrepancies (Linhart & Zucchini, 1986, p. 19). Such measures quantify the disparity between the true model (i.e., the model which generated the observed data) and a fitted candidate model. For linear regression with normally distributed error terms, the "corrected" Akaike information criterion and the "modified" conceptual predictive statistic have been proposed as exactly unbiased estimators of their respective target discrepancies. We expand on previous work to additionally show that these criteria achieve minimum variance within the class of unbiased estimators. Résumé Les critères de modèle de sélection naissent souvent de la construction de mesures d'estimation impartiales, ou approximativement impartiales, connues comme divergences globales prévues. De telles mesures quantifient la disparité entre le vrai modèle (c'est-à-dire le modèle qui a produit les données observées) et un modèle candidat correspondant. En ce qui concerne les applications de régression linéaires contenant des erreurs distribuées normalement, le modèle de critère d'information "corrigé" Akaike et le modèle conceptuel de statistique de prévision "modifié" ont été proposés comme étant des instruments exacts de mesures d'estimation impartiales de leurs objectifs respectifs de divergences. En nous appuyant sur les travaux précédents et en les développant, nous proposons de démontrer, en outre, que ces critères réalisent une variance minimum au sein de la classe des instruments de mesures d'estimation impartiales. [source]

Improving robust model selection tests for dynamic models

THE ECONOMETRICS JOURNAL, Issue 2 2010
Hwan-sik Choi
Summary, We propose an improved model selection test for dynamic models using a new asymptotic approximation to the sampling distribution of a new test statistic. The model selection test is applicable to dynamic models with very general selection criteria and estimation methods. Since our test statistic does not assume the exact form of a true model, the test is essentially non-parametric once competing models are estimated. For the unknown serial correlation in data, we use a Heteroscedasticity/Autocorrelation-Consistent (HAC) variance estimator, and the sampling distribution of the test statistic is approximated by the fixed- b,asymptotic approximation. The asymptotic approximation depends on kernel functions and bandwidth parameters used in HAC estimators. We compare the finite sample performance of the new test with the bootstrap methods as well as with the standard normal approximations, and show that the fixed- b,asymptotics and the bootstrap methods are markedly superior to the standard normal approximation for a moderate sample size for time series data. An empirical application for foreign exchange rate forecasting models is presented, and the result shows the normal approximation to the distribution of the test statistic considered appears to overstate the data's ability to distinguish between two competing models. [source]

A Bayesian Spatial Multimarker Genetic Random-Effect Model for Fine-Scale Mapping

ANNALS OF HUMAN GENETICS, Issue 5 2008
M.-Y. Tsai
Summary Multiple markers in linkage disequilibrium (LD) are usually used to localize the disease gene location. These markers may contribute to the disease etiology simultaneously. In contrast to the single-locus tests, we propose a genetic random effects model that accounts for the dependence between loci via their spatial structures. In this model, the locus-specific random effects measure not only the genetic disease risk, but also the correlations between markers. In other words, the model incorporates this relation in both mean and covariance structures, and the variance components play important roles. We consider two different settings for the spatial relations. The first is our proposal, relative distance function (RDF), which is intuitive in the sense that markers nearby are likely to correlate with each other. The second setting is a common exponential decay function (EDF). Under each setting, the inference of the genetic parameters is fully Bayesian with Markov chain Monte Carlo (MCMC) sampling. We demonstrate the validity and the utility of the proposed approach with two real datasets and simulation studies. The analyses show that the proposed model with either one of two spatial correlations performs better as compared with the single locus analysis. In addition, under the RDF model, a more precise estimate for the disease locus can be obtained even when the candidate markers are fairly dense. In all simulations, the inference under the true model provides unbiased estimates of the genetic parameters, and the model with the spatial correlation structure does lead to greater confidence interval coverage probabilities. [source]

PARTIALLY LINEAR MODEL SELECTION BY THE BOOTSTRAP

AUSTRALIAN & NEW ZEALAND JOURNAL OF STATISTICS, Issue 2 2009
Samuel Müller
Summary We propose a new approach to the selection of partially linear models based on the conditional expected prediction square loss function, which is estimated using the bootstrap. Because of the different speeds of convergence of the linear and the nonlinear parts, a key idea is to select each part separately. In the first step, we select the nonlinear components using an ,m -out-of- n' residual bootstrap that ensures good properties for the nonparametric bootstrap estimator. The second step selects the linear components from the remaining explanatory variables, and the non-zero parameters are selected based on a two-level residual bootstrap. We show that the model selection procedure is consistent under some conditions, and our simulations suggest that it selects the true model most often than the other selection procedures considered. [source]