18,218 research outputs found
Optimal Prediction Pools
A prediction model is any statement of a probability distribution for an outcome not yet observed. This study considers the properties of weighted linear combinations of n prediction models, or linear pools, evaluated using the conventional log predictive scoring rule. The log score is a concave function of the weights and, in general, an optimal linear combination will include several models with positive weights despite the fact that exactly one model has limiting posterior probability one. The paper derives several interesting formal results: for example, a prediction model with positive weight in a pool may have zero weight if some other models are deleted from that pool. The results are illustrated using S&P 500 returns with prediction models from the ARCH, stochastic volatility and Markov mixture families. In this example models that are clearly inferior by the usual scoring criteria have positive weights in optimal linear pools, and these pools substantially outperform their best components. JEL Classification: C11, C53forecasting, GARCH, log scoring, Markov mixture, model combination
Optimal Prediction Pools
A prediction model is any statement of a probability distribution for an outcome not yet observed. This study considers the properties of weighted linear combinations of n prediction models, or linear pools, evaluated using the conventional log predictive scoring rule. The log score is a concave function of the weights and, in general, an optimal linear combination will include several models with positive weights despite the fact that exactly one model has limiting posterior probability one. The paper derives several interesting formal results: for example, a prediction model with positive weight in a pool may have zero weight if some other models are deleted from that pool. The results are illustrated using S&P 500 returns with prediction models from the ARCH, stochastic volatility and Markov mixture families. In this example models that are clearly inferior by the usual scoring criteria have positive weights in optimal linear pools, and these pools substantially outperform their best components.forecasting; GARCH; log scoring; Markov mixture; model combination; S&P 500 returns; stochastic volatility
CopulaDTA: An R Package for Copula Based Bivariate Beta-Binomial Models for Diagnostic Test Accuracy Studies in a Bayesian Framework
The current statistical procedures implemented in statistical software
packages for pooling of diagnostic test accuracy data include hSROC regression
and the bivariate random-effects meta-analysis model (BRMA). However, these
models do not report the overall mean but rather the mean for a central study
with random-effect equal to zero and have difficulties estimating the
correlation between sensitivity and specificity when the number of studies in
the meta-analysis is small and/or when the between-study variance is relatively
large. This tutorial on advanced statistical methods for meta-analysis of
diagnostic accuracy studies discusses and demonstrates Bayesian modeling using
CopulaDTA package in R to fit different models to obtain the meta-analytic
parameter estimates. The focus is on the joint modelling of sensitivity and
specificity using copula based bivariate beta distribution. Essentially, we
extend the work of Nikoloulopoulos by: i) presenting the Bayesian approach
which offers flexibility and ability to perform complex statistical modelling
even with small data sets and ii) including covariate information, and iii)
providing an easy to use code. The statistical methods are illustrated by
re-analysing data of two published meta-analyses. Modelling sensitivity and
specificity using the bivariate beta distribution provides marginal as well as
study-specific parameter estimates as opposed to using bivariate normal
distribution (e.g., in BRMA) which only yields study-specific parameter
estimates. Moreover, copula based models offer greater flexibility in modelling
different correlation structures in contrast to the normal distribution which
allows for only one correlation structure.Comment: 26 pages, 5 figure
Modeling Covariate Effects in Group Independent Component Analysis with Applications to Functional Magnetic Resonance Imaging
Independent component analysis (ICA) is a powerful computational tool for
separating independent source signals from their linear mixtures. ICA has been
widely applied in neuroimaging studies to identify and characterize underlying
brain functional networks. An important goal in such studies is to assess the
effects of subjects' clinical and demographic covariates on the spatial
distributions of the functional networks. Currently, covariate effects are not
incorporated in existing group ICA decomposition methods. Hence, they can only
be evaluated through ad-hoc approaches which may not be accurate in many cases.
In this paper, we propose a hierarchical covariate ICA model that provides a
formal statistical framework for estimating and testing covariate effects in
ICA decomposition. A maximum likelihood method is proposed for estimating the
covariate ICA model. We develop two expectation-maximization (EM) algorithms to
obtain maximum likelihood estimates. The first is an exact EM algorithm, which
has analytically tractable E-step and M-step. Additionally, we propose a
subspace-based approximate EM, which can significantly reduce computational
time while still retain high model-fitting accuracy. Furthermore, to test
covariate effects on the functional networks, we develop a voxel-wise
approximate inference procedure which eliminates the needs of computationally
expensive covariance estimation. The performance of the proposed methods is
evaluated via simulation studies. The application is illustrated through an
fMRI study of Zen meditation.Comment: 36 pages, 5 figure
Meta-Functional Benefit Transfer for Wetland Valuation: Making the Most of Small Samples
This study applies functional Benefit Transfer via Meta-Regression Modeling to derive valuation estimates for wetlands in an actual policy setting of proposed groundwater transfers in Eastern Nevada. We illustrate how Bayesian estimation techniques can be used to overcome small sample problems notoriously present in Meta-functional Benefit Transfer. The highlights of our methodology are (i) The hierarchical modeling of heteroskedasticity, (ii) The ability to incorporate additional information via refined priors, and (ii) The derivation of measures of model performance with the corresponding option of model-averaged Benefit Transfer predictions. Our results indicate that economic losses associated with the disappearance of these wetlands can be substantial and that primary valuation studies are warranted.Bayesian Model Averaging; t-Error Regression Model; Meta-Analysis; Benefit Transfer; Wetland Valuation
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