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Statistical Models Commons™

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Selected Works

2018

Articles 1 - 3 of 3

Full-Text Articles in Statistical Models

Inversion Copulas From Nonlinear State Space Models With An Application To Inflation Forecasting, Michael S. Smith, Worapree Ole Maneesoonthorn May 2018

Inversion Copulas From Nonlinear State Space Models With An Application To Inflation Forecasting, Michael S. Smith, Worapree Ole Maneesoonthorn

Michael Stanley Smith

We propose the construction of copulas through the inversion of nonlinear state space models. These copulas allow for new time series models that have the same serial dependence structure as a state space model, but with an arbitrary marginal distribution, and flexible density forecasts. We examine the time series properties of the copulas, outline serial dependence measures, and estimate the models using likelihood-based methods. Copulas constructed from three example state space models are considered: a stochastic volatility model with an unobserved component, a Markov switching autoregression, and a Gaussian linear unobserved component model. We show that all three inversion copulas …

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The Fossilized Birth-Death Model For The Analysis Of Stratigraphic Range Data Under Different Speciation Modes, Tanja Stadler, Alexandra Gavryushkina, Rachel C. M. Warnock, Alexei J. Drummond, Tracy A. Heath Feb 2018

The Fossilized Birth-Death Model For The Analysis Of Stratigraphic Range Data Under Different Speciation Modes, Tanja Stadler, Alexandra Gavryushkina, Rachel C. M. Warnock, Alexei J. Drummond, Tracy A. Heath

Tracy Heath

A birth-death-sampling model gives rise to phylogenetic trees with samples from the past and the present. Interpreting “birth” as branching speciation, “death” as extinction, and “sampling” as fossil preservation and recovery, this model – also referred to as the fossilized birth-death (FBD) model – gives rise to phylogenetic trees on extant and fossil samples. The model has been mathematically analyzed and successfully applied to a range of datasets on different taxonomic levels, such as penguins, plants, and insects. However, the current mathematical treatment of this model does not allow for a group of temporally distinct fossil specimens to be assigned …

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Implicit Copulas From Bayesian Regularized Regression Smoothers, Nadja Klein, Michael S. Smith Dec 2017

Implicit Copulas From Bayesian Regularized Regression Smoothers, Nadja Klein, Michael S. Smith

Michael Stanley Smith

We show how to extract the implicit copula of a response vector from a Bayesian regularized regression smoother with Gaussian disturbances. The copula can be used to compare smoothers that employ different shrinkage priors and function bases. We illustrate with three popular choices of shrinkage priors --- a pairwise prior, the horseshoe prior and a g prior augmented with a point mass as employed for Bayesian variable selection --- and both univariate and multivariate function bases. The implicit copulas are high-dimensional and unavailable in closed form. However, we show how to evaluate them by first constructing a Gaussian copula conditional on the regularization parameters, …

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