153,884 research outputs found
Almost the Best of Three Worlds: Risk, Consistency and Optional Stopping for the Switch Criterion in Nested Model Selection
We study the switch distribution, introduced by Van Erven et al. (2012),
applied to model selection and subsequent estimation. While switching was known
to be strongly consistent, here we show that it achieves minimax optimal
parametric risk rates up to a factor when comparing two nested
exponential families, partially confirming a conjecture by Lauritzen (2012) and
Cavanaugh (2012) that switching behaves asymptotically like the Hannan-Quinn
criterion. Moreover, like Bayes factor model selection but unlike standard
significance testing, when one of the models represents a simple hypothesis,
the switch criterion defines a robust null hypothesis test, meaning that its
Type-I error probability can be bounded irrespective of the stopping rule.
Hence, switching is consistent, insensitive to optional stopping and almost
minimax risk optimal, showing that, Yang's (2005) impossibility result
notwithstanding, it is possible to `almost' combine the strengths of AIC and
Bayes factor model selection.Comment: To appear in Statistica Sinic
FATODE: A Library for Forward, Adjoint, and Tangent Linear Integration of ODEs
FATODE is a FORTRAN library for the integration of ordinary differential equations with direct and adjoint sensitivity analysis capabilities.
The paper describes the capabilities, implementation, code organization, and usage of this package.
FATODE implements four families of methods -- explicit Runge-Kutta for nonstiff problems and fully implicit Runge-Kutta, singly diagonally implicit Runge-Kutta, and Rosenbrock for stiff problems.
Each family contains several methods with different orders of accuracy; users can add new methods by simply providing their coefficients.
For each family the forward, adjoint, and tangent linear models are implemented.
General purpose solvers for dense and sparse linear algebra are used; users can easily incorporate problem-tailored linear algebra routines.
The performance of the package is demonstrated on several test problems.
To the best of our knowledge FATODE is the first publicly available general purpose package that offers forward and adjoint sensitivity
analysis capabilities in the context of Runge Kutta methods. A wide range of applications are expected to benefit from its use; examples include parameter estimation,
data assimilation, optimal control, and uncertainty quantification
SPACE-TIME ESTIMATION AND PREDICTION UNDER FIXED-DOMAIN ASYMPTOTICS WITH COMPACTLY SUPPORTED COVARIANCE FUNCTIONS
We study the estimation and prediction of Gaussian processes with spacetime covariance models belonging to the dynamical generalized Wendland (DGW) family, under fixed-domain asymptotics. Such a class is nonseparable, has dynamical compact supports, and parameterizes differentiability at the origin similarly to the space-time Matern class.Our results are presented in two parts. First, we establish the strong consistency and asymptotic normality for the maximum likelihood estimator of the microergodic parameter associated with the DGW covariance model, under fixed-domain asymptotics. The second part focuses on optimal kriging prediction under the DGW model and an asymptotically correct estimation of the mean squared error using a misspecified model. Our theoretical results are, in turn, based on the equivalence of Gaussian measures under some given families of space-time covariance functions, where both space or time are compact. The technical results are provided in the online Supplementary material
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