arXiv subjects

Tore Selland Kleppe

Publications and source records attributed to Tore Selland Kleppe.

21 records · Page 2Linked to original sources

arXiv2016

On the application of higher order symplectic integrators in Hamiltonian Monte Carlo

We explore the construction of new symplectic numerical integration schemes to be used in Hamiltonian Monte Carlo and study their efficiency. Two integration schemes from Blanes et al. (2014), and a new scheme based on optimal acceptance probability, are considered as candidates to the commonly used leapfrog method. All integration schemes are tested within the framework of the No-U-Turn sampler (NUTS), both for a logistic regression model and a student $t$-model. The results show that the leapfrog method is inferior to all the new methods both in terms of asymptotic expected acceptance probability for a model problem and the and efficient sample size per computing time for the realistic models.

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arXiv2015

Adaptive step size selection for Hessian-based manifold Langevin samplers

The usage of positive definite metric tensors derived from second derivative information in the context of the simplified manifold Metropolis adjusted Langevin algorithm (MALA) is explored. A new adaptive step length procedure that resolves the shortcomings of such metric tensors in regions where the log-target has near zero curvature in some direction is proposed. The adaptive step length selection also appears to alleviate the need for different tuning parameters in transient and stationary regimes that is typical of MALA. The combination of metric tensors derived from second derivative information and adaptive step length selection constitute a large step towards developing reliable manifold MCMC methods that can be implemented automatically for models with unknown or intractable Fisher information, and even for target distributions that do not admit factorization into prior and likelihood. Through examples of low to moderate dimension, it is shown that proposed methodology performs very well relative to alternative MCMC methods.

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arXiv2015

Bandwidth Selection In Pre-Smoothed Particle Filters

For the purpose of maximum likelihood estimation of static parameters, we apply a kernel smoother to the particles in the standard SIR filter for non-linear state space models with additive Gaussian observation noise. This reduces the Monte Carlo error in the estimates of both the posterior density of the states and the marginal density of the observation at each time point. We correct for variance inflation in the smoother, which together with the use of Gaussian kernels, results in a Gaussian (Kalman) update when the amount of smoothing turns to infinity. We propose and study of a criterion for choosing the optimal bandwidth $h$ in the kernel smoother. Finally, we illustrate our approach using examples from econometrics. Our filter is shown to be highly suited for dynamic models with high signal-to-noise ratio, for which the SIR filter has problems.

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