Hans R. Künsch

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The generalization of the sampling theorem to multidimensional signals is considered, with or without bandwidth constraints. The signal is modeled as a stationary random process and sampled on a lattice. Exact expressions for the mean-square error of the best linear interpolator are given in the frequency domain. Moreover, asymptotic expansions are derived(More)
A noninvertible function of a first order Markov process, or of a nearestneighbor Markov random field, is called a hidden Markov model. Hidden Markov models are generally not Markovian. In fact, they may have complex and long range interactions, which is largely the reason for their utility. Applications include signal and image processing, speech(More)
Importance splitting is a simulation technique to estimate very small entrance probabilities for Markov processes by splitting sample paths at various stages before reaching the set of interest. This can be done in many ways, yielding different variants of the method. In this context, we propose a new one, called fixed number of successes. We prove(More)
Even after careful calibration, the output of deterministic models of environmental systems usually still show systematic deviations from measured data. To analyse possible causes of these discrepancies, we make selected model parameters time variable by treating them as continuous time stochastic processes. This extends an approach that was proposed(More)
We present a simulation methodology for Bayesian estimation of rate parameters in Markov jump processes arising for example in stochastic kinetic models. To handle the problem of missing components and measurement errors in observed data, we embed the Markov jump process into the framework of a general state space model. We do not use diffusion(More)
To address systematic discrepancies between model simulations and measured data, we propose to make selected parameters in the model time-variant by modeling them as continuous-time stochastic processes. We present an algorithm for Bayesian estimation of such parameters that includes some special adaptations of the Markov chain Monte Carlo method. The(More)