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Hans R. Künsch

Publications and source records attributed to Hans R. Künsch.

13 recordsLinked to original sources
arXiv2026

Simultaneous estimation of the effective reproduction number and the time series of daily infections: Application to Covid-19

The time-varying effective reproduction number is an important parameter for communication and policy decisions during an epidemic. In this paper, we present new statistical methods for estimating the reproduction number based on the popular model of \citet{cori2013new} which defines the effective reproduction number based on self-exciting dynamics of new infections. Such a model is conceptually simple and less susceptible to misspecifications than more complicated multi-compartment models. However, statistical inference is challenging, and the previous literature has either relied on proxy data and/or a two-step approach in which the number of infections is first estimated. In contrast, we present a coherent Bayesian method that approximates the joint posterior of daily new infections and reproduction numbers using a novel Markov chain Monte Carlo (MCMC) algorithm. Comparing our method to the state-of-the-art three-step estimation procedure of \citet{huisman2022estimation}, both using daily confirmed cases from Switzerland in the Covid-19 epidemic and simulated data, we find that our method is more accurate in terms of point estimates and uncertainty quantification, especially near the beginning and end of an observation period.

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arXiv2019

Particle filters for high-dimensional geoscience applications: a review

Particle filters contain the promise of fully nonlinear data assimilation. They have been applied in numerous science areas, but their application to the geosciences has been limited due to their inefficiency in high-dimensional systems in standard settings. However, huge progress has been made, and this limitation is disappearing fast due to recent developments in proposal densities, the use of ideas from (optimal) transportation, the use of localisation and intelligent adaptive resampling strategies. Furthermore, powerful hybrids between particle filters and ensemble Kalman filters and variational methods have been developed. We present a state of the art discussion of present efforts of developing particle filters for highly nonlinear geoscience state-estimation problems with an emphasis on atmospheric and oceanic applications, including many new ideas, derivations, and unifications, highlighting hidden connections, and generating a valuable tool and guide for the community. Initial experiments show that particle filters can be competitive with present-day methods for numerical weather prediction suggesting that they will become mainstream soon.

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arXiv2017

A local ensemble transform Kalman particle filter for convective scale data assimilation

Ensemble data assimilation methods such as the Ensemble Kalman Filter (EnKF) are a key component of probabilistic weather forecasting. They represent the uncertainty in the initial conditions by an ensemble which incorporates information coming from the physical model with the latest observations. High-resolution numerical weather prediction models ran at operational centers are able to resolve non-linear and non-Gaussian physical phenomena such as convection. There is therefore a growing need to develop ensemble assimilation algorithms able to deal with non-Gaussianity while staying computationally feasible. In the present paper we address some of these needs by proposing a new hybrid algorithm based on the Ensemble Kalman Particle Filter. It is fully formulated in ensemble space and uses a deterministic scheme such that it has the ensemble transform Kalman filter (ETKF) instead of the stochastic EnKF as a limiting case. A new criterion for choosing the proportion of particle filter and ETKF update is also proposed. The new algorithm is implemented in the COSMO framework and numerical experiments in a quasi-operational convective-scale setup are conducted. The results show the feasibility of the new algorithm in practice and indicate a strong potential for such local hybrid methods, in particular for forecasting non-Gaussian variables such as wind and hourly precipitation.

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arXiv2016

Localization in High-Dimensional Monte Carlo Filtering

The high dimensionality and computational constraints associated with filtering problems in large-scale geophysical applications are particularly challenging for the Particle Filter (PF). Approximate but efficient methods such as the Ensemble Kalman Filter (EnKF) are therefore usually preferred. A key element of these approximate methods is localization, which is in principle a general technique to avoid the curse of dimensionality and consists in limiting the influence of observations to neighboring sites. However, while it works effectively with the EnKF, localization introduces harmful discontinuities in the estimated physical fields when applied blindly to the PF. In the present paper, we explore two possible local algorithms based on the EnKPF, a hybrid method combining the EnKF and the PF. A simulation study in a conjugate normal setup allows to highlight the trade-offs involved when applying localization to PF type of algorithms in the high-dimensional setting. Experiments with the Lorenz96 model demonstrate the ability of the local EnKPF algorithms to perform well even with a small number of particles compared to the problem size.

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arXiv2016

Localizing the Ensemble Kalman Particle Filter

Ensemble methods such as the Ensemble Kalman Filter (EnKF) are widely used for data assimilation in large-scale geophysical applications, as for example in numerical weather prediction (NWP). There is a growing interest for physical models with higher and higher resolution, which brings new challenges for data assimilation techniques because of the presence of non-linear and non-Gaussian features that are not adequately treated by the EnKF. We propose two new localized algorithms based on the Ensemble Kalman Particle Filter (EnKPF), a hybrid method combining the EnKF and the Particle Filter (PF) in a way that maintains scalability and sample diversity. Localization is a key element of the success of EnKFs in practice, but it is much more challenging to apply to PFs. The algorithms that we introduce in the present paper provide a compromise between the EnKF and the PF while avoiding some of the problems of localization for pure PFs. Numerical experiments with a simplified model of cumulus convection based on a modified shallow water equation show that the proposed algorithms perform better than the local EnKF. In particular, the PF nature of the method allows to capture non-Gaussian characteristics of the estimated fields such as the location of wet and dry areas.

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arXiv2016

Stochastic partial differential equation based modelling of large space-time data sets

Increasingly larger data sets of processes in space and time ask for statistical models and methods that can cope with such data. We show that the solution of a stochastic advection-diffusion partial differential equation provides a flexible model class for spatio-temporal processes which is computationally feasible also for large data sets. The Gaussian process defined through the stochastic partial differential equation has in general a nonseparable covariance structure. Furthermore, its parameters can be physically interpreted as explicitly modeling phenomena such as transport and diffusion that occur in many natural processes in diverse fields ranging from environmental sciences to ecology. In order to obtain computationally efficient statistical algorithms we use spectral methods to solve the stochastic partial differential equation. This has the advantage that approximation errors do not accumulate over time, and that in the spectral space the computational cost grows linearly with the dimension, the total computational costs of Bayesian or frequentist inference being dominated by the fast Fourier transform. The proposed model is applied to postprocessing of precipitation forecasts from a numerical weather prediction model for northern Switzerland. In contrast to the raw forecasts from the numerical model, the postprocessed forecasts are calibrated and quantify prediction uncertainty. Moreover, they outperform the raw forecasts, in the sense that they have a lower mean absolute error.

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arXiv2013

Particle filters

This is a short review of Monte Carlo methods for approximating filter distributions in state space models. The basic algorithm and different strategies to reduce imbalance of the weights are discussed. Finally, methods for more difficult problems like smoothing and parameter estimation and applications outside the state space model context are presented.

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arXiv2013

A dynamic nonstationary spatio-temporal model for short term prediction of precipitation

Precipitation is a complex physical process that varies in space and time. Predictions and interpolations at unobserved times and/or locations help to solve important problems in many areas. In this paper, we present a hierarchical Bayesian model for spatio-temporal data and apply it to obtain short term predictions of rainfall. The model incorporates physical knowledge about the underlying processes that determine rainfall, such as advection, diffusion and convection. It is based on a temporal autoregressive convolution with spatially colored and temporally white innovations. By linking the advection parameter of the convolution kernel to an external wind vector, the model is temporally nonstationary. Further, it allows for nonseparable and anisotropic covariance structures. With the help of the Voronoi tessellation, we construct a natural parametrization, that is, space as well as time resolution consistent, for data lying on irregular grid points. In the application, the statistical model combines forecasts of three other meteorological variables obtained from a numerical weather prediction model with past precipitation observations. The model is then used to predict three-hourly precipitation over 24 hours. It performs better than a separable, stationary and isotropic version, and it performs comparably to a deterministic numerical weather prediction model for precipitation and has the advantage that it quantifies prediction uncertainty.

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arXiv2012

Bridging the ensemble Kalman and particle filter

In many applications of Monte Carlo nonlinear filtering, the propagation step is computationally expensive, and hence, the sample size is limited. With small sample sizes, the update step becomes crucial. Particle filtering suffers from the well-known problem of sample degeneracy. Ensemble Kalman filtering avoids this, at the expense of treating non-Gaussian features of the forecast distribution incorrectly. Here we introduce a procedure which makes a continuous transition indexed by gamma in [0,1] between the ensemble and the particle filter update. We propose automatic choices of the parameter gamma such that the update stays as close as possible to the particle filter update subject to avoiding degeneracy. In various examples, we show that this procedure leads to updates which are able to handle non-Gaussian features of the prediction sample even in high-dimensional situations.

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arXiv2011

Approximate variances for tapered spectral estimates

We propose an approximation of the asymptotic variance that removes a certain discontinuity in the usual formula for the raw and the smoothed periodogram in case a data taper is used. It is based on an approximation of the covariance of the (tapered) periodogram at two arbitrary frequencies. Exact computations of the variances for a Gaussian white noise and an AR(4) process show that the approximation is more accurate than the usual formula.

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arXiv2008

A Conversation with Peter Huber

Peter J. Huber was born on March 25, 1934, in Wohlen, a small town in the Swiss countryside. He obtained a diploma in mathematics in 1958 and a Ph.D. in mathematics in 1961, both from ETH Zurich. His thesis was in pure mathematics, but he then decided to go into statistics. He spent 1961--1963 as a postdoc at the statistics department in Berkeley where he wrote his first and most famous paper on robust statistics, ``Robust Estimation of a Location Parameter.'' After a position as a visiting professor at Cornell University, he became a full professor at ETH Zurich. He worked at ETH until 1978, interspersed by visiting positions at Cornell, Yale, Princeton and Harvard. After leaving ETH, he held professor positions at Harvard University 1978--1988, at MIT 1988--1992, and finally at the University of Bayreuth from 1992 until his retirement in 1999. He now lives in Klosters, a village in the Grisons in the Swiss Alps. Peter Huber has published four books and over 70 papers on statistics and data analysis. In addition, he has written more than a dozen papers and two books on Babylonian mathematics, astronomy and history. In 1972, he delivered the Wald lectures. He is a fellow of the IMS, of the American Association for the Advancement of Science, and of the American Academy of Arts and Sciences. In 1988 he received a Humboldt Award and in 1994 an honorary doctorate from the University of Neuchâtel. In addition to his fundamental results in robust statistics, Peter Huber made important contributions to computational statistics, strategies in data analysis, and applications of statistics in fields such as crystallography, EEGs, and human growth curves.

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arXiv2006

Recursive Monte Carlo filters: Algorithms and theoretical analysis

Recursive Monte Carlo filters, also called particle filters, are a powerful tool to perform computations in general state space models. We discuss and compare the accept--reject version with the more common sampling importance resampling version of the algorithm. In particular, we show how auxiliary variable methods and stratification can be used in the accept--reject version, and we compare different resampling techniques. In a second part, we show laws of large numbers and a central limit theorem for these Monte Carlo filters by simple induction arguments that need only weak conditions. We also show that, under stronger conditions, the required sample size is independent of the length of the observed series.

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