We show how probabilistic numerics can be used to convert an initial value problem into a Gauss–Markov process parametrised by the dynamics of the initial value problem. Consequently, the often difficult problem of parameter estimation in ordinary differential equations is reduced to hyper-parameter estimation in Gauss–Markov regression, which tends to be considerably easier. The method’s relation

This article studies the maximum likelihood estimates of magnitude and scale parameters for a Gaussian process of Ornstein-Uhlenbeck type used to model a deterministic function that does not have to be a realisation of an Ornstein- Uhlenbeck process. Specifically, we derive explicit expressions for the limiting values of the maximum likelihood estimates as the number of observations increases. The

Probabilistic numerical solvers for ordinary differential equations compute posterior distributions over the solution of an initial value problem via Bayesian inference. In this paper, we leverage their probabilistic formulation to seamlessly include additional information as general likelihood terms. We show that second-order differential equations should be directly provided to the solver, inste

In this letter, we consider Gaussian approximations of the optimal importance density in sequential importance sampling for nonlinear, non-Gaussian state-space models. The proposed method is based on generalized statistical linear regression and posterior linearization using conditional expectations. Simulation results show that the method outperforms the compared methods in terms of the effective

In this article, we address the problem of estimating the state and learning of the parameters in a linear dynamic system with generalized L 1 -regularization. Assuming a sparsity prior on the state, the joint state estimation and parameter learning problem is cast as an unconstrained optimization problem. However, when the dimensionality of state or parameters is large, memory requirements and co

In this paper, we develop a novel method for approximate continuous-discrete Bayesian filtering. The projection filtering framework is exploited to develop accurate approximations of posterior distributions within parametric classes of probability distributions. This is done by formulating an ordinary differential equation for the posterior distribution that has the prior as initial value and hits

In this paper, the connection between the Matérn kernel and scale mixtures of squared exponential kernels is explored. It is shown that the Matérn kernel can be approximated by a finite scale mixture of squared exponential kernels through a quadrature approximation which in turn allows for (i) state space approximations of the Matérn kernel for arbitrary smoothness parameters using established sta

In this paper the issue of filtering and smoothing in continuous discrete time is studied when the state variable evolves in some submanifold of Euclidean space, which may not have the usual Lebesgue measure. Formal expressions for prediction and smoothing problems are reviewed, which agree with the classical results except that the formal adjoint of the generator is different in general. These re

Microelectromechanical-systems-based inertial sensors and magnetometers are low-cost, off-the-shelf sensors that are widely used in both consumer and industrial applications. However, these sensors suffer from biases and effects such as axis misalignment or scale errors, which require careful system design and periodic sensor calibration. In this paper, we propose a fast calibration method for joi

This paper is concerned with inferring the state of a Itô stochastic differential equation (SDE) from noisy discrete-time measurements. The problem is approached by considering basis function expansions of Brownian motion, that as a consequence give approximations to the underlying stochastic differential equation in terms of an ordinary differential equation with random coefficients. This allows

Alla blir vi rädda någon gång, både människor och djur. Ibland är det samma saker som skrämmer och ibland är det något helt annat som djuren tycker är läskigt.Vad gör djuren när de blir skrämda? Kanske gömmer de sig? Försöker de springa därifrån? Eller försöker djuren lura den som skräms att titta åt ett helt annat håll? Ska vi kolla hur djuren gör?Vad gör djuren när de blir rädda? är en bok som g

This extended abstract compiles statistics and information regarding the process of gathering water damage statistics. A questionnaire wasused to determine similarities, differences, and tendencies in the water damage statistics, in the Nordic countries Sweden, Norway, Denmark,Finland and Iceland. The study aimed to answer what lessons were learned and what knowledge could be shared between the No

Third Party Funding (TPF) is presented as a tool to help fund the cost of expensive litigation. In the context of Investment Arbitration, however, TPF has instead led to the commodification of justice, and raises concerns around its assetization. Arbitration often comes at a net loss for States, and the extraordinary expenditures required my pique the interest of third party funders who wish to pr

The emergence of nodding syndrome (NS) in Northern Uganda has generated controversial views with respect to patterns, natural history, and aetiology of the disease which is yet unknown. This study explored spatial patterns of NS using spatial-temporal methods to establish its clustering patterns across both space and time. Village and year of NS onset for individual patients between the years 1990

Socialminister Hallengren måste ompröva sin ståndpunkt. Att utesluta kriminaliseringen av narkotikabruk från den kommande utredningen vore ett allvarligt misstag, menar experterna Björn Johnson och Petter Karlsson.

This paper extends the half-panel jackknife (HPJ) estimator to GMM models with fixed effects. The Monte Carlo results show that the HPJ significantly reduces finite-sample bias for both the difference and system GMM estimators of the dynamic panel model.

The compelling images and promises attached to autonomous drive vehicles can easily create an impression that one can speak of a radical distinction between a self-driving future and a manual-driving present. Yet today’s drivers can already refer to their everyday driving as being experienced as though on ‘auto-pilot’, in which they are able to drive their cars while lost in things such as daydrea

Om mordet på Caesar.