Related papers: State and parameter estimation using Monte Carlo e…
A large variety of dynamical systems, such as chemical and biomolecular systems, can be seen as networks of nonlinear entities. Prediction, control, and identification of such nonlinear networks require knowledge of the state of the system.…
Particle Markov Chain Monte Carlo methods are used to carry out inference in non-linear and non-Gaussian state space models, where the posterior density of the states is approximated using particles. Current approaches usually perform…
In this paper, we begin our discussion with some of the well-known methods available in the literature for the estimation of the parameters of a univariate/multivariate stable distribution. Based on the available methods, a new hybrid…
Information theoretic measures (entropies, entropy rates, mutual information) are nowadays commonly used in statistical signal processing for real-world data analysis. The present work proposes the use of Auto Mutual Information (Mutual…
Implicit sampling is a weighted sampling method that is used in data assimilation, where one sequentially updates estimates of the state of a stochastic model based on a stream of noisy or incomplete data. Here we describe how to use…
This article investigates stochastic epidemic models with partial information and addresses the estimation of current values of not directly observable states. The latter is also called nowcasting and related to the so-called "dark figure"…
State-space models provide an important body of techniques for analyzing time-series, but their use requires estimating unobserved states. The optimal estimate of the state is its conditional expectation given the observation histories, and…
We present a method of parameter estimation for large class of nonlinear systems, namely those in which the state consists of output derivatives and the flow is linear in the parameter. The method, which solves for the unknown parameter by…
Monte Carlo sampling of any system may be analyzed in terms of an associated glass model -- a variant of the Random Energy Model -- with, whenever there is a sign problem, complex fields. This model has three types of phases (liquid, frozen…
One of the pivotal tasks in scientific machine learning is to represent underlying dynamical systems from time series data. Many methods for such dynamics learning explicitly require the derivatives of state data, which are not directly…
This paper introduces a probabilistic approach for tracking the dynamics of unweighted and directed graphs using state-space models (SSMs). Unlike conventional topology inference methods that assume static graphs and generate point-wise…
The dynamics of systems of many degrees of freedom evolving on multiple scales are often modeled in terms of stochastic differential equations. Usually the structural form of these equations is unknown and the only manifestation of the…
In stochastic processes with absorbing states, the quasi-stationary distribution provides valuable insights into the long-term behaviour prior to absorption. In this work, we revisit two well-established numerical methods for its…
We consider the problem of estimating parameters of stochastic differential equations (SDEs) with discrete-time observations that are either completely or partially observed. The transition density between two observations is generally…
In this paper, we develop methods of nonlinear filtering and prediction of an unobservable Markov chain with a finite set of states. This Markov chain controls coefficients of AR(p) model. Using observations generated by AR(p) model we have…
State estimation for a class of linear time-invariant systems with distributed output measurements (distributed sensors) and unknown inputs is addressed in this paper. The objective is to design a network of observers such that the state…
This paper is devoted to the offline multiple changes detection for long-range dependence processes. The observations are supposed to satisfy a semi-parametric long-range dependence assumption with distinct memory parameters on each stage.…
A dynamical system is observable if there is a one-to-one mapping from the system's measured outputs and inputs to all of the system's states. Analytical and empirical tools exist for quantifying the (full state) observability of linear and…
Online parameter identification is of importance, e.g., for model predictive control. Since the parameters have to be identified simultaneously to the process of the modeled system, dynamical update laws are used for state and parameter…
Partial identification approaches are a flexible and robust alternative to standard point-identification approaches in general instrumental variable models. However, this flexibility comes at the cost of a ``curse of cardinality'': the…