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We show that, in strongly chaotic dynamical systems, the average particle velocity can be calculated analytically by consideration of Brownian dynamics in phase space, the method of images and use of the classical diffusion equation. The…
When classical particle filtering algorithms are used for maximum likelihood parameter estimation in nonlinear state-space models, a key challenge is that estimates of the likelihood function and its derivatives are inherently noisy. The…
This paper considers M-estimation of a nonlinear regression model with multiple change-points occuring at unknown times. The multi-phase random design regression model, discontinuous in each change-point, have an arbitrary error $\epsilon$.…
Normalizing flows provide a general mechanism for defining expressive probability distributions, only requiring the specification of a (usually simple) base distribution and a series of bijective transformations. There has been much recent…
Estimating density ratios between pairs of intractable data distributions is a core problem in probabilistic modeling, enabling principled comparisons of sample likelihoods under different data-generating processes across conditions and…
Humans can easily describe, imagine, and, crucially, predict a wide variety of behaviors of liquids--splashing, squirting, gushing, sloshing, soaking, dripping, draining, trickling, pooling, and pouring--despite tremendous variability in…
In this paper we introduce a novel particle filter scheme for a class of partially-observed multivariate diffusions. %continuous-time dynamic models where the %signal is given by a multivariate diffusion process. We consider a variety of…
We develop an Euler-type particle method for the simulation of a McKean--Vlasov equation arising from a mean-field model with positive feedback from hitting a boundary. Under assumptions on the parameters which ensure differentiable…
Parameter estimation in linear errors-in-variables models typically requires that the measurement error distribution be known (or estimable from replicate data). A generalized method of moments approach can be used to estimate model…
The generalised linear model (GLM) is a very important tool for analysing real data in biology, sociology, agriculture, engineering and many other application domain where the relationship between the response and explanatory variables may…
We introduce manifold-learning flows (M-flows), a new class of generative models that simultaneously learn the data manifold as well as a tractable probability density on that manifold. Combining aspects of normalizing flows, GANs,…
Models for prediction of drag forces within a particle cloud following shock-acceleration are evaluated with the aid of results from particle-resolved simulations in order to quantify how much the disturbances introduced by the proximity of…
Particle deposition in fully-developed turbulent pipe flow is quantified taking into account uncertainty in electric charge, van der Waals strength, and temperature effects. A framework is presented for obtaining variance-based sensitivity…
A simple criterion is presented for a practical construction of generalized moments that allow one to approach the theoretical Rao-Cramer limit for parameter estimation while avoiding the complexity of the maximum likelihood method in the…
The stochastic motions of a diffusing particle contain information concerning the particle's interactions with binding partners and with its local environment. However, accurate determination of the underlying diffusive properties, beyond…
We describe a method to extract force and diffusion parameters from single trajectories of Brownian particles based on the principle of maximum likelihood. The analysis is well-suited for out-of-equilibrium trajectories, even when a limited…
We present a general framework for Bayesian estimation of incompletely observed multivariate diffusion processes. Observations are assumed to be discrete in time, noisy and incomplete. We assume the drift and diffusion coefficient depend on…
A recently introduced particle-based model for fluid dynamics with continuous velocities is generalized to model fluids with excluded volume effects. This is achieved through the use of biased stochastic multi-particle collisions which…
The method of maximum likelihood estimation (MLE) is a widely used statistical approach for estimating the values of one or more unknown parameters of a probabilistic model based on observed data. In this tutorial, I briefly review the…
We mainly study the M-estimation method for the high-dimensional linear regression model, and discuss the properties of M-estimator when the penalty term is the local linear approximation. In fact, M-estimation method is a framework, which…