Related papers: Adaptive nonparametric drift estimation for diffus…
The nonparametric volatility estimation problem of a scalar diffusion process observed at equidistant time points is addressed. Using the spectral representation of the volatility in terms of the invariant density and an eigenpair of the…
We study nonparametric estimation of the diffusion coefficient from discrete data, when the observations are blurred by additional noise. Such issues have been developed over the last 10 years in several application fields and in particular…
We consider the adaptive test for the parameter change in discretely observed ergodic diffusion processes based on the cusum test. Using two test statistics based on the two quasi-log likelihood functions of the diffusion parameter and the…
In this note, we connect two seemingly unrelated objects: On the one hand is a two-dimensional drift-diffusion process $X$ with divergence-free and time-independent drift $b$. The drift is given by a stationary Gaussian ensemble, and we…
Posterior drift refers to changes in the relationship between responses and covariates while the distributions of the covariates remain unchanged. In this work, we explore functional linear regression under posterior drift with transfer…
This paper studies a problem of Bayesian parameter estimation for a sequence of scaled counting processes whose weak limit is a Brownian motion with an unknown drift. The main result of the paper is that the limit of the posterior…
Recent works have shown an interest in investigating the frequentist asymptotic properties of Bayesian procedures for high-dimensional linear models under sparsity constraints. However, there exists a gap in the literature regarding…
We consider parametric estimation and tests for multi-dimensional diffusion processes with a small dispersion parameter $\varepsilon$ from discrete observations. For parametric estimation of diffusion processes, the main target is to…
Sampling from the posterior is a key technical problem in Bayesian statistics. Rigorous guarantees are difficult to obtain for Markov Chain Monte Carlo algorithms of common use. In this paper, we study an alternative class of algorithms…
Diffusion-based posterior samplers use pretrained diffusion priors to sample from measurement- or reward-conditioned posteriors, and are widely used for inverse problems. Yet their theoretical behavior remains poorly understood: even with…
We introduce verifiable criteria for weak posterior consistency of identifiable Bayesian nonparametric inference for jump diffusions with unit diffusion coefficient and uniformly Lipschitz drift and jump coefficients in arbitrary dimension.…
Parametric estimation for diffusion processes is considered for high frequency observations over a fixed time interval. The processes solve stochastic differential equations with an unknown parameter in the diffusion coefficient. We find…
We develop an encounter-based approach for describing restricted diffusion with a gradient drift towards a partially reactive boundary. For this purpose, we introduce an extension of the Dirichlet-to-Neumann operator and use its eigenbasis…
Besov priors are nonparametric priors that can model spatially inhomogeneous functions. They are routinely used in inverse problems and imaging, where they exhibit attractive sparsity-promoting and edge-preserving features. A recent line of…
Data attribution for generative models seeks to quantify the influence of individual training examples on model outputs. Existing methods for diffusion models typically require access to model gradients or retraining, limiting their…
We study the long-range effective drift and diffusivity of a particle in a random medium moving subject to a given molecular diffusivity and a local drift. The local drift models the effect of a random electrostatic field on a neutral but…
We derive rates of contraction of posterior distributions on nonparametric models resulting from sieve priors. The aim of the paper is to provide general conditions to get posterior rates when the parameter space has a general structure,…
In this paper, we consider the nonparametric estimation problem of the drift function of stochastic differential equations driven by $\alpha$-stable L\'{e}vy motion. First, the Kullback-Leibler divergence between the path probabilities of…
Parameter estimation in diffusion processes from discrete observations up to a first-hitting time is clearly of practical relevance, but does not seem to have been studied so far. In neuroscience, many models for the membrane potential…
We consider a problem of statistical estimation of an unknown drift parameter for a stochastic differential equation driven by fractional Brownian motion. Two estimators based on discrete observations of solution to the stochastic…