Related papers: Asymptotic theory for the detection of mixing in a…
A mathematical model is proposed where the classical Maxwell-Stefan diffusion model for gas mixtures is coupled to an advection-type equation for the temperature of the physical system. This coupled system is derived from first principles…
Detection of sparse signals arises in a wide range of modern scientific studies. The focus so far has been mainly on Gaussian mixture models. In this paper, we consider the detection problem under a general sparse mixture model and obtain…
The paper concerns the asymptotic distribution of the mixture density estimator, proposed by Oppenheim et al 2006, in the aggregation/disaggregation problem of random parameter AR(1) process. We prove that, under mild conditions on the…
We develop a Bayesian inference method for diffusions observed discretely and with noise, which is free of discretisation bias. Unlike existing unbiased inference methods, our method does not rely on exact simulation techniques. Instead,…
We consider statistical inference for a class of mixed-effects models with system noise described by a non-Gaussian integrated Ornstein-Uhlenbeck process. Under the asymptotics where the number of individuals goes to infinity with possibly…
To improve the identification of potential anomaly patterns in complex user behavior, this paper proposes an anomaly detection method based on a deep mixture density network. The method constructs a Gaussian mixture model parameterized by a…
We introduce a novel technique to find the asymptotic time behaviour of deterministic systems exhibiting anomalous diffusion. The procedure is tested for various classes of simple but physically relevant 1-D maps and possible relevance of…
We study parametric inference for diffusion processes when observations occur nonsynchronously and are contaminated by market microstructure noise. We construct a quasi-likelihood function and study asymptotic mixed normality of…
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 give a new algorithm for learning mixtures of $k$ Gaussians (with identity covariance in $\mathbb{R}^n$) to TV error $\varepsilon$, with quasi-polynomial ($O(n^{\text{poly\,log}\left(\frac{n+k}{\varepsilon}\right)})$) time and sample…
We consider a unified framework of sequential change-point detection and hypothesis testing modeled by means of hidden Markov chains. One observes a sequence of random variables whose distributions are functionals of a hidden Markov chain.…
This work is concerned with the detection of a mixture distribution from a $\mathbb{R}$-valued sample. Given a sample $X_1,\dots,X_n$ and an even density $\phi$, our aim is to detect whether the sample distribution is $\phi(\cdot-\mu)$ for…
We study maximum-likelihood-type estimation for diffusion processes when the coefficients are nonrandom and observation occurs in nonsynchronous manner. The problem of nonsynchronous observations is important when we consider the analysis…
The Gaussian mixed-effects model driven by a stationary integrated Ornstein-Uhlenbeck process has been used for analyzing longitudinal data having an explicit and simple serial-correlation structure in each individual. However, the…
Nonparametric estimation of a mixing density based on observations from the corresponding mixture is a challenging statistical problem. This paper surveys the literature on a fast, recursive estimator based on the predictive recursion…
When we use the normal mixture model, the optimal number of the components describing the data should be determined. Testing homogeneity is good for this purpose; however, to construct its theory is challenging, since the test statistic…
In this paper Gaussian models of retarded and accelerated anomalous diffusion are considered. Stochastic differential equations of fractional order driven by single or multiple fractional Gaussian noise terms are introduced to describe…
Diffusion models, which convert noise into new data instances by learning to reverse a diffusion process, have become a cornerstone in contemporary generative modeling. In this work, we develop non-asymptotic convergence theory for a…
Diffusion models have found valuable applications in anomaly detection by capturing the nominal data distribution and identifying anomalies via reconstruction. Despite their merits, they struggle to localize anomalies of varying scales,…
We propose a novel approach to the recognition of particular classes of non-conventional events in signals from phase-sensitive optical time-domain-reflectometry-based sensors. Our algorithmic solution has two main features: filtering aimed…