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Non-linear latent variable models have become increasingly popular in a variety of applications. However, there has been little study on theoretical properties of these models. In this article, we study rates of posterior contraction in…

Thesis is devoted to the application of cumulant analysis in the estimation of impulse response functions for continuous time-invariant linear systems, including systems with inner noises. The main assumption of the work is the second-order…

The non-stationary evolution of observable quantities in complex systems can frequently be described as a juxtaposition of quasi-stationary spells. Given that standard theoretical and data analysis approaches usually rely on the assumption…

Standard model-based control design deteriorates when the system dynamics change during operation. To overcome this challenge, online and adaptive methods have been proposed in the literature. In this work, we consider the class of…

Although stochastic models driven by latent Markov processes are widely used, the classical importance sampling methods based on the exponential tilting for these models suffers from the difficulties in computing the eigenvalues and…

We consider varying-coefficient models for mixed synchronous and asynchronous longitudinal covariates, where asynchronicity refers to the misalignment of longitudinal measurement times within an individual. We propose three different…

In many practical applications, evaluating the joint impact of combinations of environmental variables is important for risk management and structural design analysis. When such variables are considered simultaneously, non-stationarity can…

Understanding and predicting environmental phenomena often requires the construction of spatio-temporal statistical models, which are typically Gaussian processes. A common assumption made on Gaussian processes is that of covariance…

The paper considers the problem of robust estimating a periodic function in a continuous time regression model with dependent disturbances given by a general square integrable semimartingale with unknown distribution. An example of such a…

Marginalization of latent variables or nuisance parameters is a fundamental aspect of Bayesian inference and uncertainty quantification. In this work, we focus on scalable marginalization of latent variables in modeling correlated data,…

The estimation of the covariance structure from a discretely observed multivariate Gaussian process under asynchronicity and noise is analysed under high-frequency asymptotics. Asymptotic lower and upper bounds are established for a general…

The asymptotic behavior of estimates and information criteria in linear models are studied in the context of hierarchically correlated sampling units. The work is motivated by biological data collected on species where autocorrelation is…

In this paper we study covariance estimation with missing data. We consider missing data mechanisms that can be independent of the data, or have a time varying dependency. Additionally, observed variables may have arbitrary (non uniform)…

We consider a discrete time semi-Markov process where the characteristics defining the process depend on a small perturbation parameter. It is assumed that the state space consists of one finite communicating class of states and, in…

We consider the problem of simultaneous variable selection and estimation in additive, partially linear models for longitudinal/clustered data. We propose an estimation procedure via polynomial splines to estimate the nonparametric…

A method is proposed for estimating the potential function of a non-parametric estimator for stationary and isotropic pairwise interaction point process. The relation between a pair potential and the corresponding Papangelou conditional…

This paper introduces the class of ambiguity sparse processes, containing subsets of popular nonstationary time series such as locally stationary, cyclostationary and uniformly modulated processes. The class also contains aggregations of…

We develop a timescale synthesis-based probabilistic approach for the modeling of locally stationary signals. Inspired by our previous work, the model involves zero-mean, complex Gaussian wavelet coefficients, whose distribution varies as a…

Hierarchical parametric models consisting of observable and latent variables are widely used for unsupervised learning tasks. For example, a mixture model is a representative hierarchical model for clustering. From the statistical point of…

This paper considers a semiparametric approach within the general Bayesian linear model where the innovations consist of a stationary, mean zero Gaussian time series. While a parametric prior is specified for the linear model coefficients,…