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Nonsinusoidal oscillatory signals are everywhere. In practice, the nonsinusoidal oscillatory pattern, modeled as a 1-periodic wave-shape function (WSF), might vary from cycle to cycle. When there are finite different WSFs, $s_1,\ldots,s_K$,…
We propose a Bayesian hidden Markov model for analyzing time series and sequential data where a special structure of the transition probability matrix is embedded to model explicit-duration semi-Markovian dynamics. Our formulation allows…
We develop the methodology and a detailed case study in use of a class of Bayesian predictive synthesis (BPS) models for multivariate time series forecasting. This extends the recently introduced foundational framework of BPS to the…
The remarkable generalization performance of large-scale models has been challenging the conventional wisdom of the statistical learning theory. Although recent theoretical studies have shed light on this behavior in linear models and…
Functional data analysis, which models data as realizations of random functions over a continuum, has emerged as a useful tool for time series data. Often, the goal is to infer the dynamic connections (or time-varying conditional…
Multivariate spatial fields are of interest in many applications, including climate model emulation. Not only can the marginal spatial fields be subject to nonstationarity, but the dependence structure among the marginal fields and between…
This article discusses a partially adapted particle filter for estimating the likelihood of a nonlinear structural econometric state space models whose state transition density cannot be expressed in closed form. The filter generates the…
This paper deals with inference and prediction for multiple correlated time series, where one has also the choice of using a candidate pool of contemporaneous predictors for each target series. Starting with a structural model for the…
We study a generalized geometric Brownian motion framework that incorporates both entries of new units and exit mechanisms for the current population, extending earlier stochastic resetting models where these rates are treated as identical.…
The parameters of a discrete stationary Markov model are transition probabilities between states. Traditionally, data consist in sequences of observed states for a given number of individuals over the whole observation period. In such a…
Spatio-temporal prediction of levels of an environmental exposure is an important problem in environmental epidemiology. Our work is motivated by multiple studies on the spatio-temporal distribution of mobile source, or traffic related,…
This paper introduces the novel class of modulated cyclostationary processes, a class of non-stationary processes exhibiting frequency coupling, and proposes a method of their estimation from repeated trials. Cyclostationary processes also…
Stationary points embedded in the derivatives are often critical for a model to be interpretable and may be considered as key features of interest in many applications. We propose a semiparametric Bayesian model to efficiently infer the…
The paper introduces a general framework for statistical analysis of functional time series from a Bayesian perspective. The proposed approach, based on an extension of the popular dynamic linear model to Banach-space valued observations…
Nonstationary time series data exist in various scientific disciplines, including environmental science, biology, signal processing, econometrics, among others. Many Bayesian models have been developed to handle nonstationary time series.…
In this paper, we study two standard (Keynesian) dynamic macroeconomic models (one is piecewise linear and the other is nonlinear). Our purpose is twofold: (1)~For each model, we give a complete characterisation for the existence of a…
This paper focuses on modeling the dynamic attributes of a dynamic network with a fixed number of vertices. These attributes are considered as time series which dependency structure is influenced by the underlying network. They are modeled…
The analysis of data from multiple experiments, such as observations of several individuals, is commonly approached using mixed-effects models, which account for variation between individuals through hierarchical representations. This makes…
$\alpha$-stable distributions are utilised as models for heavy-tailed noise in many areas of statistics, finance and signal processing engineering. However, in general, neither univariate nor multivariate $\alpha$-stable models admit closed…
Multi-state models are frequently applied for representing processes evolving through a discrete set of state. Important classes of multi-state models arise when transitions between states may depend on the time since entry into the current…