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We consider the use of randomised forward models and log-likelihoods within the Bayesian approach to inverse problems. Such random approximations to the exact forward model or log-likelihood arise naturally when a computationally expensive…
We study the convergence rates of empirical Bayes posterior distributions for nonparametric and high-dimensional inference. We show that as long as the hyperparameter set is discrete, the empirical Bayes posterior distribution induced by…
Stochastic processes are a flexible and widely used family of models for statistical modeling. While stochastic processes offer attractive properties such as inclusion of uncertainty properties, their inference is typically intractable,…
We extend the theory from Fan and Li (2001) on penalized likelihood-based estimation and model-selection to statistical and econometric models which allow for non-negativity constraints on some or all of the parameters, as well as…
We compare systematically several classes of stochastic volatility models of stock market fluctuations. We show that the long-time return distribution is either Gaussian or develops a power-law tail, while the short-time return distribution…
Volatility clustering is a common phenomenon in financial time series. Typically, linear models can be used to describe the temporal autocorrelation of the (logarithmic) variance of returns. Considering the difficulty in estimating this…
Traditional approaches to estimating beta in finance often involve rigid assumptions and fail to adequately capture beta dynamics, limiting their effectiveness in use cases like hedging. To address these limitations, we have developed a…
We introduce a class of Bayesian matrix dynamic factor models that accommodates time-varying volatility, outliers, and cross-sectional correlation in the idiosyncratic components. For model comparison, we employ an importance-sampling…
We consider the estimation of large covariance and precision matrices from high-dimensional sub-Gaussian or heavier-tailed observations with slowly decaying temporal dependence. The temporal dependence is allowed to be long-range so with…
We present elliptical processes, a family of non-parametric probabilistic models that subsume Gaussian processes and Student's t processes. This generalization includes a range of new heavy-tailed behaviors while retaining computational…
Given discrete time observations over a fixed time interval, we study a nonparametric Bayesian approach to estimation of the volatility coefficient of a stochastic differential equation. We postulate a histogram-type prior on the volatility…
Agents' heterogeneity is recognized as a driver mechanism for the persistence of financial volatility. We focus on the multiplicity of investment strategies' horizons, we embed this concept in a continuous time stochastic volatility…
Mixtures of linear mixed models are widely used for modelling longitudinal data for which observation times differ between subjects. In typical applications, temporal trends are described using a basis expansion, with basis coefficients…
Variational Bayes (VB) has been used to facilitate the calculation of the posterior distribution in the context of Bayesian inference of the parameters of nonlinear models from data. Previously an analytical formulation of VB has been…
Models for heteroskedastic data are relevant in a wide variety of applications ranging from financial time series to environmental statistics. However, the topic of modeling the variance function conditionally has not seen near as much…
We propose a unified, yet simple to code, non-conjugate variational Bayes algorithm for posterior approximation of generic Bayesian generalized mixed effect models. Specifically, we consider regression models identified by a linear…
A Bayesian non-parametric framework for studying time-to-event data is proposed, where the prior distribution is allowed to depend on an additional random source, and may update with the sample size. Such scenarios are natural, for…
The stochastic volatility model is a popular tool for modeling the volatility of assets. The model is a nonlinear and non-Gaussian state space model, and consequently is difficult to fit. Many approaches, both classical and Bayesian, have…
Multivariate point processes are widely applied to model event-type data such as natural disasters, online message exchanges, financial transactions or neuronal spike trains. One very popular point process model in which the probability of…
Meta-analysis is widely used to integrate results from multiple experiments to obtain generalized insights. Since meta-analysis datasets are often heteroscedastic due to varying subgroups and temporal heterogeneity arising from experiments…