Related papers: Efficient Bayesian inference for long memory proce…

This paper reviews recent developments of robust estimation in linear time series models, with short and long memory correlation structures, in the presence of additive outliers. Based on the manuscripts Fajardo et al. (2009) and…

We make an observation that facilitates exact likelihood-based inference for the parameters of the popular ARFIMA model without requiring stationarity by allowing the upper bound $\bar{d}$ for the memory parameter $d$ to exceed $0.5$:…

Across many domains of science, stochastic models are an essential tool to understand the mechanisms underlying empirically observed data. Models can be of different levels of detail and accuracy, with models of high-fidelity (i.e., high…

We analyze the dynamics of an algorithm for approximate inference with large Gaussian latent variable models in a student-teacher scenario. To model nontrivial dependencies between the latent variables, we assume random covariance matrices…

Likelihood-based inference in stochastic non-linear dynamical systems, such as those found in chemical reaction networks and biological clock systems, is inherently complex and has largely been limited to small and unrealistically simple…

Estimating the parameters of mathematical models is a common problem in almost all branches of science. However, this problem can prove notably difficult when processes and model descriptions become increasingly complex and an explicit…

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…

Selection bias arises when the probability that an observation enters a dataset depends on variables related to the quantities of interest, leading to systematic distortions in estimation and uncertainty quantification. For example, in…

Quantifying and reducing uncertainty in Earth system model parameterizations is essential to improving their reliability in decision-making. Forward uncertainty propagation is used to derive parameter sensitivity but requires physically…

Modelling physical data with linear discrete time series, namely Fractionally Integrated Autoregressive Moving Average (ARFIMA), is a technique which achieved attention in recent years. However, these models are used mainly as a statistical…

Long memory processes driven by L\'evy noise with finite second-order moments have been well studied in the literature. They form a very rich class of processes presenting an autocovariance function which decays like a power function. Here,…

Pervasive across diverse domains, stochastic systems exhibit fluctuations in processes ranging from molecular dynamics to climate phenomena. The Langevin equation has served as a common mathematical model for studying such systems, enabling…

Mediation analysis aims to separate the indirect effect through mediators from the direct effect of the exposure on the outcome. It is challenging to perform mediation analysis with neuroimaging data which involves high dimensionality,…

We investigate minimax results for the anisotropic functional deconvolution model when observations are affected by the presence of long-memory. Under specific conditions about the covariance matrices of the errors, we follow a standard…

Automatic machine learning of empirical models from experimental data has recently become possible as a result of increased availability of computational power and dedicated algorithms. Despite the successes of non-parametric inference and…

Inference for mechanistic models is challenging because of nonlinear interactions between model parameters and a lack of identifiability. Here we focus on a specific class of mechanistic models, which we term stable differential equations.…

Branching Time Active Inference (Champion et al., 2021b,a) is a framework proposing to look at planning as a form of Bayesian model expansion. Its root can be found in Active Inference (Friston et al., 2016; Da Costa et al., 2020; Champion…

Memory effects are a key feature in the description of the dynamical systems governed by the generalized Langevin equation, which presents an exact reformulation of the equation of motion. A simple measure for the estimation of memory…

For a multivariate stationary process, we develop explicit representations for the finite predictor coefficient matrices, the finite prediction error covariance matrices and the partial autocorrelation function (PACF) in terms of the…

Motivated by the application to German interest rates, we propose a timevarying autoregressive model for short and long term prediction of time series that exhibit a temporary non-stationary behavior but are assumed to mean revert in the…