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The availability of data sets with large numbers of variables is rapidly increasing. The effective application of Bayesian variable selection methods for regression with these data sets has proved difficult since available Markov chain…
Hidden Markov models can describe time series arising in various fields of science, by treating the data as noisy measurements of an arbitrarily complex Markov process. Sequential Monte Carlo (SMC) methods have become standard tools to…
In many scientific fields, such as economics and neuroscience, we are often faced with nonstationary time series, and concerned with both finding causal relations and forecasting the values of variables of interest, both of which are…
Leaving posterior sensitivity concerns aside, non-identifiability of the parameters does not raise a difficulty for Bayesian inference as far as the posterior is proper, but multi-modality or flat regions of the posterior induced by the…
A new method is introduced for analysis of interactions between time-dependent coupled oscillators, based on the signals they generate. It distinguishes unsynchronized dynamics from noise-induced phase slips, and enables the evolution of…
Causal discovery in time series is a rapidly evolving field with a wide variety of applications in other areas such as climate science and neuroscience. Traditional approaches assume a stationary causal graph, which can be adapted to…
We present a scalable approach to performing approximate fully Bayesian inference in generic state space models. The proposed method is an alternative to particle MCMC that provides fully Bayesian inference of both the dynamic latent states…
A Bayesian probability based approach is applied to the problem of detecting and parameterizing oscillations in the upper solar atmosphere for the first time. Due to its statistical origin, this method provides a mechanism for determining…
Functional concurrent, or varying-coefficient, regression models are commonly used in biomedical and clinical settings to investigate how the relation between an outcome and observed covariate varies as a function of another covariate. In…
In the following article we consider approximate Bayesian parameter inference for observation driven time series models. Such statistical models appear in a wide variety of applications, including econometrics and applied mathematics. This…
The aim of sequential change-point detection is to issue an alarm when it is thought that certain probabilistic properties of the monitored observations have changed. This work is concerned with nonparametric, closed-end testing procedures…
It is proposed in the literature that in some complicated problems maximum likelihood estimates (MLE) are not suitable or even do not exist. An alternative to MLE for estimation of the parameters is the Bayesian method. The Markov chain…
Fine-grained time series data are crucial for accurate and timely online change detection. While both collective anomalies and change points can coexist in such data, their joint online detection has received limited attention. In this…
We propose an analytical solution to the on-off problem within the framework of Bayesian statistics. Both the statistical significance for the discovery of new phenomena and credible intervals on model parameters are presented in a…
A method based on wavelet transform and genetic programming is proposed for characterizing and modeling variations at multiple scales in non-stationary time series. The cyclic variations, extracted by wavelets and smoothened by cubic…
Single-particle tracking allows to infer the motion of single molecules in living cells. When we observe a long trajectory (more than 100 points), it is possible that the particle switches mode of motion over time. Then, fitting a single…
Empirical time series often contain observational noise. We investigate the effect of this noise on the estimated parameters of models fitted to the data. For data of physiological tremor, i.e. a small amplitude oscillation of the…
We address the new problem of estimating a piece-wise constant signal with the purpose of detecting its change points and the levels of clusters. Our approach is to model it as a nonparametric penalized least square model selection on a…
Improving health worldwide will require rigorous quantification of population-level trends in health status. However, global-level surveys are not available, forcing researchers to rely on fragmentary country-specific data of varying…
Markov chains are simple yet powerful mathematical structures to model temporally dependent processes. They generally assume stationary data, i.e., fixed transition probabilities between observations/states. However, live, real-world…