Related papers: Hidden Markov model analysis for fluorescent time …
The statistics of the diffusive motion of particles often serve as an experimental proxy for their interaction with the environment. However, inferring the physical properties from the observed trajectories is challenging. Inspired by a…
We consider the filtering problem of estimating a hidden random variable $X$ by noisy observations. The noisy observation process is constructed by a randomised Markov bridge (RMB) $(Z_t)_{t\in [0,T]}$ of which terminal value is set to…
In this paper we prove that the asymptotic rate of exponential loss of memory of a finite state hidden Markov model is bounded above by the difference of the first two Lyapunov exponents of a certain product of matrices. We also show that…
We develop a (nearly) unbiased particle filtering algorithm for a specific class of continuous-time state-space models, such that (a) the latent process $X_t$ is a linear Gaussian diffusion; and (b) the observations arise from a Poisson…
Semiconductor nano-crystals, known as quantum dots (QDs), have attracted significant attention for their unique fluorescence properties. Under continuous excitation, QDs emit photons with intricate intensity fluctuation: the intensity of…
We propose an interferometric scheme for the estimation of a linear combination with non-negative weights of an arbitrary number $M>1$ of unknown phase delays, distributed across an $M$-channel linear optical network, with…
There is a lack of methodological results for continuous time change detection due to the challenges of noninformative prior specification and efficient posterior inference in this setting. Most methodologies to date assume data are…
The Hidden Quantum Markov Model (HQMM) has significant potential for analyzing time-series data and studying stochastic processes in the quantum domain as an upgrading option with potential advantages over classical Markov models. In this…
The hidden Markov model (HMM) provides a powerful framework for inference in time-varying environments, where the underlying state evolves according to a Markov chain. To address the optimal filtering problem in general dynamic settings, we…
Progressive diseases worsen over time and are characterised by monotonic change in features that track disease progression. Here we connect ideas from two formerly separate methodologies -- event-based and hidden Markov modelling -- to…
This report addresses state inference for hidden Markov models. These models rely on unobserved states, which often have a meaningful interpretation. This makes it necessary to develop diagnostic tools for quantification of state…
This paper proposes a probabilistic approach for the detection and the tracking of particles in fluorescent time-lapse imaging. In the presence of a very noised and poor-quality data, particles and trajectories can be characterized by an a…
We consider a Hidden Markov Model (HMM) where the integrated continuous-time Markov chain can be observed at discrete time points perturbed by a Brownian motion. The aim is to derive a filter for the underlying continuous-time Markov chain.…
We derive new concentration bounds for time averages of measurement outcomes in quantum Markov processes. This generalizes well-known bounds for classical Markov chains which provide constraints on finite time fluctuations of time-additive…
We present a method for describing and characterizing the state of N particles that may be distinguishable in principle but not in practice due to experimental limitations. The technique relies upon a careful treatment of the exchange…
Factorial hidden Markov models (FHMMs) are powerful tools of modeling sequential data. Learning FHMMs yields a challenging simultaneous model selection issue, i.e., selecting the number of multiple Markov chains and the dimensionality of…
We propose a robust framework for interpretable, few-shot analysis of non-stationary sequential data based on flexible graphical models to express the structured distribution of sequential events, using prototype radial basis function (RBF)…
A numerical modeling of the radiation emitted from a Luminescent dye embedded in a finite one-dimensional photonic crystal is presented. The Photonic Band Structure and the Photonic Density of States are derived using classical…
We introduce multiple hidden Markov models (MHMMs) where an observed multivariate categorical time series depends on an unobservable multivariate Mar- kov chain. MHMMs provide an elegant framework for specifying various independence…
We present a feature-resolved methodology to analyse the photoluminescence dynamics of single emitters using a combination of lifetime, spectral, and photon correlation analyses. By integrating conventional ensemble photon statistics…