Related papers: Information Geometry Approach to Parameter Estimat…
Hyperspectral images can be represented either as a set of images or as a set of spectra. Spectral classification and segmentation and data reduction are the main problems in hyperspectral image analysis. In this paper we propose a Bayesian…
Dynamical modelling lies at the heart of our understanding of physical systems. Its role in science is deeper than mere operational forecasting, in that it allows us to evaluate the adequacy of the mathematical structure of our models.…
Consider the problem of joint parameter estimation and prediction in a Markov random field: i.e., the model parameters are estimated on the basis of an initial set of data, and then the fitted model is used to perform prediction (e.g.,…
This work aims efficiently estimating the posterior distribution of kinetic parameters for dynamic positron emission tomography (PET) imaging given a measurement of time of activity curve. Considering the inherent information loss from…
The estimation of absorption time distributions of Markov jump processes is an important task in various branches of statistics and applied probability. While the time-homogeneous case is classic, the time-inhomogeneous case has recently…
Determining the adsorption isotherms is an issue of significant importance in preparative chromatography. A modern technique for estimating adsorption isotherms is to solve an inverse problem so that the simulated batch separation coincides…
In this paper, we provide a novel algorithm for solving planning and learning problems of Markov decision processes. The proposed algorithm follows a policy iteration-type update by using a rank-one approximation of the transition…
A possibly time-dependent transition intensity matrix or generator $(Q(t))$ characterizes the law of a Markov jump process (MP). For a time homogeneous MP, the transition probability matrix (TPM) can be expressed as a matrix exponential of…
Information geometry provides a geometric approach to families of statistical models. The key geometric structures are the Fisher quadratic form and the Amari-Chentsov tensor. In statistics, the notion of sufficient statistic expresses the…
Optimal designs minimize the number of experimental runs (samples) needed to accurately estimate model parameters, resulting in algorithms that, for instance, efficiently minimize parameter estimate variance. Governed by knowledge of past…
Implicit sampling is a weighted sampling method that is used in data assimilation, where one sequentially updates estimates of the state of a stochastic model based on a stream of noisy or incomplete data. Here we describe how to use…
When is keeping a memory of observations worthwhile? We use hidden Markov models to look at phase transitions that emerge when comparing state estimates in systems with discrete states and noisy observations. We infer the underlying state…
Many biological and medical questions can be modeled using time-to-event data in finite-state Markov chains, with the phase-type distribution describing intervals between events. We solve the inverse problem: given a phase-type…
Bayesian inference for models with intractable likelihoods, such as Markov random fields, poses a fundamental computational challenge due to the tradeoff between inferential accuracy and computational cost. Various MCMC methods have been…
In this paper, we propose a class of efficient, accurate, and general methods for solving state-estimation problems with equality and inequality constraints. The methods are based on recent developments in variable splitting and partially…
Markov random fields area popular model for high-dimensional probability distributions. Over the years, many mathematical, statistical and algorithmic problems on them have been studied. Until recently, the only known algorithms for…
Partially observable Markov decision processes (POMDPs) provide an elegant mathematical framework for modeling complex decision and planning problems in stochastic domains in which states of the system are observable only indirectly, via a…
Conformal prediction is a widely used method to quantify the uncertainty of a classifier under the assumption of exchangeability (e.g., IID data). We generalize conformal prediction to the Hidden Markov Model (HMM) framework where the…
We consider the problem of estimating filamentary structure from planar point process data. We make some connections with computational geometry and we develop nonparametric methods for estimating the filaments. We show that, under weak…
We provide a sufficient criterion for the unique parameter identification of combinatorially symmetric Hidden Markov Models based on the structure of their transition matrix. If the observed states of the chain form a zero forcing set of…