1,721,100 research outputs found
Explicit-duration Hidden Markov Models for quantum state estimation
Full text linkAn explicit-duration Hidden Markov Model with a nonparametric kernel estimator of
the state duration distribution is specified. The motivation comes from the physical
problem of extracting the maximum information from an open quantum system subject
to an external perturbation, which induces a change in the dynamics of the system.
A nonparametric kernel estimator for discrete data is introduced, which is consistent
and improves the estimates accuracy in presence of sparse data. To reconstruct the
hidden dynamics, a Viterbi algorithm is used, which is robust against the underflow
problem. Finite sample properties are investigated through an extensive Monte Carlo
study showing that our formulation outperforms the original one both in small and in
large samples
Quasi Maximum Likelihood Estimation of Value at Risk and Expected Shortfall
No full textQuasi maximum likelihood estimation of Value at Risk (VaR) and Expected Shortfall (ES) is
discussed. The reference likelihood is that of a location-scale asymmetric Laplace distribution, related to a family of loss functions that lead to strictly consistent scoring functions
for joint estimation of VaR and ES. The case of zero mean processes is considered, where
quasi maximum likelihood estimators (QMLE) are consistent and asymptotically normal, as
well as the case of non-zero mean processes, where quasi maximum likelihood estimators lead to inconsistent estimates due to lack of identification. In the latter situation, the
asymptotic properties of two stage quasi maximum likelihood estimators (2SQMLE) are
derived. QMLE and 2SQMLE are related with sample and M-estimators and compared in
terms of asymptotic efficiency. A simulation study investigates the finite sample properties
of QMLE, 2SQMLE, sample and M-estimators of expected shortfall
The Hammersley–Chapman–Robbins inequality for repeatedly monitored quantum system
Full text linkWe derive the Hammersley–Chapman–Robbins inequality for discrete quantum parameter
models in the presence of time dependent measurements. The extension determines
a discrete counterpart of the classical Fisher information. We provide an illustration
concerning a quantum optics problem
Discussion of the paper: Bayesian Spatiotemporal Modeling Using Hierarchical Spatial Priors, with Applications to Functional Magnetic Resonance Imaging
No full textGeneralized linear spectral models
No full textIn this chapter we consider a class of parametric spectrum esti- mators based on a generalized linear model for exponential random variables with power link. The power transformation of the spectrum of a stationary process can be expanded in a Fourier series, with the coefficients representing generalised autocovariances. Direct Whittle estimation of the coefficients is generally unfeasible, as they are subject to constraints (the autocovariances need to be a positive semidefinite sequence). The problem can be overcome by using an ARMA repre- sentation for the power transformation of the spectrum. Estimation is carried out by maximising the Whittle likelihood, whereas the se- lection of a spectral model, as a function of the power transformation parameter and the ARMA orders, can be carried out by information criteria. The proposed methods are applied to the estimation of the inverse autocorrelation function and the related problem of selecting the optimal interpolator, and for the identification of spectral peaks. More generally, they can be applied to spectral estimation with pos- sibly misspecified models
Fused graphical lasso for brain networks with symmetries
Full text linkNeuroimaging is the growing area of neuroscience devoted to produce data with the goal of capturing processes and dynamics of the human brain. We consider the problem of inferring the brain connectivity network from time- dependent functional magnetic resonance imaging (fMRI) scans. To this aim we propose the symmetric graphical lasso, a penalized likelihood method with a fused type penalty function that takes into explicit account the natural symmetrical structure of the brain. Symmetric graphical lasso allows one to learn simultaneously both the network structure and a set of symmetries across the two hemispheres. We implement an alternating directions method of multipliers algorithm to solve the corresponding convex optimization problem. Furthermore, we apply our methods to estimate the brain networks of two subjects, one healthy and one affected by mental disorder, and to compare them with respect to their symmetric structure. The method applies once the temporal dependence characterizing fMRI data have been accounted for and we compare the impact on the analysis of different detrending techniques on the estimated brain networks. Although we focus on brain networks, symmetric graphical lasso is a tool which can be more generally applied to learn multiple networks in a context of dependent samples
Generalised Linear Cepstral Models for the Spectrum of a Time Series
Full text linkThe paper introduces the class of generalised linear models with Box-Cox link for the spectrum of a time series. The Box-Cox transformation of the spectral density is represented as a finite Fourier polynomial, with coefficients, that we term generalised cepstral coefficients, providing a complete characterisation of the properties of the random process. The link function depends on a power transformation parameter and encompasses the exponential model (logarithmic link), the autoregressive model (inverse link), and the moving average model (identity link). One of the merits of this model class is the possibility of nesting alternative spectral estimation methods under the same likelihood-based framework, so that the selection of a particular parametric spectrum amounts to estimating the transformation parameter. We also show that the generalised cepstral coefficients are a one to one function of the inverse partial autocorrelations of the process, which can be used to evaluate the mutual information between the past and the future of the process
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