Linear State Space Modeling of Gamma-Ray Burst Lightcurves

Linear State Space Modeling determines the hidden autoregressive (AR) process in a noisy time series; for an AR process the time series' current value is the sum of current stochastic ``noise'' and a linear combination of previous values. We present preliminary results from modeling a sample of 4 channel BATSE LAD lightcurves. We determine the order of the AR process necessary to model the bursts. The comparison of decay constants for different energy bands shows that structure decays more rapidly at high energy. The resulting models can be interpreted physically; for example, they may reveal the response of the burst emission region to the injection of energy.Comment: 5 pages, 2 figures, AIPPROC LaTeX, to appear in "Gamma-Ray Bursts, 4th Huntsville Symposium," eds. C. Meegan, R. Preece and T. Koshu

Estimating hidden semi-Markov chains from discrete sequences.

International audienceThis article addresses the estimation of hidden semi-Markov chains from nonstationary discrete sequences. Hidden semi-Markov chains are particularly useful to model the succession of homogeneous zones or segments along sequences. A discrete hidden semi-Markov chain is composed of a nonobservable state process, which is a semi-Markov chain, and a discrete output process. Hidden semi-Markov chains generalize hidden Markov chains and enable the modeling of various durational structures. From an algorithmic point of view, a new forward-backward algorithm is proposed whose complexity is similar to that of the Viterbi algorithm in terms of sequence length (quadratic in the worst case in time and linear in space). This opens the way to the maximum likelihood estimation of hidden semi-Markov chains from long sequences. This statistical modeling approach is illustrated by the analysis of branching and flowering patterns in plants