Period Analysis using the Least Absolute Shrinkage and Selection Operator (Lasso)

We introduced least absolute shrinkage and selection operator (lasso) in obtaining periodic signals in unevenly spaced time-series data. A very simple formulation with a combination of a large set of sine and cosine functions has been shown to yield a very robust estimate, and the peaks in the resultant power spectra were very sharp. We studied the response of lasso to low signal-to-noise data, asymmetric signals and very closely separated multiple signals. When the length of the observation is sufficiently long, all of them were not serious obstacles to lasso. We analyzed the 100-year visual observations of delta Cep, and obtained a very accurate period of 5.366326(16) d. The error in period estimation was several times smaller than in Phase Dispersion Minimization. We also modeled the historical data of R Sct, and obtained a reasonable fit to the data. The model, however, lost its predictive ability after the end of the interval used for modeling, which is probably a result of chaotic nature of the pulsations of this star. We also provide a sample R code for making this analysis.Comment: 9 pages, 13 figures, accepted for publication in PAS

Approximate cross-validation formula for Bayesian linear regression

Cross-validation (CV) is a technique for evaluating the ability of statistical models/learning systems based on a given data set. Despite its wide applicability, the rather heavy computational cost can prevent its use as the system size grows. To resolve this difficulty in the case of Bayesian linear regression, we develop a formula for evaluating the leave-one-out CV error approximately without actually performing CV. The usefulness of the developed formula is tested by statistical mechanical analysis for a synthetic model. This is confirmed by application to a real-world supernova data set as well.Comment: 5 pages, 2 figures, invited paper for Allerton2016 conferenc

Characterization of Dwarf Novae Using SDSS Colors

We have developed a method for estimating the orbital periods of dwarf novae from the Sloan Digital Sky Survey (SDSS) colors in quiescence using an artificial neural network. For typical objects below the period gap with sufficient photometric accuracy, we were able to estimate the orbital periods with an accuracy to a 1 sigma error of 22 %. The error of estimation is worse for systems with longer orbital periods. We have also developed a neural-network-based method for categorical classification. This method has proven to be efficient in classifying objects into three categories (WZ Sge type, SU UMa type and SS Cyg/Z Cam type) and works for very faint objects to a limit of g=21. Using this method, we have investigated the distribution of the orbital periods of dwarf novae from a modern transient survey (Catalina Real-Time Survey). Using Bayesian analysis developed by Uemura et al. (2010, arXiv:1003.0945), we have found that the present sample tends to give a flatter distribution toward the shortest period and a shorter estimate of the period minimum, which may have resulted from the uncertainties in the neural network analysis and photometric errors. We also provide estimated orbital periods, estimated classifications and supplementary information on known dwarf novae with quiescent SDSS photometry.Comment: 70 pages, 7 figures, Accepted for publication in PASJ, minor correction

Discovery of a short plateau phase in the early evolution of a gamma-ray burst afterglow

We report optical observations during the first hour of the gamma-ray burst (GRB) afterglow of GRB021004. Our observation revealed the existence of a short plateau phase, in which the afterglow remained at almost constant brightness, before an ordinary rapid fading phase. This plateau phase lasted for about 2 hours from 0.024 to 0.10 d after the burst, which corresponds to a missing blank of the early afterglow light curve of GRB990123. We propose that the plateau phase can be interpreted as the natural evolution of synchrotron emission from the forward shock region of a blast wave. The time when the typical frequency of the synchrotron emission passes through the optical range has been predicted to be about 0.1 d after the burst, which is consistent with the observed light curve. Our scenario hence implies that the observed feature in GRB021004 is a common nature of GRB afterglows.Comment: 3 pages, 1 figure, accepted for publication in PAS