2. The basic principles of Tycho de-censoring
The mean and magnitudes must be derived by taking the missing measurements into account. Various techniques for solving statistical problems involving missing data were developped during the last decades (Little & Rubin 1987). Some of them were successfully applied in astronomy (Feigelson & Nelson 1985, Isobe et al. 1986). According to the definition given by Kendall & Stuart (1961), the data in Tycho photometry are affected by a "Type I censoring", since the measurements smaller than a threshold were lost. However, their treatment is rather complicated, because two different censorings must be considered: the censoring coming from detection, that depends on the photon counts in the T channel, and, when a transit is detected, the censoring coming from the possible failure to evaluate the signal amplitude in or in . Moreover, the censoring threshold is not constant, but it depends on the circumstances of the transits: the most important ones are the slit group, and the background in the photon counts. Therefore, an iteration technique is preferred to the sophisticated methods of "survival analysis" presented in the papers mentioned above.
The algorithm is based on a model describing the data acquisition. The model is used to compute the mean luminosity corresponding to each censored measurement, assuming the and magnitudes of the star are known. The mean luminosities are imputed to the censored measurements. The next step is the calculation of the mean and magnitude of the star, taking all transits into account. The values thus obtained are input for another iteration, until the calculation has converged.
© European Southern Observatory (ESO) 1997
Online publication: May 5, 1998