Difference between revisions of "Scary words"
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Here are the "scary words" describing in formal terms what you do to a time series data set to find the periodic objects: | Here are the "scary words" describing in formal terms what you do to a time series data set to find the periodic objects: | ||
| − | We used the standard methodology for finding a periodic signal in unevenly sampled data described by Scargle (1982, ApJ, 263, 835), Horne & Baliunas (1986, ApJ, 302, 757), Gilliland & Baliunas (1987, ApJ, 314, 766), and more generally by Press et al. (1992, Numerical Recipes in C (2d ed.; Cambridge: Cambridge Univ. Press)). The algorithm calculates the Lomb normalized periodogram for the data stream and assigns a significance (false-alarm probability, FAP) based on the peak height in the periodogram. However, the generalized prescription for assigning the FAP assumes that each point in the data stream is statistically independent. As Stassun et al. (1999, AJ, 117, 2941) and Herbst & Wittenmyer (1996, BAAS, 189, No. 49.08) point out, this is not necessarily a good assumption for our specific case of young stars, as there are likely to be fluctuations intrinsic to the source that are not periodic, but which may be correlated over some of the timescales sampled. In order to understand how best to set the FAP for our data, we carried out Monte Carlo experiments with both uncorrelated and correlated Gaussian noise, as described in Rebull (2001, AJ, 121, 1676). | + | We used the standard methodology for finding a periodic signal in unevenly sampled data described by Scargle (1982, ApJ, 263, 835), Horne & Baliunas (1986, ApJ, 302, 757), Gilliland & Baliunas (1987, ApJ, 314, 766), and more generally by Press et al. (1992, Numerical Recipes in C (2d ed.; Cambridge: Cambridge Univ. Press)). The algorithm calculates the Lomb normalized periodogram for the data stream and assigns a significance (false-alarm probability, FAP) based on the peak height in the periodogram. However, the generalized prescription for assigning the FAP assumes that each point in the data stream is statistically independent. As Stassun et al. (1999, AJ, 117, 2941) and Herbst & Wittenmyer (1996, BAAS, 189, No. 49.08) point out, this is not necessarily a good assumption for our specific case of young stars, as there are likely to be fluctuations intrinsic to the source that are not periodic, but which may be correlated over some of the timescales sampled. In order to understand how best to set the FAP for our data, we carried out Monte Carlo experiments with both uncorrelated and correlated Gaussian noise, as described in Rebull (2001, AJ, 121, 1676). We used those experiments to empirically set the FAP level appropriate for our data set. |
Revision as of 21:48, 19 November 2007
Here are the "scary words" describing in formal terms what you do to a time series data set to find the periodic objects:
We used the standard methodology for finding a periodic signal in unevenly sampled data described by Scargle (1982, ApJ, 263, 835), Horne & Baliunas (1986, ApJ, 302, 757), Gilliland & Baliunas (1987, ApJ, 314, 766), and more generally by Press et al. (1992, Numerical Recipes in C (2d ed.; Cambridge: Cambridge Univ. Press)). The algorithm calculates the Lomb normalized periodogram for the data stream and assigns a significance (false-alarm probability, FAP) based on the peak height in the periodogram. However, the generalized prescription for assigning the FAP assumes that each point in the data stream is statistically independent. As Stassun et al. (1999, AJ, 117, 2941) and Herbst & Wittenmyer (1996, BAAS, 189, No. 49.08) point out, this is not necessarily a good assumption for our specific case of young stars, as there are likely to be fluctuations intrinsic to the source that are not periodic, but which may be correlated over some of the timescales sampled. In order to understand how best to set the FAP for our data, we carried out Monte Carlo experiments with both uncorrelated and correlated Gaussian noise, as described in Rebull (2001, AJ, 121, 1676). We used those experiments to empirically set the FAP level appropriate for our data set.
