Variability statistics

[Michael Sallman <msallman@pro-ns.net>]

Hello all,

Happy New Year! The list has been awfully quiet lately, maybe I can
liven things up a bit.
I have been working on improving the reliability of the W-S statistic
(or getting rid of the spurious detections, take your pick).
I first tried excluding all measurements >5 sigma from the mean when
calculating the W-S. This didn't seem to produce much of an improvement
(sorry, I don't have any hard figures for this one).
Then, I tried excluding the minimum and maximum observations for each
star. This seems to have improved things greatly. There are far fewer of
the "one high measurement" stars in the top W-S. Of the top 100 W-S
values, 96 match a known GCVS/NSV variable. The other 4 look obviously
variable.
These new statistics are now available online.

I have just recently tried using the modifications to the W-S statistic
described in:
http://cdsads.u-strasbg.fr/cgi-bin/nph-bib_query?bibcode=1996PASP..108..851S
which were also was used by Ackerlof et al:
http://cdsads.u-strasbg.fr/cgi-bin/nph-bib_query?bibcode=2000AJ....119.1901A
in analyzing the ROTSE-I data.
This procedure also seems to produce better results, though I just
completed it yesterday, so I haven't had time to look at the data in
great detail.

Below are the min/max/average/std deviation of the W-S statistic using
the 3 methods.
star_stats is the original W-S
test_star_stats is excluding the min/max observations for each star
stetson_stats is the modified W-S statistic.

Would anyone care to comment on whether any of these would be
significant in determining which method is best, or what metrics I could
use to make that determination?

Mike


mysql> select max(ws),min(ws),avg(ws),stddev(ws) from star_stats;
+----------+---------+----------+------------+
| max(ws)  | min(ws) | avg(ws)  | stddev(ws) |
+----------+---------+----------+------------+
| 17143.49 |    NULL | 6.412805 |  36.235592 |
+----------+---------+----------+------------+
1 row in set (13.28 sec)

mysql> select max(ws),min(ws),avg(ws),stddev(ws) from test_star_stats;
+---------+----------+----------+------------+
| max(ws) | min(ws)  | avg(ws)  | stddev(ws) |
+---------+----------+----------+------------+
| 4901.17 | -1614.17 | 1.088818 |  12.909869 |
+---------+----------+----------+------------+
1 row in set (22.15 sec)

mysql> select max(ws),min(ws),avg(ws),stddev(ws) from stetson_stats;
+---------+---------+----------+------------+
| max(ws) | min(ws) | avg(ws)  | stddev(ws) |
+---------+---------+----------+------------+
|   80.56 |  -25.69 | 0.687546 |   1.358058 |
+---------+---------+----------+------------+
1 row in set (3.91 sec)