curve is inconsistent with a constant flux, without any of the more quantitative variability selection criteria we discuss in the next section. This led to a sample of 205 X-ray candidates, of which 160 were also mid-IR-selected candidates and 99 satisfy the variability cuts presented in Section \[sec:varsel\].

Variability-selected AGN Candidates {#sec:varsel}
-----------------------------------

The OGLE-III database (@2008AcA....58...69U [@2008AcA....58...89U]) contains the data for 9 years (2001–2009) of continuously monitoring $\sim$35 million objects toward the LMC. We used this database to search for variable objects that are likely quasars based on the DRW model of their light curves (e.g., @2009ApJ...698..895K [@2010ApJ...708..927K; @2010ApJ...721.1014M]).

We prepared and analyzed the light curves as described in [@2010ApJ...708..927K]. We use the timescale $\tau$, scaled amplitude $\hat{\sigma}^2=2\sigma^2/\tau$, and the likelihood ratio $\ln L_{\rm best}/\ln L_{\rm noise}$ between the best fitting model and a white noise model corresponding to simply expanding the photometric errors. We also fit a power-law structure function (SF) and estimated its slope $\gamma$ between 30 days and 2 years, and an amplitude $A$ defined by the magnitude difference between the first and third quartile of the sorted light curve.

To remove unwanted variable sources, we use the following cuts: [*Cut 1.*]{} The average light curve 