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Previous work reported a bar signature in color-selected IRAS variable stars. Here, we estimate the source density of these variables while consistently accounting for spatial incompleteness in the data using a likelihood approach. The existence of the bar is confirmed with a shoulder at a approx 3 kpc, an axis ratio of a:b = 2.2-2.7, and a position angle of 19° ± 1°. The ratio of nonaxisymmetric to axisymmetric components gives a similar estimate for the bar size of a = 3.3 ± 0.1 kpc and a position angle of phi0 = 24° ± 2°. We estimate a scale length of 4.00 ± 0.55 kpc for the IRAS variable population, suggesting that these stars represent the old disk population. We use this density reconstruction to estimate the optical depth to microlensing for the large-scale bar in the Galactic disk. We find an enhancement over an equivalent axisymmetric disk by up to 40%, but this still too small to account for the MACHO result. In addition, we note a possibility for a significant asymmetry at positive and negative longitudes with optical depths comparable to those in Baade's window. Independent of our reconstruction, an infrared microlensing survey may be a sensitive tool for detecting or constraining structural asymmetries. More generally, this is a pilot study for Bayesian star count analyses. The Bayesian approach allows the assessment of prior probabilities to the unknown parameters of the model; the resulting likelihood function is straightforwardly modified to incorporate all available data.


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