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 data using a likelihood approach .
The existence of the bar is confirmed with shoulder at a \approx 4 kpc , axis ratio a:b = 2.2 – 2.7 and position angle of 19 ^ { \circ } \pm 1 ^ { \circ } degrees .
The ratio of non-axisymmetric to axisymmetric components gives similar estimate for the bar size a = 3.3 \pm 0.1 kpc and position angle \phi _ { 0 } = 24 ^ { \circ } \pm 2 ^ { \circ } .
We estimate a scale length 4.00 \pm 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 30 % but still too small to account for the MACHO result .
In addition , we predict a significant asymmetry at positive and negative longitudes along lines of sight through the end of the bar ( |l| \approx 30 ^ { \circ } ) with optical depths comparable to that in Baade ’ s window .
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 .
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 .
However , this method requires the evaluation of multidimensional density functions over the data and optimization of the function over a parameter space .
We address the resulting computational extremization problem with a hybrid use of a directed search algorithm which locates the global maximum and the conjugate gradient method which converges quickly near a likelihood maximum .
Both methods are parallelizable and therefore of potential use with very large databases .