We report our efforts to constrain the form of the low-mass star and brown dwarf mass function via Bayesian inference .
Recent surveys of M , L , and T dwarfs in the local solar neighborhood are an essential component of our study .
Uncertainties in the age distribution of local field stars make reliable inference complicated .
We adopt a wide range of plausible assumptions about the rate of galactic star formation and show that their deviations from a uniform rate produce little effect on the resulting luminosity function for a given mass function .
As an ancillary result , we calculate the age distribution for M , L , and T spectral types .
We demonstrate that late-L dwarfs , in particular , are systematically younger than objects with earlier or later spectral types , with a mean age of 3 Gyr .
Finally , we use a Bayesian statistical formalism to evaluate the probability of commonly used mass functions in light of recent discoveries .
We consider three functional forms of the mass function , include a two-segment power law , a single power law with a low-mass cutoff , and a log-normal distribution .
Our results show that , at a 60 % confidence level , the power-law index , \alpha , for the low-mass arm of a two-segment power law has a value between -0.5 and 0.5 for objects with masses between 0.04 ~ { } M _ { \odot } and 0.10 ~ { } M _ { \odot } .
The best-fit index is \alpha = 0.3 \pm 0.6 at the 60 % confidence level for a single-segment mass function .
Current data require this function extend to at least 0.05 ~ { } M _ { \odot } with no restrictions placed on a lower mass cutoff .
Inferences of the parameter values for a log-normal mass function are virtually unaffected by recent estimates of the local space density of L and T dwarfs .
We find no preference among these three forms using this method .
We discuss current and future capabilities that may eventually discriminate between mass-function models and refine estimates of their associated parameter values .