There is some work (by James, Ferro-Luzzi, and other I recall) form about 20 years ago. This was in the other tail (i.e. for wasting) and the idea was that we could use MUAC (a supposedly poor measure) to predict BMI (a supposedly golden measure). The problem with this is that BMI is not a good measure because (like all W/H type measures) it is biassed by body-shape and requires correction for body-shape (the Cormic index) or needs different thresholds in different populations. There is also the "fit vs. unfit" (body composition) problem in which BMI tells us that marathon runners are wasted and rugby players are obese. There is also the (contentious) findings from recent analyses of NHANES that a BMI between 25 and 30 is associated with better survival than a BMI below 25 or above 30. It may be that "overweight" is the new thin. BMI is falling out of fashion. There may also be differential fat distribution between sexes needing different MUAC cut-point for males and females. I am sceptical of the value of predicting BMI from MUAC. There has been some work on using measures such as the waist-to-hip ratio or just waist circumference. I suppose the thinking here is that we are directly measuring central adiposity and this is associated with the negative sequelae of overweight and obesity. Simple waist circumference could be measured with a coloured tape. This seems to me worth exploring. I hope this is of some use. Other's may be more encouraging.

To build up on Mark’s message, you have an interesting discussion on the value, or rather lack of value of BMI to assess the risk associated with over nutrition in the following Lancet editorial commenting a large longitudinal study. Kragelund C, Omland T. A farewell to body-mass index? Lancet. 2005 Nov 5;366(9497):1589-91. It claims that waist hip ratio is best for risk assessment. Its conclusion starts with: “The main message from the new INTERHEART report is that current practice with body-mass index as the measure of obesity is obsolete, …" So trying to correlate MUAC with BMI supposed to be a gold standard is not a good idea for assessing overnutrition (as it is not a good idea for assessment of risk associated with undernutrition to relate MUAC to weigh-for-height). Better to see how MUAC relates to waist /hip ratio.