Before revision:  However, derivative data is a set of conditional expectations that are already observed in the market, so rather than use filtering techniques we compute animplied distribution by inverting the market's option prices. Robustness is an issue when model parameters are probably unknown, but isn't crippling in practical settings because the data is sufficiently imprecise and prevents us from reducing the fitting error down to levels where parameter uncertainty will show .
After revision:  However, derivative data is a set of conditional expectations that are already observed in the market, so rather than use filtering techniques we compute animplied distribution and which can be used as input to an inverse problem whose solution is an implied conditional density on volatility. Our analysis relies on a specification of the martingale change of measure, which we refer to as .