But it illustrates vividly that the interpretation of ex post outcomes depends critically on understanding the ex ante process which generated those outturns. Another example shows that it is not just lay people who find statistical inference difficult. Experts of all kinds do too. The advent of DNA profiling in the 1980s led to the use of match probabilities in criminal cases. The jury is told that the probability of finding a match between the sample taken from the scene of the crime and the DNA of the defendant is, for example, only 1 in 500,000. That is sometimes taken as evidence that the probability of the defendant being innocent is also only 1 in 500,000. Such an inference is incorrect. In a city such as London where there might be about 5 million people who could have committed the crime, around ten people would have DNA that matched the relevant sample. Hence, in the absence of any other evidence, the probability that the defendant is guilty, far from being overwhelming, is only one in 10. Of course, in practice other evidence is usually available. But this incorrect statistical reasoning has swayed enough cases to be given its own name - the prosecutor’s fallacy.11 The cases of Sally Clark and Angela Cannings, both convicted and imprisoned for the alleged murder of their own children, show the desperate consequences of the false use of statistics to create a presumption of guilt to resolve the cause of apparently inexplicable events.
Meeting these challenges has not been straightforward in recent years as the euro area economy was hit by several shocks: financial instability in the aftermath of the stock market  6  BIS Review 113/2007  collapse in 2000, exceptionally high economic and geopolitical uncertainty between 2001 and 2003, just to name a few. -  First of all, we have to identify and account for temporary “special factors” or “distortions” that may affect monetary developments and blur their information content. To some extent it is the aim of the methodology developed at the ECB which allows for periodic adjustments to measured monetary aggregates in order to account for portfolio shifts which impact the demand for money without any incidence on future inflation. This approach has met with great success in the period 2000-2004, allowing the Eurosystem to enter an easing cycle despite a rapid growth of M3. -  Second, and more permanently, it is necessary to disentangle, in monetary and credit evolutions, those which reflect structural and permanent changes from those which simply result from moves in the level of interest rates and the position in the economic cycle. -  Finally, we must be able to assess whether these developments result from money supply shocks, in which case they clearly entail some risks to price stability, or whether they are caused by money demand shocks that may raise the desired level of money balances without necessarily impacting aggregate demand.