This recent article at Slate thinks so:
It turns out that even very young children reason [using Bayes Theorem]. For example, my student Tamar Kushnir, now at Cornell, and I showed 4-year-olds a toy and told them that blocks made it light up. Then we gave the kids a block and asked them how to make the toy light up. Almost all the children said you should put the block on the toy—they thought, sensibly, that touching the toy with the block was very likely to make it light up. That hypothesis had a high “prior.”
Then we showed 4-year-olds that when you put a block right on the toy it did indeed make it light up, but it did so only two out of six times. But when you waved a block over the top of the toy, it lit up two out of three times. Then we just asked the kids to make the toy light up.
The children adjusted their hypotheses appropriately when they saw the statistical data, just like good Bayesians—they were now more likely to wave the block over the toy, and you could precisely predict how often they did so. What’s more, even though both blocks made the machine light up twice, the 4-year-olds, only just learning to add, could unconsciously calculate that two out of three is more probable than two out of six. (In a current study, my colleagues and I have found that even 24-month-olds can do the same).
There also seems to be a reference to the Singularity Institute:
The Bayesian idea is simple, but it turns out to be very powerful. It’s so powerful, in fact, that computer scientists are using it to design intelligent learning machines, and more and more psychologists think that it might explain human intelligence.
(Of course, I don't know how many other AI researchers are using Bayes Theorem, so the author also might not have the SI in mind)
If children really are natural Bayesians, then why and how do you think we change?