recognizing the target, assuming that
it was simply not there. But they grew
worse in a very particular way. People’s
behavior closely mirrored what Bayesian math predicted, the team reported
in the June issue of Nature Neuroscience .
“A visual search starts involving pretty
complicated mathematics,” Pouget says.
Yet in the study, the human subjects
were “as good as they could possibly be.”
Now the team is wondering just how
good humans’ Bayesian thinking can get.
“The lab is on a quest to find out, ‘OK,
where do we break down? How much
complexity do we have to put in the task
before we can no longer come up with
the optimal solution?’” Pouget says.
“And so far we haven’t found where that
boundary is.”
Psychologist Wilson Geisler of the
University of Texas at Austin prefers an
approach that starts with the outside
world. His team uses carefully calibrated
cameras to capture a scene and range-
finders to measure the distance from the
cameras to each point in the scene and
the brightness of the light coming from
each of those pixels. These tools allow
the researchers to construct an exact
mathematical description of the natu-
ral world.
Optimal performers Study participants who were shown intact or distorted patches of leaf
images (top panel), and were asked to determine whether the patches came from the same leaf
or different leaves, performed nearly as well as an ideal Bayesian observer (gray line in graphs).
Full Patches
Full Patches
Same leaf
Different
leaves
Performance before practice
Unchanged Texture removed
Performance with practice
Unchanged Texture removed
0.8
0.8
Accuracy
0.7
0.6
¼½ 1
0.5
¼½ 1
Distance between patch centers
(in leaf diameters)
SOURCE: A.D. ING ET AL/JOURNAL OF VISION 2010
Participant 1
¼ ½ 1
Distance between patch centers
(in leaf diameters)
Participant 1
Participant 2 Bayesian ideal
the same leaf or different ones would get
worse at the task as the mushroom grew
bigger and hid more of the scene. Unreliable information leads people astray in a
way that Bayesian math predicts.
In a study published last year in the
Journal of Vision, Geisler and colleagues
showed participants close-up pictures of
leaves photographed at a nearby botanical garden. People’s performance at
distinguishing t wo overlapping leaves in
patches from a two-dimensional image
mirrored the performance of an ideal
observer. Participants seemed to operate with existing knowledge of how to
visually unjumble a pile of leaves.
In a way, it’s self-evident that humans
rely on existing knowledge. A brain that
didn’t rely on its experiences would be a
pretty pathetic brain. “You could argue
that it would be a little strange if we were
bad at it,” Geisler says. “It’s something
that we have enormous experience with,
evolutionarily. The same problem has
been there for a billion years. But nonetheless, the statistics are complicated.”
Parsing these statistics isn’t just a
task for the visual system. So far, some
scientists have turned up hints that
movements, smells, hearing, cognition
and the ability to perform easy addition
problems may be based on Bayesian
techniques. And these abilities might be
present well before a child learns 2 + 2.
A’s, Bayes, C’s
By studying babies and young children,
scientists can test whether probabilistic reasoning is present before life
experiences begin sculpting the mind.
Babies haven’t been alive long enough
to develop strong beliefs about how the
world works. If babies act Bayesian, then
they may have been born that way.
Sixteen-month-olds can make correct assumptions when faced with
complicated data, cognitive scientists
Laura Schulz and Hyowon Gweon of
MIT reported June 24 in Science (SN
Online: 6/28/11). In the study, babies
watched as experimenters pressed a
button on a toy, causing music to play. In
some cases, the toy worked beautifully
the first time each experimenter pushed
