Biomedical Engineering Reference
In-Depth Information
mechanism is able to account for the behavioural data, based on the iring rate of a
neuronal population tuned to ITD in a similar manner as barn owl neurons.
4.5
Probabilistic Population Codes
The PV is not the only method for decoding sensory responses from a population
of neurons. An alternative scheme is based on a probabilistic population code
(PPC; Ma et al.
2006
). The PPC assumes that neuronal populations encode proba-
bility distributions through their joint iring rate tuning curves. As a result, the
entire tuning curve of the neuronal population and not just the preferred direction
is used in the decoding process. Let
k
= …
12
represent the response in a
single trial of
N
neurons to a ixed sound source direction
θ
. The posterior distribu-
tion has the form
(, ,
kk k
N
,
)
p
(|)
q
k
∝
p
( |)(),
k
q
p
q
(4.12)
where
p
(
θ
) is the same as in Eq. (
4.6
) and
p
(
k
|
θ
) is a distribution which models the
probability of a neuronal response given the stimulus.
If we assume that the neurons representing
p
(
k
|
θ
) are independent and Poisson,
then the probabilistic population code for the distribution
p
(
k
|
θ
) has the form
r
()
!
q
k
N
n
∏
1
−
r
()
q
(4.13)
p
(|
k
q
)
=
n
e
,
n
k
n
=
n
where
k
n
is the response of neuron
n
and
r
n
(
θ
) is its tuning function. We model the
tuning functions similarly as in Sect.
4.4
,
r
n
(
θ
) =
r
n
(ITD(
θ
)) using Eqs. (
4.9
) and (
4.3
),
but with a uniform distribution of preferred directions over the unit circle instead of
being normally distributed. Note that the right-hand side of Eq. (
4.13
) is formed by
taking products of Eq. (
4.8
) with
k
i
replacing
k
and
r
i
(
θ
) replacing
λ
, since we assume
independent Poisson neurons.
Based on this probabilistic population code, an alternative decision rule to averag-
ing over unit vectors is to pick the azimuth that maximizes the posterior probability.
This rule is called the maximum a posteriori probability (MAP) rule and has the form
ˆ
()
q
k
=
arg
max(| .
p
q
k
q
The result of this estimation method based on the probabilistic population code is
given in Fig.
4.3
d as the grey starred curve. It is signiicantly different from the
population vector result and does not match the behavioural data very well. On the
other hand, a probabilistic population code has been successfully used to explain the
sensory integration of visual and vestibular cues in neurons of the monkey visual
cortex using a slightly different decoding mechanism (Fetsch et al.
2011
).
