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Unformatted text preview: evidence
ent 1. weight ofrepresents the barrier height of evidence(1
or trialto2
)
Pr(x,yh0)
rence; note the linear relationship.
honFor two mutually exclusive hypotheses
numerous
1.
1
Pr(h1m) or,
)
(
ese probabili equivalently,1numerous 1 and lowered until
Note that Pr(hthe)barrier is1 factors could cause nonzero values
0
anderror, in which 0
raised
·
· (x y) (6)
t
the maximum rate of reward is achieved. Interestingly, in
the 2
constant
assuming the weight of evidenceof(xproportionality thatofrelates the( ) like7)
2.total weight of evidencethis case,time t iskto ex factors d ( attention and arousal
at difference (1 the weight ) y
easurements
of , including intrinsic () evidence
accumulated
y)
0
is not needed to find the barrier height that leads to the
ans, this rearrangesand extrinsicoffactors likeisthe light level or other variations
to: maximum rate reward. That information not lost,
neurons) to a
however: could cause nonzero
the
corresponds
Note that numerous factorsoncelevelbarrier height is fixed, itnot equal values
if For example,
to a particular
g thewhere k is a constant. Note that of overalldoesevidence, such forthe motiondiscriminadistribuin the stimulus. ofk performance and thus can
the
be expressed in units
the weight of
1
of , including intrinsic factorsNote that this quantity is not the weight value
like attention the
as natural Equation 6,
constant of proportionality inbans. would be calculatedathen and arousal is typically prethat
based on knowleightPr(hsuch
tion task,themotion in and associated direction
3. of extrinsic factors B. of evidencestimulus motion strength(4)thegivenvariations
1m)
edge of
and is computed1is merely response distributions becauseto informa weight
like theproportional other
light level
that
1 sentedsensory a variety or that the
0
stimulus (e.g.,
at
of strengths (i.e., h0 and h1 each
tion would lead to perfect performance at all motion
in the stimulus. For example, forthe weight of evidence that correof evidence. Regardlessstrengths. Rather, it is the motiondiscriminaof the value of k, however, the
sponds to a fixed level of uncertainty across all stimulus
ndicates that the posterior strengths weight of quantity willtypically preprobability of
algorithm motion in a the in theexperiment (this evidence
tion task, for updating overestimate an directionstimuli andtend to is the
given evidence from weakh1is underly onsented accumulatebarrier,evidenceevidence fromin spike0 rates h1 each
the value a the the thestrengths strong stimuli). Accordingly,
B, that accumulates on
same: at of variety ofestimate the and not during ah can be over
difference (i.e., trial and
interpreted as a fraction of this quantity and thus in units
time. of evidence, Figure 2, thiswhen the In
r samplesAs illustrated inm, ofencountered.scaling between accumunatural bans—even temporally the
decision variable and the weight of evidence is not
lating evidence can be known (e.g., if the reaches
thought of as simply of
, as long as the weight of evidencebrain does not know the shapes a single
the sensory response distributions).
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This note was uploaded on 09/15/2011 for the course COGS 1 taught by Professor Lewis during the Spring '08 term at UCSD.
 Spring '08
 LEWIS

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