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Unformatted text preview: and McClelland, 2001;
od, Howposterior probabilities. In this case, for a given weight
df the co“natural
of evidence (e.g., is analogous to in Banburismus):
This problem the stopping point one-dimensional
ponses and Turing’s Weight of Evidence
ted quanlar responses from a pair of sensory neurons when h a pairtrue, barriers (Link, 1992; Ratcliff
Brownian motion to or h is of as indicated. For
of tradePr(h1|mmotion. The lower curve would
es of a direction-selective neuron that prefers upward The weight of evidence
and Rouder, 1998).
means of the normal B
ron” that prefers downward motion. Here wePr(h the simplifying assumption that the
r can be equal variances ( represent the drift rates, i (where the subscript i
tions ). Note that other0 forms of the distribution, including
old and Shadlen, 2001). The panelthe particular Turing’s weight of evidenceThe psychometon the
reflects B is a right shows motion strength).the barrier height
constant that represents
of their difference; note the linear relationship.
m of base
ric function describing the probability of correctly reachexclusive hypotheses
in favor of h1. For two mutually accumulate/integrate over
tion-time Figure 2. ing eitherh the is“up” r(h difference between equivalently, given) antineuron is:
or “down” barrier on a Pr(h trial
The weight (Pr(h favor of
evidence in |m) over h
the accumulated |m) or, responses of a neuron that prefers h and an
1depicted P computed under thetcondition) thatyh( is)true. The thin, wavy line depicts a simulated
ntlities has that prefers weight of7).evidence atare
total h (see Equation The curves
ihich the trajectory that represents how the weight of evidence might grow on a single trial as a function of time. The dashed line depicts the expectation
Pr(h1)), and assuming the weight of evidence is exn motion
(mean value) of this trajectory at each time point. Note that changing the constant of proportionality used to rel...
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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