Honfor two mutually exclusive hypotheses numerous 1 1

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Unformatted text preview: evidence ent 1. weight ofrepresents the barrier height of evidence(1 or trial-to2 ) Pr(x,y|h0) rence; note the linear relationship. honFor two mutually exclusive hypotheses numerous 1. 1 Pr(h1|m) or, ) ( ese probabili- equivalently,1numerous 1 and lowered until Note that Pr(hthe)barrier is1 factors could cause nonzero values 0 and-error, 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) 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 motion-discriminadistribuin 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 1|m) 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 motion-discriminaof 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). Review 305...
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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.

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