1007:
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50:). For example, to determine sensitivity to a dim light in a two-interval forced choice procedure, an observer could be presented with series of trials comprising two sub-trials (intervals) in which the dim light is presented randomly in the first or the second interval. After each trial, the observer responds only "first" or "second".
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86:, the Posner Cueing Task uses a 2AFC design to present two stimuli representing two given locations. In this design there is an arrow that cues which stimulus (location) to attend to. The person then has to make a response between the two stimuli (locations) when prompted. In animals, the 2AFC task has been used to test
2563:{\displaystyle {\begin{aligned}dy_{\text{1}}\ =\ (-ky_{\text{1}}-wy_{\text{3}}+vy_{\text{1}}+I_{\text{1}})dt\ +\ cdW_{\text{1}}\\dy_{\text{2}}\ =\ (-ky_{\text{2}}-wy_{\text{3}}+vy_{\text{2}}+I_{\text{2}})dt\ +\ cdW_{\text{2}}\\dy_{\text{3}}\ =\ (-k_{\text{inh}}y_{\text{3}}+w'(y_{\text{1}}+y_{\text{2}}))dt\end{aligned}}}
929:{\displaystyle {\boldsymbol {w}}={\begin{bmatrix}\sigma _{a}^{2}&-\sigma _{b}^{2}\end{bmatrix}},\;{\boldsymbol {k}}={\begin{bmatrix}1&1\end{bmatrix}},\;{\boldsymbol {\lambda }}={\frac {\mu _{a}-\mu _{b}}{\sigma _{a}^{2}-\sigma _{b}^{2}}}{\begin{bmatrix}\sigma _{a}^{2}&\sigma _{b}^{2}\end{bmatrix}}.}
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At time zero, the evidence accumulated, x, is set equal to zero. At each time step, some evidence, A, is accumulated for one of the two possibilities in the 2AFC. A is positive if the correct response is represented by the upper threshold, and negative if the lower. In addition, a noise term, cdW, is
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model. The DDM assumes that in a 2AFC task, the subject is accumulating evidence for one or other of the alternatives at each time step, and integrating that evidence until a decision threshold is reached. As the sensory input which constitutes the evidence is noisy, the accumulation to the threshold
62:
than 2AFC tasks. For example, with extremely dim lights, a person might respond, completely truthfully, "no" (i.e., "I did not see any light") on every trial, whereas the results of a 2AFC task will show the person can reliably determine the location (top or bottom) of the same, extremely dim light.
38:
and response times to two versions of the sensory input. For example, to determine a person's sensitivity to dim light, the observer would be presented with a series of trials in which a dim light was randomly either in the top or bottom of the display. After each trial, the observer responds "top"
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The mutual inhibition model also uses two accumulators to model the accumulation of evidence, as with the race model. In this model the two accumulators have an inhibitory effect on each other, so as evidence is accumulated in one, it dampens the accumulation of evidence in the other. In addition,
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In the race model, evidence for each alternative is accumulated separately, and a decision made either when one of the accumulators reaches a predetermined threshold, or when a decision is forced and then the decision associated with the accumulator with the highest evidence is chosen. This can be
2197:
Wang suggested the pooled inhibition model, where a third, decaying accumulator is driven by accumulation in both of the accumulators used for decision making, and in addition to the decay used in the mutual inhibition model, each of the decision driving accumulators self-reinforce based on their
57:
a participant observes a string of characters and must respond whether the string is a "word" or "non-word". Another example is the random dot kinetogram task, in which a participant must decide whether a group of moving dots are predominately moving "left" or "right". The results of these tasks,
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supports the DDM, as firing rates for the direction selective neuronal populations sensitive to the two directions used in the 2AFC task increase firing rates at stimulus onset, and average activity in the neuronal populations is biased in the direction of the correct response. In addition, it
128:
dots. The percentage of dots moving together in a given direction determines the coherence of motion towards the direction. In most experiments, the participant must make a choice response between two directions of motion (e.g. up or down), usually indicated by a motor response such as a
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This model can also extend to the cases when each of the two stimuli is itself a multivariate normal vector, and also to the situations when the two categories have different prior probabilities, or the decisions are biased due to different values attached to the possible outcomes.
2160:{\displaystyle {\begin{aligned}dy_{\text{1}}\ =\ I_{\text{1}}dt\ +\ cdW_{\text{1}}\ -\ u(I_{\text{2}}dt\ +\ cdW_{\text{2}})\\dy_{\text{2}}\ =\ I_{\text{2}}dt\ +\ cdW_{\text{2}}\ -\ u(I_{\text{1}}dt\ +\ cdW_{\text{1}})\end{aligned}},\quad y_{\text{1}}(0)\ =\ y_{\text{2}}(0)=0}
695:
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The feedforward inhibition model is similar to the mutual inhibition model, but instead of being inhibited by the current value of the other accumulator, each accumulator is inhibited by a fraction of the input to the other. It can be formally stated thus:
1777:{\displaystyle {\begin{aligned}dy_{\text{1}}\ =\ (-ky_{\text{1}}-wy_{\text{2}}+I_{\text{1}})dt\ +\ cdW_{\text{1}}\\dy_{\text{2}}\ =\ (-ky_{\text{2}}-wy_{\text{1}}+I_{\text{2}})dt\ +\ cdW_{\text{2}}\end{aligned}},\quad y_{\text{1}}(0)\ =\ y_{\text{2}}(0)=0}
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It is typically assumed that the difference in evidence favoring each alternative is the quantity tracked over time and that which ultimately informs the decision; however, evidence for different alternatives could be tracked separately.
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leaky accumulators are used, so that over time evidence accumulated decays – this helps to prevent runaway accumulation towards one alternative based on a short run of evidence in one direction. Formally, this can be shown as:
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Example of ten evidence accumulation sequences for the DDM, where the true result is assigned to the upper threshold. Due to the addition of noise, two sequences have produced an inaccurate decision.
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1470:{\displaystyle {\begin{aligned}dy_{\text{1}}\ =\ I_{\text{1}}dt\ +\ cdW_{\text{1}}\\dy_{\text{2}}\ =\ I_{\text{2}}dt\ +\ cdW_{\text{2}}\end{aligned}},\quad y_{\text{1}}(0)\ =\ y_{\text{2}}(0)=0}
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The 2AFC task has yielded consistent behavioral results on decision-making, which lead to the development of theoretical and computational models of the dynamics and results of decision-making.
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or "bottom". The observer is not allowed to say "I do not know", or "I am not sure", or "I did not see anything". In that sense the observer's choice is forced between the two alternatives.
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1179:, to the accumulation that is dependent on the current accumulation of evidence – this has the net effect of increasing the rate of accumulation towards the initially preferred option.
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Example of six evidence accumulation sequences from an unbiased (100% noise) source. The dotted lines indicate the thresholds for decision making for each of the two alternatives.
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There are various manipulations in the design of the task, engineered to test specific behavioral dynamics of choice. In one well known experiment of attention that examines the
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The term 2AFC is sometimes used to describe a task in which an observer is presented with a single stimulus and must choose between one of two alternatives. For example in a
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Monkeys were trained to look at a center stimulus and were then presented with two salient stimuli side by side. A response can then be made in the form of a
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The drift-diffusion model (DDM) is a well defined model, that is proposed to implement an optimal decision policy for 2AFC. It is the continuous analog of a
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to the left or to the right stimulus. A juice reward is then administered after each response. The amount of juice reward is then varied to modulate choice.
2907:
Britten, Kenneth H.; Michael N. Shadlen, William T. Newsome, J. Anthony
Movshon (1993). "Responses of neurons in macaque MT to stochastic motion signals".
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Shadlen, Michael N.; William T. Newsome (2001-10-01). "Neural Basis of a
Perceptual Decision in the Parietal Cortex (Area LIP) of the Rhesus Monkey".
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Busemeyer, J. R; J. T Townsend (1993). "Decision field theory: a dynamic-cognitive approach to decision making in an uncertain environment".
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firing rate in monkeys predicted the choice response of direction of motion suggesting this area is involved in decision making in the 2AFC.
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probability learning, for example such as choices in pigeons after reinforcement of trials. A 2AFC task has also been designed to test
3223:
Pike, A. R. (1966). "Stochastic Models of Choice
Behaviour: Response Probabilities and Latencies of Finite Markov Chain Systems1".
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The race model is not mathematically reducible to the DDM, and hence cannot be used to implement an optimal decision procedure.
2964:
Gold, Joshua I.; Michael N. Shadlen (2000-03-23). "Representation of a perceptual decision in developing oculomotor commands".
690:{\displaystyle p(e)=p\left({\tilde {\chi }}_{{\boldsymbol {w}},{\boldsymbol {k}},{\boldsymbol {\lambda }},0,0}^{2}\right)<0}
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fluctuations; and iii) the decision is made when sufficient evidence has accumulated favoring one alternative over the other.
3048:"The Physics of Optimal Decision Making: A Formal Analysis of Models of Performance in Two-Alternative Forced-Choice Tasks"
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added to represent noise in input. On average, the noise will integrate to zero. The extended DDM allows for selection of
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365:, and the task is to decide which was which. A common model is to assume that the stimuli came from normal distributions
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Both options can be presented concurrently (as in the above example) or sequentially in two intervals (also known as
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from separate distributions – this provides a better fit to experimental data for both accuracy and reaction times.
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Usher, M.; J. L McClelland (2001). "The time course of perceptual choice: the leaky, competing accumulator model".
4045:"Response of neurons in the lateral intraparietal area during a combined visual discrimination reaction time task"
1006:
973:
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Platt, Michael L.; Paul W. Glimcher (1999-07-15). "Neural correlates of decision variables in parietal cortex".
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than the other, then the frequency of exposure to the stimuli may influence the participant's beliefs about the
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Ratcliff, R.; J. N Rouder (2000). "A diffusion model account of masking in two-choice letter identification".
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appears that a fixed threshold of neuronal spiking rate is used as the decision boundary for each 2AFC task.
994:– this gives rise to the directed random-walk-like behavior. The DDM has been shown to describe accuracy and
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368:
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1019:
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Smith, P. L (2000). "Stochastic dynamic models of response time and accuracy: A foundational primer".
4004:"Banburismus and the brain: decoding the relationship between sensory stimuli, decisions, and reward"
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Schall, J. D; K. G Thompson (1999). "Neural selection and control of visually guided eye movements".
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Ratcliff, R.; T. Van Zandt, G. McKoon (1999). "Connectionist and diffusion models of reaction time".
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2599:, and increases based on the current values of the other two accumulators, at a rate modulated by
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467:) is to decide which of two bivariate normal distributions is more likely to produce the tuple
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of the occurrence of the alternatives. Introducing biases in the 2AFC task is used to modulate
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i) evidence favoring each alternative is integrated over time; ii) the process is subject to
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Vickers, D. (1970). "Evidence for an accumulator model of psychophysical discrimination".
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Bogacz, Rafal; Eric Brown, Jeff
Moehlis, Philip Holmes, Jonathan D. Cohen (October 2006).
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8:
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Link, S. W.; R. A. Heath (1975). "A sequential theory of psychological discrimination".
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The accumulation of evidence in the DDM is governed according to the following formula:
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Ratcliff, R.; J. N Rouder (1998). "Modeling response times for two-choice decisions".
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Hanes, D. P; J. D Schall (1996). "Neural control of voluntary movement initiation".
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The optimal strategy in a 2AFC task for univariate normal stimuli from categories
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dot kinetogram, with a percentage of net coherent motion distributed across the
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Link, S. W (1975). "The relative judgment theory of two choice response time".
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is the fraction of accumulator input that inhibits the alternate accumulator.
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sometimes called yes-no tasks, are much more likely to be affected by various
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The probability of error with this ideal decision strategy is given by the
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In a different application, the 2AFC is designed to test discrimination of
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3808:"Probabilistic decision making by slow reverberation in cortical circuits"
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3457:"A comparison of sequential sampling models for two-choice reaction time"
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Journal of
Experimental Psychology: Human Perception and Performance
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in the 2AFC task are random variables from two different categories
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is to classify between the two joint bivariate normal distributions
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and the interaction of reward and probability learning in monkeys.
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463:. Under this normal model, the optimal decision strategy (of the
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LaBerge, D. (1962). "A recruitment theory of simple behavior".
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956:
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The third accumulator has an independent decay coefficient,
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British
Journal of Mathematical and Statistical Psychology
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Example of a random dot kinetogram as used in a 2AFC task.
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3511:"A method to integrate and classify normal distributions"
2788:"Probabilistically reinforced choice behavior in pigeons"
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3338:
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880:
780:
717:
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Ratcliff, R. (1978). "A theory of memory retrieval".
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Stone, M. (1960). "Models for choice-reaction time".
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Bogacz et al., The
Physics of Optimal Decision Making
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267:. The probability of the correct choice is 0.74 here.
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26:) is a method for measuring the sensitivity of a
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2792:Journal of the Experimental Analysis of Behavior
2706:(2nd ed.). Leipzig: Breitkopf & Härtel.
1806:is a shared decay rate of the accumulators, and
3745:Proceedings of the National Academy of Sciences
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3157:
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2198:current value. It can be formally stated thus:
1829:
3727:
1248:{\displaystyle dx\ =\ (\lambda x+A)dt\ +\ cdW}
1159:model extends the DDM by adding another term,
947:There are typically three assumptions made by
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3739:Shadlen, M. N.; W. T. Newsome (1996-01-23).
3108:: CS1 maint: multiple names: authors list (
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2730:Quarterly Journal of Experimental Psychology
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30:or animal to some particular sensory input,
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3741:"Motion Perception: Seeing and Deciding"
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120:dot motion coherence task, introduces a
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16:Method to measure individual sensitivity
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3509:Das, Abhranil; Geisler, Wilson (2021).
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456:{\displaystyle N(\mu _{b},\sigma _{b})}
407:{\displaystyle N(\mu _{a},\sigma _{a})}
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161:and examine the underlying processes.
145:in the 2AFC task. For example, if one
141:It is possible to introduce biases in
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2785:
2703:Elemente der Psychophysik (2 Volumes)
1083:{\displaystyle dx=Adt+cdW\ ,\ x(0)=0}
34:, through that observer's pattern of
4043:Roitman, J. D; M. N Shadlen (2002).
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3614:Laming, Donald Richard John (1968).
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2628:Neural correlates of decision making
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592:generalized chi-square distribution
13:
4061:10.1523/JNEUROSCI.22-21-09475.2002
3581:Journal of Mathematical Psychology
3237:10.1111/j.2044-8317.1966.tb00351.x
3195:Journal of Mathematical Psychology
1826:is the rate of mutual inhibition.
14:
4110:
4002:Gold, J. I; M. N Shadlen (2002).
3455:Ratcliff, R.; P. L Smith (2004).
2700:Fechner, Gustav Theodor (1889).
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2786:Shimp, Charles P. (July 1966).
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2592:{\displaystyle k_{\text{inh}}}
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998:in human data for 2AFC tasks.
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4021:10.1016/s0896-6273(02)00971-6
3961:Annual Review of Neuroscience
3825:10.1016/s0896-6273(02)01092-9
2720:Posner, M I (February 1980).
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507:: the joint distributions of
20:Two-alternative forced choice
3930:10.1126/science.274.5286.427
3207:10.1016/0022-2496(75)90053-x
2643:lateral intraparietal cortex
1830:Feedforward inhibition model
7:
4049:The Journal of Neuroscience
3473:10.1037/0033-295x.111.2.333
3434:10.1037/0033-295x.108.3.550
3396:10.1037/0033-295x.106.2.261
3353:10.1037/0033-295x.100.3.432
3074:10.1037/0033-295x.113.4.700
2664:
500:{\displaystyle x_{1},x_{2}}
10:
4115:
3849:Journal of Neurophysiology
3678:10.1037/0096-1523.26.1.127
1113:and the starting value of
44:two-interval forced choice
3861:10.1152/jn.2001.86.4.1916
3315:10.1037/0033-295x.85.2.59
3275:10.1080/00140137008931117
2921:10.1017/S0952523800010269
2743:10.1080/00335558008248231
1263:represented formally by:
173:Normal distribution model
165:Models of decision making
137:Biases in decision making
2722:"Orienting of attention"
1172:{\displaystyle \lambda }
1151:Ornstein–Uhlenbeck model
271:Suppose the two stimuli
3643:10.1111/1467-9280.00067
2804:10.1901/jeab.1966.9-443
2193:Pooled inhibition model
1483:Mutual inhibition model
78:Behavioural experiments
3593:10.1006/jmps.1999.1260
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133:or pressing a button.
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3766:10.1073/pnas.93.2.628
3631:Psychological Science
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318:{\displaystyle x_{2}}
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55:lexical decision task
3461:Psychological Review
3422:Psychological Review
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3052:Psychological Review
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66:2AFC is a method of
3912:1996Sci...274..427H
3806:Wang, X. J (2002).
3757:1996PNAS...93..628S
3537:10.1167/jov.21.10.1
2978:2000Natur.404..390G
2909:Visual Neuroscience
2862:1999Natur.400..233P
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897:
871:
853:
754:
734:
676:
3713:10.1007/bf02289645
3172:10.1007/bf02291481
3137:10.1007/bf02289729
2617:{\displaystyle w'}
2614:
2589:
2560:
2558:
2179:
2157:
2098:
1816:
1796:
1774:
1715:
1467:
1408:
1245:
1169:
1157:Ornstein–Uhlenbeck
1132:
1103:
1080:
1012:
979:
926:
917:
900:
883:
857:
839:
793:
757:
740:
720:
687:
623:
577:
557:
537:
517:
497:
453:
404:
355:
335:
315:
288:
269:
260:{\displaystyle ba}
257:
237:{\displaystyle ab}
234:
211:
191:
103:
4055:(21): 9475–9489.
3906:(5286): 427–430.
3515:Journal of Vision
2972:(6776): 390–394.
2856:(6741): 233–238.
2586:
2541:
2528:
2504:
2494:
2480:
2474:
2469:
2452:
2438:
2432:
2418:
2405:
2389:
2373:
2356:
2350:
2345:
2328:
2314:
2308:
2294:
2281:
2265:
2249:
2232:
2226:
2221:
2182:{\displaystyle u}
2139:
2131:
2125:
2111:
2090:
2076:
2070:
2059:
2045:
2039:
2034:
2020:
2014:
2003:
1995:
1989:
1984:
1964:
1950:
1944:
1933:
1919:
1913:
1908:
1894:
1888:
1877:
1869:
1863:
1858:
1819:{\displaystyle w}
1799:{\displaystyle k}
1756:
1748:
1742:
1728:
1710:
1696:
1690:
1676:
1663:
1647:
1630:
1624:
1619:
1602:
1588:
1582:
1568:
1555:
1539:
1522:
1516:
1511:
1449:
1441:
1435:
1421:
1403:
1389:
1383:
1372:
1364:
1358:
1353:
1336:
1322:
1316:
1305:
1297:
1291:
1286:
1235:
1229:
1202:
1196:
1106:{\displaystyle A}
1061:
1055:
873:
633:
580:{\displaystyle a}
560:{\displaystyle b}
540:{\displaystyle b}
520:{\displaystyle a}
358:{\displaystyle b}
338:{\displaystyle a}
214:{\displaystyle b}
194:{\displaystyle a}
149:occurs with more
114:motion perception
84:attentional shift
4106:
4083:
4082:
4072:
4040:
4034:
4033:
4023:
3999:
3993:
3992:
3956:
3950:
3949:
3923:
3895:
3889:
3888:
3855:(4): 1916–1936.
3844:
3838:
3837:
3827:
3803:
3797:
3796:
3786:
3768:
3736:
3725:
3724:
3696:
3690:
3689:
3661:
3655:
3654:
3626:
3620:
3619:
3611:
3605:
3604:
3576:
3567:
3566:
3548:
3530:
3506:
3495:
3494:
3484:
3452:
3446:
3445:
3417:
3408:
3407:
3379:
3373:
3372:
3336:
3327:
3326:
3298:
3287:
3286:
3258:
3249:
3248:
3220:
3211:
3210:
3190:
3184:
3183:
3155:
3149:
3148:
3120:
3114:
3113:
3107:
3099:
3097:
3096:
3067:
3043:
3014:
3013:
2986:10.1038/35006062
2961:
2955:
2954:
2948:
2940:
2915:(6): 1157–1169.
2904:
2898:
2897:
2845:
2834:
2833:
2823:
2783:
2777:
2776:
2774:
2773:
2726:
2717:
2711:
2707:
2697:
2671:Choice modelling
2623:
2621:
2620:
2615:
2613:
2598:
2596:
2595:
2590:
2588:
2587:
2584:
2569:
2567:
2566:
2561:
2559:
2543:
2542:
2539:
2530:
2529:
2526:
2517:
2506:
2505:
2502:
2496:
2495:
2492:
2478:
2472:
2471:
2470:
2467:
2454:
2453:
2450:
2436:
2430:
2420:
2419:
2416:
2407:
2406:
2403:
2391:
2390:
2387:
2375:
2374:
2371:
2354:
2348:
2347:
2346:
2343:
2330:
2329:
2326:
2312:
2306:
2296:
2295:
2292:
2283:
2282:
2279:
2267:
2266:
2263:
2251:
2250:
2247:
2230:
2224:
2223:
2222:
2219:
2188:
2186:
2185:
2180:
2166:
2164:
2163:
2158:
2141:
2140:
2137:
2129:
2123:
2113:
2112:
2109:
2099:
2092:
2091:
2088:
2074:
2068:
2061:
2060:
2057:
2043:
2037:
2036:
2035:
2032:
2018:
2012:
2005:
2004:
2001:
1993:
1987:
1986:
1985:
1982:
1966:
1965:
1962:
1948:
1942:
1935:
1934:
1931:
1917:
1911:
1910:
1909:
1906:
1892:
1886:
1879:
1878:
1875:
1867:
1861:
1860:
1859:
1856:
1825:
1823:
1822:
1817:
1805:
1803:
1802:
1797:
1783:
1781:
1780:
1775:
1758:
1757:
1754:
1746:
1740:
1730:
1729:
1726:
1716:
1712:
1711:
1708:
1694:
1688:
1678:
1677:
1674:
1665:
1664:
1661:
1649:
1648:
1645:
1628:
1622:
1621:
1620:
1617:
1604:
1603:
1600:
1586:
1580:
1570:
1569:
1566:
1557:
1556:
1553:
1541:
1540:
1537:
1520:
1514:
1513:
1512:
1509:
1476:
1474:
1473:
1468:
1451:
1450:
1447:
1439:
1433:
1423:
1422:
1419:
1409:
1405:
1404:
1401:
1387:
1381:
1374:
1373:
1370:
1362:
1356:
1355:
1354:
1351:
1338:
1337:
1334:
1320:
1314:
1307:
1306:
1303:
1295:
1289:
1288:
1287:
1284:
1254:
1252:
1251:
1246:
1233:
1227:
1200:
1194:
1178:
1176:
1175:
1170:
1141:
1139:
1138:
1133:
1112:
1110:
1109:
1104:
1089:
1087:
1086:
1081:
1059:
1053:
965:
935:
933:
932:
927:
922:
921:
913:
908:
896:
891:
874:
872:
870:
865:
852:
847:
837:
836:
835:
823:
822:
812:
807:
798:
797:
771:
762:
761:
753:
748:
733:
728:
708:
696:
694:
693:
688:
680:
675:
670:
657:
649:
641:
635:
634:
626:
586:
584:
583:
578:
566:
564:
563:
558:
546:
544:
543:
538:
526:
524:
523:
518:
506:
504:
503:
498:
496:
495:
483:
482:
462:
460:
459:
454:
449:
448:
436:
435:
413:
411:
410:
405:
400:
399:
387:
386:
364:
362:
361:
356:
344:
342:
341:
336:
324:
322:
321:
316:
314:
313:
297:
295:
294:
289:
287:
286:
266:
264:
263:
258:
243:
241:
240:
235:
220:
218:
217:
212:
200:
198:
197:
192:
4114:
4113:
4109:
4108:
4107:
4105:
4104:
4103:
4089:
4088:
4087:
4086:
4041:
4037:
4000:
3996:
3957:
3953:
3921:10.1.1.408.5678
3896:
3892:
3845:
3841:
3804:
3800:
3737:
3728:
3697:
3693:
3662:
3658:
3627:
3623:
3612:
3608:
3577:
3570:
3507:
3498:
3453:
3449:
3418:
3411:
3380:
3376:
3337:
3330:
3299:
3290:
3259:
3252:
3221:
3214:
3191:
3187:
3156:
3152:
3121:
3117:
3101:
3100:
3094:
3092:
3065:10.1.1.212.9187
3044:
3017:
2962:
2958:
2942:
2941:
2905:
2901:
2846:
2837:
2784:
2780:
2771:
2769:
2724:
2718:
2714:
2698:
2694:
2689:
2667:
2635:
2630:
2606:
2604:
2601:
2600:
2583:
2579:
2577:
2574:
2573:
2557:
2556:
2538:
2534:
2525:
2521:
2510:
2501:
2497:
2491:
2487:
2466:
2462:
2456:
2455:
2449:
2445:
2415:
2411:
2402:
2398:
2386:
2382:
2370:
2366:
2342:
2338:
2332:
2331:
2325:
2321:
2291:
2287:
2278:
2274:
2262:
2258:
2246:
2242:
2218:
2214:
2207:
2205:
2202:
2201:
2195:
2174:
2171:
2170:
2136:
2132:
2108:
2104:
2097:
2096:
2087:
2083:
2056:
2052:
2031:
2027:
2000:
1996:
1981:
1977:
1971:
1970:
1961:
1957:
1930:
1926:
1905:
1901:
1874:
1870:
1855:
1851:
1844:
1842:
1839:
1838:
1832:
1811:
1808:
1807:
1791:
1788:
1787:
1753:
1749:
1725:
1721:
1714:
1713:
1707:
1703:
1673:
1669:
1660:
1656:
1644:
1640:
1616:
1612:
1606:
1605:
1599:
1595:
1565:
1561:
1552:
1548:
1536:
1532:
1508:
1504:
1497:
1495:
1492:
1491:
1485:
1446:
1442:
1418:
1414:
1407:
1406:
1400:
1396:
1369:
1365:
1350:
1346:
1340:
1339:
1333:
1329:
1302:
1298:
1283:
1279:
1272:
1270:
1267:
1266:
1260:
1186:
1183:
1182:
1164:
1161:
1160:
1153:
1148:
1118:
1115:
1114:
1098:
1095:
1094:
1021:
1018:
1017:
1004:
966:
963:
951:using the 2AFC:
945:
916:
915:
909:
904:
898:
892:
887:
876:
875:
866:
861:
848:
843:
838:
831:
827:
818:
814:
813:
811:
803:
792:
791:
786:
776:
775:
767:
756:
755:
749:
744:
735:
729:
724:
713:
712:
704:
702:
699:
698:
671:
653:
645:
637:
636:
625:
624:
619:
599:
596:
595:
572:
569:
568:
552:
549:
548:
532:
529:
528:
512:
509:
508:
491:
487:
478:
474:
472:
469:
468:
444:
440:
431:
427:
419:
416:
415:
395:
391:
382:
378:
370:
367:
366:
350:
347:
346:
330:
327:
326:
309:
305:
303:
300:
299:
282:
278:
276:
273:
272:
249:
246:
245:
226:
223:
222:
206:
203:
202:
186:
183:
182:
175:
167:
159:decision making
143:decision making
139:
92:decision making
80:
60:response biases
17:
12:
11:
5:
4112:
4102:
4101:
4085:
4084:
4035:
4014:(2): 299–308.
3994:
3967:(1): 241–259.
3951:
3890:
3839:
3818:(5): 955–968.
3798:
3751:(2): 628–633.
3726:
3707:(4): 375–396.
3691:
3672:(1): 127–140.
3656:
3637:(5): 347–356.
3621:
3606:
3587:(3): 408–463.
3568:
3496:
3467:(2): 333–367.
3447:
3428:(3): 550–592.
3409:
3390:(2): 261–300.
3374:
3347:(3): 432–459.
3328:
3288:
3250:
3212:
3201:(1): 114–135.
3185:
3150:
3131:(3): 251–260.
3115:
3058:(4): 700–765.
3015:
2956:
2899:
2835:
2798:(4): 443–455.
2778:
2712:
2691:
2690:
2688:
2685:
2684:
2683:
2678:
2673:
2666:
2663:
2658:rhesus monkeys
2634:
2631:
2629:
2626:
2612:
2609:
2582:
2555:
2552:
2549:
2546:
2537:
2533:
2524:
2520:
2516:
2513:
2509:
2500:
2490:
2486:
2483:
2477:
2465:
2461:
2458:
2457:
2448:
2444:
2441:
2435:
2429:
2426:
2423:
2414:
2410:
2401:
2397:
2394:
2385:
2381:
2378:
2369:
2365:
2362:
2359:
2353:
2341:
2337:
2334:
2333:
2324:
2320:
2317:
2311:
2305:
2302:
2299:
2290:
2286:
2277:
2273:
2270:
2261:
2257:
2254:
2245:
2241:
2238:
2235:
2229:
2217:
2213:
2210:
2209:
2194:
2191:
2178:
2156:
2153:
2150:
2147:
2144:
2135:
2128:
2122:
2119:
2116:
2107:
2102:
2095:
2086:
2082:
2079:
2073:
2067:
2064:
2055:
2051:
2048:
2042:
2030:
2026:
2023:
2017:
2011:
2008:
1999:
1992:
1980:
1976:
1973:
1972:
1969:
1960:
1956:
1953:
1947:
1941:
1938:
1929:
1925:
1922:
1916:
1904:
1900:
1897:
1891:
1885:
1882:
1873:
1866:
1854:
1850:
1847:
1846:
1831:
1828:
1815:
1795:
1773:
1770:
1767:
1764:
1761:
1752:
1745:
1739:
1736:
1733:
1724:
1719:
1706:
1702:
1699:
1693:
1687:
1684:
1681:
1672:
1668:
1659:
1655:
1652:
1643:
1639:
1636:
1633:
1627:
1615:
1611:
1608:
1607:
1598:
1594:
1591:
1585:
1579:
1576:
1573:
1564:
1560:
1551:
1547:
1544:
1535:
1531:
1528:
1525:
1519:
1507:
1503:
1500:
1499:
1484:
1481:
1466:
1463:
1460:
1457:
1454:
1445:
1438:
1432:
1429:
1426:
1417:
1412:
1399:
1395:
1392:
1386:
1380:
1377:
1368:
1361:
1349:
1345:
1342:
1341:
1332:
1328:
1325:
1319:
1313:
1310:
1301:
1294:
1282:
1278:
1275:
1274:
1259:
1256:
1244:
1241:
1238:
1232:
1226:
1223:
1220:
1217:
1214:
1211:
1208:
1205:
1199:
1193:
1190:
1168:
1152:
1149:
1147:
1144:
1131:
1128:
1125:
1122:
1102:
1079:
1076:
1073:
1070:
1067:
1064:
1058:
1052:
1049:
1046:
1043:
1040:
1037:
1034:
1031:
1028:
1025:
1003:
1000:
996:reaction times
961:
944:
941:
925:
920:
912:
907:
903:
899:
895:
890:
886:
882:
881:
879:
869:
864:
860:
856:
851:
846:
842:
834:
830:
826:
821:
817:
810:
806:
801:
796:
790:
787:
785:
782:
781:
779:
774:
770:
765:
760:
752:
747:
743:
739:
736:
732:
727:
723:
719:
718:
716:
711:
707:
686:
683:
679:
674:
669:
666:
663:
660:
656:
652:
648:
644:
640:
632:
629:
622:
618:
615:
612:
609:
606:
603:
576:
556:
536:
516:
494:
490:
486:
481:
477:
465:ideal observer
452:
447:
443:
439:
434:
430:
426:
423:
403:
398:
394:
390:
385:
381:
377:
374:
354:
334:
312:
308:
285:
281:
256:
253:
233:
230:
210:
190:
174:
171:
166:
163:
138:
135:
79:
76:
15:
9:
6:
4:
3:
2:
4111:
4100:
4099:Psychophysics
4097:
4096:
4094:
4080:
4076:
4071:
4066:
4062:
4058:
4054:
4050:
4046:
4039:
4031:
4027:
4022:
4017:
4013:
4009:
4005:
3998:
3990:
3986:
3982:
3978:
3974:
3970:
3966:
3962:
3955:
3947:
3943:
3939:
3935:
3931:
3927:
3922:
3917:
3913:
3909:
3905:
3901:
3894:
3886:
3882:
3878:
3874:
3870:
3866:
3862:
3858:
3854:
3850:
3843:
3835:
3831:
3826:
3821:
3817:
3813:
3809:
3802:
3794:
3790:
3785:
3780:
3776:
3772:
3767:
3762:
3758:
3754:
3750:
3746:
3742:
3735:
3733:
3731:
3722:
3718:
3714:
3710:
3706:
3702:
3701:Psychometrika
3695:
3687:
3683:
3679:
3675:
3671:
3667:
3660:
3652:
3648:
3644:
3640:
3636:
3632:
3625:
3618:. Academic P.
3617:
3610:
3602:
3598:
3594:
3590:
3586:
3582:
3575:
3573:
3564:
3560:
3556:
3552:
3547:
3542:
3538:
3534:
3529:
3524:
3520:
3516:
3512:
3505:
3503:
3501:
3492:
3488:
3483:
3478:
3474:
3470:
3466:
3462:
3458:
3451:
3443:
3439:
3435:
3431:
3427:
3423:
3416:
3414:
3405:
3401:
3397:
3393:
3389:
3385:
3378:
3370:
3366:
3362:
3358:
3354:
3350:
3346:
3342:
3335:
3333:
3324:
3320:
3316:
3312:
3309:(2): 59–108.
3308:
3304:
3297:
3295:
3293:
3284:
3280:
3276:
3272:
3268:
3264:
3257:
3255:
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3226:
3219:
3217:
3208:
3204:
3200:
3196:
3189:
3181:
3177:
3173:
3169:
3166:(1): 77–105.
3165:
3161:
3160:Psychometrika
3154:
3146:
3142:
3138:
3134:
3130:
3126:
3125:Psychometrika
3119:
3111:
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3091:
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2870:10.1038/22268
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2662:
2659:
2655:
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2610:
2607:
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2570:
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2015:
2009:
2006:
1997:
1990:
1978:
1974:
1958:
1954:
1951:
1945:
1939:
1936:
1927:
1920:
1914:
1902:
1898:
1895:
1889:
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1880:
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1827:
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1100:
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1035:
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984:
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960:
958:
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940:
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910:
905:
901:
893:
888:
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877:
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667:
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658:
650:
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627:
620:
616:
613:
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601:
593:
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574:
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514:
492:
488:
484:
479:
475:
466:
445:
441:
437:
432:
428:
421:
396:
392:
388:
383:
379:
372:
352:
332:
310:
306:
283:
279:
254:
251:
231:
228:
208:
188:
179:
170:
162:
160:
156:
152:
148:
144:
134:
132:
127:
123:
119:
115:
110:
108:
99:
95:
93:
89:
88:reinforcement
85:
75:
73:
70:developed by
69:
68:psychophysics
64:
61:
56:
51:
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3460:
3450:
3425:
3421:
3387:
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3302:
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3266:
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1146:Other models
1091:
1016:
1013:
1002:Formal model
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980:
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270:
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2633:Brain areas
983:random walk
155:probability
3528:2012.14331
3263:Ergonomics
3095:2012-06-09
2772:2012-06-12
2687:References
2676:Choice set
1258:Race model
988:stochastic
3916:CiteSeerX
3869:1522-1598
3775:1091-6490
3721:120502141
3563:229934512
3521:(10): 1.
3145:121644881
3082:0033-295X
3060:CiteSeerX
2994:0028-0836
2878:0028-0836
2812:0022-5002
2751:0033-555X
2485:−
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2253:−
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902:σ
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655:λ
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429:μ
393:σ
380:μ
151:frequency
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547:, or of
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3753:Bibcode
3651:1045352
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3323:1166147
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2929:8257671
2894:4389701
2858:Bibcode
2830:5961513
2821:1338246
2767:2842391
2759:7367577
2654:neurons
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131:saccade
107:saccade
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116:. The
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3717:S2CID
3647:S2CID
3559:S2CID
3523:arXiv
3365:S2CID
3319:S2CID
3176:S2CID
3141:S2CID
3006:S2CID
2933:S2CID
2890:S2CID
2763:S2CID
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863:b
850:2
845:a
833:b
820:a
809:=
800:,
795:]
789:1
784:1
778:[
773:=
769:k
764:,
759:]
751:2
746:b
731:2
726:a
715:[
710:=
706:w
685:0
678:)
673:2
668:0
665:,
662:0
659:,
651:,
647:k
643:,
639:w
621:(
617:p
614:=
611:)
608:e
605:(
602:p
575:a
555:b
535:b
515:a
493:2
489:x
485:,
480:1
476:x
451:)
446:b
438:,
433:b
425:(
422:N
402:)
397:a
389:,
384:a
376:(
373:N
353:b
333:a
311:2
307:x
284:1
280:x
255:a
252:b
232:b
229:a
209:b
189:a
22:(
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