lecture 2 - evidence accumulation models & psychometric curves

Question 1

why is the SDT model too simple

Answer 1

• SDT works with a single, instantaneous sample of the decision variable.
• this isn’t natural, as in life, time is continuous and it often takes time to integrate evidence to make decisions

Question 2

evidence integration

Answer 2

1. when we have prolonged access to information, we must integrate evidence over time, rather than relying on a single, instantaneous sample as in SDT. this means that the decision variable that used to be a simple number now is an integral over time
2. subsequent samples are drawn randomly from our SDT distributions, meaning that evidence can fluctuate, sometimes supporting a decision and other times not, depending on the sample.
3. we decide upon sufficient evidence: ‘harder decisions take longer’
4. more realistic than simple SDT, linking information processing and action

Question 3

sequential sampling process

Answer 3

• done by accumulating instantaneous inputs, and then comparing these accumulated traces with one another

1. two response options are presented (yes/no)
2. evidence is sampled sequentially and integrated over time
3. accumulated signal hits a threshold (yes/no)

Question 4

sequential sampling (mathematically)

Answer 4

change in decision variable = drift + noise

Question 5

what is possible with the drift diffusion model

Answer 5

• we can model complete reaction time distributions (not just mean RT)
• we can interpret intricate patterns, such as shifts in error RTs relative to correct RTs
• we can manipulate: given a sensitivity (drift rate) shift both criterion (bias), and the speed-accuracy trade-off (boundary separation)

Question 6

boundary separation (a)

Answer 6

• the distance between the upper and lower decision boundaries
• influences how much evidence must be accumulated until a response is executed
• a lower threshold makes responding faster in general but increases the influence of noise on decision making and can hence lead to errors or impulsive choice
• a higher threshold leads to more cautious responding (slower, more skewed RT distributions, but more accurate).

Question 7

response time

Answer 7

• is not solely comprised of the decision making process
• perception, movement initiation and execution all take time and are lumped in the DDM by a single non-decision time parameter (t)

Question 8

drift rate

Answer 8

• rate of accumulation of evidence (how fast one of the boundary is reached)
• captures average speed and direction of information accumulation
• determined by the quality of the information extracted from the stimulus (i.e. the value to the drift rate would be different for each stimulus condition that differed in difficulty)

Question 9

positive vs negative drift rate

Answer 9

• positive drift rate: towards upper boundary/signal
• negative drift rate: towards lower boundary/noise

Question 10

What effect does noise have in relation to the drift rate

Answer 10

due to noise, processes with the same mean drift rate do not always terminate at the same time or boundary between trials

Question 11

drift rate and reaction time

Answer 11

• the reaction times become shorter as the drift rate increases
• slower reaction times occur for weaker or noisier evidence

Question 12

Ornstein-Uhlenbeck process

Answer 12

• variation of the standard Drift Diffusion Model (DDM)
• shows that accumulation can accelerate or decelerate
• λ controls the rate of drift deceleration or reversion
• negative lambda slows down evidence accumulation, making decisions take longer and harder to finalize.
• with a positive lambda, the decision variable accelerates away from 0, amplifying any drift

Question 13

starting point (z)

Answer 13

• the initial evidence position, centered between boundaries
• affects the starting point of the drift process relative to the two boundaries
• reflects bias
• changes the ratios of hits and false alarms

Question 14

unbiased starting point

Answer 14

boundary separation / 2

Question 15

starting point/bias (z) value interpretation

Answer 15

• Errors are faster when downward bias is strong (z< a/2)
• because the starting point is closer to the lower boundary, making errors more likely and faster
• Correct RTs are faster when upward bias is strong (z>a/2)
• because the starting point is closer to the upper boundary, favoring correct decisions

Question 16

bias (z): link to SDT

Answer 16

• Manipulating z affects the balance of hits and false alarms
• Higher z: More hits, fewer false alarms (biased toward signal).
• Lower z: Fewer hits, more false alarms (biased toward noise).
• this is because z reflects pre-decision bias, just like c does in SDT
• Adjusting z affects the likelihood of terminating at each boundary and the corresponding reaction times.

Question 17

impact of changing DDM parameters

Answer 17

• faster drift rate: shorter RT for both signal and error trials
• changes in bias: changes the ratios of hits and false alarms. Errors are faster when downward bias is strong. Correct RTs are faster when upward bias is strong.

Question 18

DDM and SDT parallels

Answer 18

1. drift rate corresponds to sensitivity
   - larger drift rate means faster accumulation toward the correct decision boundary, analogous to better sensitivity
   - so, both represent how easily the decision-maker can differentiate signal from noise.
2. criterion corresponds to the bias before the drift begins/startingpoint
   - they both represent pre-decision biases in the system

Question 19

signal/noise trial difference SDT and DDM

Answer 19

• DDM: noise and signal trials are distinguished by whether the accumulation process drifts up (signal) or down (noise)
• SDT: noise and signal trials are distinguished by where the fixed criterion lies relative to the signal and noise distributions
• so, the move from SDT to DDM reflects a shift from modeling decisions as a single comparison at a fixed time (SDT) to modeling them as a dynamic process over time (DDM), where decisions emerge from the gradual accumulation of evidence.

Question 20

In the present implementation, we used time in ms. What effect would changing the simulations to occur in seconds have on the parameters v and z in the model?

Answer 20

• changing the time scale (from ms to s) requires scaling all parameters related to time
• drift rate (v) would be rescaled because it reflects the accumulation of evidence per unit of time
• starting point (z) does not need to change because it is defined relative to the boundary separation, which is independent of time

Question 21

psychometric curves

Answer 21

• extension of SDT
• based on varying signal levels
• s-shaped curve (sigmoidal) that plots the probability of a certain response (e.g., correct response)

Question 22

psychometric curves: stimulus intensities

Answer 22

• At very low stimulus intensities, the probability of detecting the stimulus is close to zero.
• At very high stimulus intensities, detection approaches certainty (probability = 1).
• In between, there is a transition region where detection is more variable, reflecting uncertainty or noise.

Question 23

psychometric curves: effect of criterion

Answer 23

• liberal criterion shifts the bottom of the curve up, meaning people will say ‘yes’, even when the signal is weak
• conservative criterion shifts the curve down, meaning people will only say “yes” when the signal is quite strong

Question 24

2-alternative forced-choice experiment

Answer 24

instead of yes/no, the task is about discrimination between two alternatives

Question 25

psychometric curves: bias

Answer 25

• reflects a systematic tendency to favor one response option over another, regardless of the actual evidence.
• point where the curve shifts along the 0.5 mark on the y-axis. if this corresponds to 0 on the x-axis, it is ubiased

Question 26

psychometric curves: meaning of shifting the bias when the y-axis represents ‘proportion left’

Answer 26

• Shift to the right (positive bias): The observer favors “right” responses, requiring stronger evidence to choose “left.”
• Shift to the left (negative bias): The observer favors “left” responses, requiring stronger evidence to choose “right.”

Question 27

psychometric curves: sensitivity definition

Answer 27

reflects the observer’s ability to distinguish between the two options.

Question 28

psychometric curves: sensitivity value meaning

Answer 28

• Higher sensitivity = low noise: σ- = Steeper curve.
• Lower sensitivity = high noise: σ+ = Flatter curve.

Question 29

psychometric curves: proportion of correct answers

Answer 29

higher sensitivity leads to a steeper curve and a greater proportion of correct answers, even for smaller differences between stimuli.

Question 30

psychometric curves: sources of error

Answer 30

1. lower sensitivity
2. lapses (finger errors)

Question 31

psychometric curves: sensitivity expressed as λ

Answer 31

• shift to the left = λ+ = more sensitivity
• shift to the right = λ- = less sensitivity

Question 32

psychometric curves: more alternatives

Answer 32

• more alternatives will increase sensitivity
• because its easier to see the one image that has a signal versus all the other ones that do not
• more alternatives also put chance level at a lower proportion correct

Question 33

manipulation of coherence experiment

Answer 33

• produces a psychometric curve
• as motion coherence increases, accuracy in detecting the correct direction increases and mean RT decreases
• firing rates increase faster with higher motion strength resulting in steeper firing rate curves
• corresponds with the process of accumulating sensory evidence until a decision threshold is reached, highlighting the neural basis of decision-making (in humans)