- 207 Views
- Updated On :

Adaptive Methods. Research Methods Fall 2010 Tamás Bőhm. Adaptive methods. Classical (Fechnerian) methods: stimulus is often far from the threshold inefficient A daptive methods: accelerated testing Modifications of the method of constant stimuli and method of limits. Adaptive methods.

Related searches for Adaptive Methods

Download Presentation
## PowerPoint Slideshow about 'Adaptive Methods' - bidelia

**An Image/Link below is provided (as is) to download presentation**

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.

- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -

Presentation Transcript

Adaptive methods

- Classical (Fechnerian) methods: stimulus is often far from the thresholdinefficient
- Adaptive methods: accelerated testing
- Modifications of the method of constant stimuli and method of limits

Adaptive methods

- Classical methods: stimulus values to be presented are fixed before the experiment
- Adaptive methods: stimulus values to be presented depend critically on preceding responses

Adaptive methods

- Constituents
- Stepping rule: which stimulus level to use next?
- Stopping criterion: when to finish the session?
- What is the final threshold estimate?

- Performance
- Bias: systematic error
- Precision: related to random error
- Efficiency: # of trials needed for a specific precision; measured by the sweat factor

Notations

Xn stimulus level at trial n

Zn response at trial n

Zn= 1 detected / correct

Zn = 0 not detected / incorrect

φtarget probability

absolute threshold: φ = 50%

difference threshold: φ = 75%

2AFC: φ = 50% + 50% / 2 = 75%

4AFC: φ = 25% + 75% / 2 = 62.5%

xφ threshold

Adaptive methods

- Classical methods: stimulus values to be presented are fixed before the experiment
- Adaptive methods: stimulus values to be presented depend critically on preceding responses
Xn+1 = f(φ, n, Zn, Xn, Zn-1, Xn-1,…, Z1, X1)

Adaptive methods

- Nonparametric methods:
- No assumptions about the shape of the psychometric function
- Can measure threshold only

- Parametric methods:
- General form of the psychometric function is known, only its parameters (threshold and slope) need to be measured
- If slope is also known: measure only threshold

Nonparametric adaptive methods

- Staircase method (aka. truncated method of limits, simple up-down)
- Transformed up-down method
- Nonparametric up-down method
- Weighted up-down method
- Modified binary search
- Stochastic approximation
- Accelerated stochastic approximation
- PEST and More Virulent PEST

Stepping rule:Xn+1 = Xn - δ(2Zn - 1)

fixed step size δ

if response changes:direction of steps is reversed

Stopping criterion:after a predetermined number of reversals

Threshold estimate: average of reversal points(mid-run estimate)

Converges to φ = 50% cannot be used for e.g. 2AFC

Staircase methodImprovement of the simple up-down (staircase) method

Xn+1 depends on 2 or more preceding responses

E.g.1-up/2-down or 2-step rule:

Increase stimulus level after each incorrect response

Decrease only after 2 correct responses

φ = 70.7%

Threshold:mid-run estimate

8 rules for 8 different φ values(15.9%, 29.3%, 50%, 70.7%, 79.4%, 84.1%)

Transformed up-down methodreversal points

Nonparametric up-down method

- Stepping rule: Xn+1= Xn- δ(2ZnSφ - 1)
- Sφ: random number p(Sφ=1) = 1 / 2φ p(Sφ=0) = 1 – (1 / 2φ)
- After a correct answer: stimulus decreased with p = 1 / 2φ stimulus increased with p = 1 - (1 / 2φ)
- After an incorrect answer: stimulus increased

- Can converge to any φ≥ 50%

Weighted up-down method

- Different step sizes for upward (δup) and downward steps (δdown)

Stimulus interval containing the threshold is halved in every step(one endpoint is replaced by the midpoint)

Stopping criterion: a lower limit on the step size

Threshold estimate:last tested level

Heuristic, no theoreticalfoundation

Modified binary searchFigure from Sedgewick & Wayne

Stochastic approximation

- A theoretically sound variant of the modified binary search
- Stepping rule:
- c: initial step size
- Stimulus value increases for correct responses,decreases for incorrect ones
- If φ = 50%: upward and downward steps are equal; otherwise asymmetric
- Step size (both upward and downward) decreases from trial to trial

- Can converge to any φ

Accelerated stochastic approximation

- Stepping rule:
- First 2 trials: stochastic approximation
- n > 2:step size is changed only when response changes (mreversals: number of reversals)

- Otherwise the same as stochastic approximation
- Less trials than stochastic approximation

Parameter Estimation by Sequential Testing (PEST)

- Sequential testing:
- Run multiple trials at the same stimulus level x
- If x is near the threshold, the expected number of correct responses mc after nx presentations will be around φnx the stimulus level is changed if mcis not in φnx ± w
- w: deviation limit; w=1 for φ=75%

- If the stimulus level needs to be changed:step size determined by a set of heuristic rules
- Variants: MOUSE, RAT, More Virulent PEST

Adaptive methods

- Nonparametric methods:
- No assumptions about the shape of the psychometric function
- Can measure threshold only

- Parametric methods:
- General form of the psychometric function is known, only its parameters (threshold and slope) need to be measured
- If slope is also known: measure only threshold

Parametric adaptive methods

- A template for the psychometric function is chosen:
- Cumulative normal
- Logistic
- Weibull
- Gumbel

Parametric adaptive methods

- Only the parameters of the template need to be measured:
- Threshold
- Slope

Fitting the psychometric function

- Linearization (inverse transformation)of data points
- Inverse cumulative normal (probit)
- Inverse logistic(logit)

Fitting the psychometric function

- Linear regression
- Transformation of regression line parameters

X-intercept & linear slope

Threshold & logistic slope

Contour integration experiment

5-day perceptual learning

Adaptive probit estimation

- Short blocks of method of constant stimuli
- Between blocks: threshold and slope is estimated (psychometric function is fitted to the data) and stimulus levels adjusted accordingly
- Assumes a cumulative normal function probit analysis

- Stopping criterion: after a fixed number of blocks
- Final estimate of threshold and slope: re-analysis of all the responses

Adaptive probit estimation

- Start with an educated guess of the threshold and slope
- In each block: 4 stimulus levels presented 10 times each
- After each block: threshold ( ) and slope ( ) is estimatedby probit analysis of the responses in block
- Stimulus levels for the next block are adjusted accordingly
- Estimated threshold and slopeapplied only through correctionfactors inertia

Function shape (form & slope) is predetermined by the experimenter

Only the position along the x-axis (threshold) needs to be measured

Iteratively estimating the threshold and adapting the stimulus levels

Two ways to estimate the threshold:

Maximum likelihood (ML)

Bayes’ estimation

QUEST, BEST PEST, ML-TEST, Quadrature Method, IDEAL, YAAP, ZEST

Measuring the threshold onlyMaximum likelihood estimation experimenter

- Construct the psychometric function with each possible threshold value
- Calculate the probability of the responses with each threshold value (likelihood)
- Choose the threshold value for which the likelihood is maximal (i.e. the psychometric function that is the most likely to produce such responses)

- - - +

- - + +

- + + +

Bayes’ estimation experimenter

- Prior information is also used
- Distribution of the threshold in the population(e.g. from a survey of the literature)
- The experimenter’s beliefs about the threshold

values of the psychometric functions at the tested stimulus levels

a priori distribution of the threshold

Download Presentation

Connecting to Server..