Stimulus Sampling Theory. Agenda Stimulus Sampling Theory overview Analytic & simulation models Estes & Straughan, 1954 Homeworks 1 & 2.

Stimulus Sampling Theory

Agenda

• Stimulus Sampling Theory overview

• Analytic & simulation models

• Estes & Straughan, 1954

• Homeworks 1 & 2

Stimulus Sampling Theory

Stimulus Elements

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Trial n

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Stimulus Sampling Theory

Stimulus Elements

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P(A) = 1/4

Stimulus Sampling Theory

Stimulus Elements

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Feedback for A

Stimulus Sampling Theory

Stimulus Elements

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Stimulus Sampling Theory

Stimulus Elements

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P(A) = 1/2

Stimulus Sampling Theory

Stimulus Elements

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Feedback for B

An Example

• One of two stimuli, Red A or Blue B, appear.

• You are simply to learn when to press a button.

An Example

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.3P(Press) = 0/3

An Example

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.3Feedback = Press

An Example

B

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.3P(Press) = 1/2

An Example

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.3Feedback = No Press

An Example

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.3P(Press) = 0/2

An Example

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.3Feedback = Press

A Modern Example

2 5 1 7 2 3 9 5 2 3 7 8

Phonology Orthography Semantics Context

What are Stimulus Elements?• “The concept of stimulus element is not defined

in terms of observable events; it has the status of a primitive term within the theory” (p. 4).

• “Relating experimental manipulations to a stimulus sampling parameter … is by no means necessary … for the derivation of testable predictions. To the extent that directly testable implications of the theory are supported by evidence, the concepts of stimulus sampling remain tenable” (p. 4).

Is Stimulus Sampling Theory a Model?

• “The term ‘stimulus sampling theory’ refers to a number of theories differing with respect to special assumptions and their mathematical expression, yet sharing a common approach to conceptual representation of the stimulus situation and the formation of associative connections, rather than to a single coherent set of assumptions formulated to apply to all the experimental procedures employed in the study of learning” (p. 1).

Analytic & Simulation Models

• An analytic solution to a model is one in which an equation is used to describe the output of the model.

• A simulation result is produced by following a set of procedures.

Analytic & Simulation Models

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P(A |θ,n) =1−1

Nθ θ i 1−θ i( )

n

i

∑

1) Sample S’ from S on Trial n

2) P(A) = Proportion A from S’

3) Associate S’ with feedback

4) Go to 1

Analytic & Simulation Models

• In general, an analytic solution is preferred.– Less prone to specific sequences.– Can often make the same predictions as

simulation.– Faster.

• Especially in fitting programs.

– Easier.