Wagner-Rescorla Surprise ModelThe Wagner-Rescorla Model is a well-known linear-operator model of Pavlovian Conditioning.

The model is based on the notion that the key aspect of experience that drives change in behavior is the psychological effects of surprise.

Wagner-Rescorla Real-Time Linear-Operator ModelThe Wagner-Rescorla Model of Pavlovian Conditioning is a linear-operator model.

An operator is a mathematical expression or computational algorithm that is applied to a series of calculations.

The Wagner-Rescorla operator is applied to a series arranged in a straight line or linear dimension.

The straight line dimension on which the algorithm operates is the linear dimension of real-time.

The model is applied to Pavlovian procedures, which are experienced sequentially in a straight line sequence along the linear dimension of real-time.

The Wagner-Rescorla ModelThe Wagner-Rescorla Model attempts to capture computationally the psychological impact of surprise.

According to the model, the presentation of the US will increase CS-US association to the extent that the presentation of the US is surprising or unexpected.

If the presentation of the US occurs in the presence of CSs that are not associated with the US, then that US presentation is surprising and will produce a large increase in CS-US association.

If,on the other hand, the presentation of the US occurs in the presence of CSs that are highly associated with the US, then that US presentation is not surprising and will produce little or no increase in CS-US association.

The Wagner-Rescorla Model

VA = A US (US - ), where:

VA = Delta VA

VA = Change in association between CSA and the US on this trial.

The Wagner-Rescorla Model VA = A US (US - ), where:

A = growth rate parameter for CSA (this is a constant, 0< A< 1.0)

US = growth rate parameter for US (this is a constant, 0< US < 1.0)

The Wagner-Rescorla Model VA = A US (US - ), where:

US = lambdaUS

US = maximum amount of associative strength possible with this US.

The Wagner-Rescorla Model VA = A US (US - ), where:

= sum of the V values of all stimuli present on this trial.

If only CSX is present on this trial, then, = VX.

If CSX and CSA are both present on this trial, then, = VX + VA.

using equationVXVX 1 2 3 4 5 6 7 8 9 10 X X X X X X X X X XPeriodsPositive Correlation V VAVA using equationA*A*A*00Group :

Computational Equations1. CSA and US: VA = A US (US - )

2. CSX and US: VX = X US (US - )

3. CSA and NO US: VA = A US (EXT - )

4. CSX and NO US: VX = X US (EXT - )

Using the following constants:A = 0.5X = 0.6US = 0.7US = 1.0EXT = 0.0

using equationVXVX 1 2 3 4 5 6 7 8 9 10 X X X X X X X X X XPeriodsPositive Correlation V VAVA using equationA*A*A*00Group :

Associative Account Ledgers for CSA and CSXCSA is the discrete CS that is presented during periods 4, 7, and 10.

CSX is all of the other stimuli (context, situation, environment) other than CSA and the US.

CSX is present during all periods.

Associative Account Ledgers for CSA and CSXThe ledger works like your checking account:

The V line is the credit and debit ledger, where each transaction [deposit (credit) or purchase (debit)] is entered.

The V line is the balance of the account after each transaction has been entered.

Check Down List On each period:

Step 1. Which CS stimuli are actually present on this period? Calculate V only for stimuli that are actually present on this period.

Step 2. Calculate for this period. Add the V values for only those stimuli that are actually present on this period.

Check Down List On each period:

Step 3. Was the US presented during this period? If yes, then use US = 1.0. If no, then use EXT = 0.0.

Step 4. Calculate V for each stimulus that was present during this period.

Step 5. Update V values for all stimuli.

using equationVXVX 1 2 3 4 5 6 7 8 9 10 X X X X X X X X X XPeriodsPositive Correlation V VAVA using equationA*A*A*00Group :

using equationVXVX 1 2 3 4 5 6 7 8 9 10 X X X X X X X X X XPeriodsPositive Correlation V VAVA using equationA*A*A*00Group : --- --- --- ------ --- ---

using equationVXVX 1 2 3 4 5 6 7 8 9 10 X X X X X X X X X XPeriodsPositive Correlation V VAVA using equationA*A*A*00Group : 0 4 0 0---0 --- --- ------ --- ---

using equationVXVX 1 2 3 4 5 6 7 8 9 10 X X X X X X X X X XPeriodsPositive Correlation V VAVA using equationA*A*A*00Group : 00 4 4 0 0 00---0 --- ---0 ------ --- ---

using equationVXVX 1 2 3 4 5 6 7 8 9 10 X X X X X X X X X XPeriodsPositive Correlation V VAVA using equationA*A*A*00Group : 00 0 4 4 40 00 000---0 --- ---00 ------ --- ---

using equationVXVX 1 2 3 4 5 6 7 8 9 10 X X X X X X X X X XPeriodsPositive Correlation V VAVA using equationA*A*A*00Group : 00 0 4 4 40 00 000---0 --- ---0002 1------ --- ---.42.35.42.35

using equationVXVX 1 2 3 4 5 6 7 8 9 10 X X X X X X X X X XPeriodsPositive Correlation V VAVA using equationA*A*A*00Group : 00 0 4 4 40 00 000---0 --- ---00024 1------ --- ---.42.35.42.35.35.42-.18.24

Do It YourselfExecute the calculations for Periods 6-10 on your own.

using equationVXVX 1 2 3 4 5 6 7 8 9 10 X X X X X X X X X XPeriodsPositive Correlation V VAVA using equationA*A*A*00Group : 00 0 4 4 40 00 000---0 --- ---000244 2442 111------ --- ---.42.35.42.35.35.35.42-.18.24.24-.10.14.49.21.18.53.35.35.20.65-.15.20-.08.15.12.27.53.53.12.65

*X is everything other than A and * CS is A Is US The model says that X can be associated with US X can be liable to be hooked up to US.