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2

0

1 0

0

0

1

1

1

1

1

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1

1

1

1

1

1

1

1

1

1

1

1

0

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0

0

0

0

0

0

0

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-.5

0

.5

1

1.5

2

2.5

3

3.5

-2 -1 0 1 2 3 4 5

InterpolantData

-.5

0

.5

1

1.5

2

2.5

3

3.5

-2 -1 0 1 2 3 4 5

InterpolantError bars

Data

-.5

0

.5

1

1.5

2

2.5

3

3.5

-2 -1 0 1 2 3 4 5x

InterpolantData

0

6

0

0

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0

0

0

0

0

0

0

0

0

0

0

0

0

0

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-200

-150

-100

-50

0

50

100

150

200

0.0001 0.001 0.01 .1 1 10 100 1000Alpha

Log EvidenceData X^2

W X^2Log Occam Factor

-100

-50

0

50

100

150

200

250

0.0001 0.001 0.01 .1 1 10 100 1000Alpha

Log Evidence

Test Error 1Test Error 2

GammaX^2_w

0

0

0

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0

0

0

0

0

1

1

0

1 1

6

6

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-3000

-2500

-2000

-1500

-1000

-500

0

500

5 10 15 20 25 30 35

Log

Ev

idence

Number of basis functions

Hermite polynomialsHermite functions

-100

-80

-60

-40

-20

0

20 30 40 50 60 70 80

Log

Ev

idence

Number of basis functions

Cauchy functionsGaussians

-100

-80

-60

-40

-20

0

20 40 60 80 100 120 140

Log

Ev

idence

Number of coefficients

0

1

2

3

4

6

012346

0

.2

.4

.6

.8

1

1.2

20 40 60 80 100 120

Test

error

Number of coefficients

012346

6

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0

1

1

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-.5

0

.5

1

1.5

2

2.5

3

3.5

-2 -1 0 1 2 3 4 5

y(x

)

x

Data set Y with interpolant using Splines 2.5

InterpolantError bars

Data

0

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6

6

6

6

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