An unscaled but appealing version The full definition Simple example with no noise

An unscaled but appealing version

2

2

1

22

1

model

model

Ni i

i i

N

i ii

x

x

The full definition

Simple example with no noise

An unscaled but appealing version

2

2

1

22

1

model

model

Ni i

i i

N

i ii

x

x

The full definition

An unscaled but appealing version

2

2

1

22

1

model

model

Ni i

i i

N

i ii

x

x

The full definition

An unscaled but appealing version

2

2

1

22

1

model

model

Ni i

i i

N

i ii

x

x

The full definition

An unscaled but appealing version

2

2

1

22

1

model

model

Ni i

i i

N

i ii

x

x

The full definition

An unscaled but appealing version

2

2

1

22

1

model

model

Ni i

i i

N

i ii

x

x

The full definition

An unscaled but appealing version

2

2

1

22

1

model

model

Ni i

i i

N

i ii

x

x

The full definition

An unscaled but appealing version

2

2

1

22

1

model

model

Ni i

i i

N

i ii

x

x

The full definition

An unscaled but appealing version

2

2

1

22

1

model

model

Ni i

i i

N

i ii

x

x

The full definition

An unscaled but appealing version

2

2

1

22

1

model

model

Ni i

i i

N

i ii

x

x

The full definition

An unscaled but appealing version

2

2

1

22

1

model

model

Ni i

i i

N

i ii

x

x

The full definition

An unscaled but appealing version

2

2

1

22

1

model

model

Ni i

i i

N

i ii

x

x

The full definition

An unscaled but appealing version

2

2

1

22

1

model

model

Ni i

i i

N

i ii

x

x

The full definition

2

2

1

modelNi i

i i

x

Add noise to calculation

2

2

1

modelNi i

i i

x

2

2

1

modelNi i

i i

x

Can’t we get more information that just the location of a minimum?

2 PDF and CDF

2

2

1

model1,

Ni i

ri i

xdf N

df

Divide by degrees of

freedom for “reduced χ2”

Reduced χ2 with noise

2

2

1

model1,

Ni i

ri i

xdf N

df

Divide by degrees of

freedom for “reduced χ2”

2

2

1

model1,

Ni i

ri i

xdf N

df

Divide by degrees of

freedom for “reduced χ2”

Photometric redshifts and the T-z degeneracy

max

max, restmax, observed max, observed

constant

1 constant1

T

z Tz

Wien’s displacement law

Modified for redshift

3.689

0.025

Moral: it’s hard to pin down the center of a peak with only values near the peak itself!

Harris et al. 2012

Blue: CO, Harris et al. 2012Magenta: Optical, Chapman et al. 2005

350 and 850 m select the same “classical SMG” population

Redshift distributions fromCO 1—0 and optical observations

Harris et al. 2012

Blue: CO, Harris et al. 2012Magenta: Optical, Chapman et al. 2005

350 and 850 m select the same “classical SMG” population

Redshift distributions fromCO 1—0 and optical observations

Poisson and Normal PDFs