Post on 26-Dec-2015
transcript
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