Overview¶
The default model parametrization is the one described in Section 4.4 of Hand et al. 2017. See this section for a detailed discussion of the free and constrained parameters, as well as the priors used during parameter fitting. There are 13 free parameters that are varied during the fitting procedure.
The default set of parameters can be easily loaded from a
GalaxySpectrum object as
In [1]: from pyRSD.rsd import GalaxySpectrum
In [2]: model = GalaxySpectrum()
In [3]: params = model.default_params()
---------------------------------------------------------------------------
AttributeError Traceback (most recent call last)
<ipython-input-3-20168f551e3a> in <module>()
----> 1 params = model.default_params()
~/checkouts/readthedocs.org/user_builds/pyrsd/conda/latest/lib/python3.6/site-packages/pyRSD/rsd/power/gal/power_gal.py in default_params(self)
128 """
129 from pyRSD.rsdfit.theory import GalaxyPowerParameters
--> 130 return GalaxyPowerParameters.from_defaults(model=self)
131
132 #---------------------------------------------------------------------------
~/checkouts/readthedocs.org/user_builds/pyrsd/conda/latest/lib/python3.6/site-packages/pyRSD/rsdfit/theory/base.py in from_defaults(cls, model, extra_params)
155 """
156 # initialize an empty class
--> 157 params = cls()
158
159 # add extra parameters
~/checkouts/readthedocs.org/user_builds/pyrsd/conda/latest/lib/python3.6/site-packages/pyRSD/rsdfit/parameters/parameterset.py in __init__(self, *args, **kwargs)
35 def __init__(self, *args, **kwargs):
36
---> 37 kwargs['asteval'] = lmfit.asteval.Interpreter(symtable=SmartSymTable(self))
38 super(ParameterSet, self).__init__(*args, **kwargs)
39 self._prepared = False
AttributeError: module 'lmfit' has no attribute 'asteval'
In [4]: print(params)
---------------------------------------------------------------------------
NameError Traceback (most recent call last)
<ipython-input-4-1b9f0c7a8c29> in <module>()
----> 1 print(params)
NameError: name 'params' is not defined
The params variable here is a pyRSD.rsdfit.parameters.ParameterSet object,
which is a dictionary of pyRSD.rsdfit.parameters.Parameter objects.
The Parameter object not only stores the value
of the parameter (as the value attribute), but also stores
information about the prior and whether the parameter is freely varied or constrained.
For example, the satellite fraction fs can be accessed as
In [5]: fsat = params['fs']
---------------------------------------------------------------------------
NameError Traceback (most recent call last)
<ipython-input-5-0bdcc73fb526> in <module>()
----> 1 fsat = params['fs']
NameError: name 'params' is not defined
In [6]: print(fsat.value)
---------------------------------------------------------------------------
AttributeError Traceback (most recent call last)
<ipython-input-6-fa43826f61de> in <module>()
----> 1 print(fsat.value)
AttributeError: 'numpy.float64' object has no attribute 'value'
# freely varying
In [7]: print(fsat.vary)
---------------------------------------------------------------------------
AttributeError Traceback (most recent call last)
<ipython-input-7-631a00d377f3> in <module>()
----> 1 print(fsat.vary)
AttributeError: 'numpy.float64' object has no attribute 'vary'
In [8]: fsat.value = 0.12 # change the value to 0.12
---------------------------------------------------------------------------
AttributeError Traceback (most recent call last)
<ipython-input-8-1245a81779b7> in <module>()
----> 1 fsat.value = 0.12 # change the value to 0.12
AttributeError: 'numpy.float64' object has no attribute 'value'
# uniform prior assumed by default
In [9]: print(fsat.prior)
---------------------------------------------------------------------------
AttributeError Traceback (most recent call last)
<ipython-input-9-eccca42b31f4> in <module>()
----> 1 print(fsat.prior)
AttributeError: 'numpy.float64' object has no attribute 'prior'
The Free Parameters¶
The 13 free parameters by default are:
In [10]: for par in params.free:
....: print(par)
....:
---------------------------------------------------------------------------
NameError Traceback (most recent call last)
<ipython-input-10-5cecc5874546> in <module>()
----> 1 for par in params.free:
2 print(par)
3
NameError: name 'params' is not defined
| Parameter | Name | Description |
| \(N_{s,\mathrm{mult}}\) | Nsat_mult | The mean number of satellites in halos with >1 sat |
| \(\alpha_\parallel\) | alpha_par | The Alcock-Paczynski effect parameter for parallel to the line-of-sight |
| \(\alpha_\perp\) | alpha_perp | The Alcock-Paczynski effect parameter for perpendicular to the line-of-sight |
| \(b_{1,c_A}\) | b1_cA | The linear bias of type A centrals (no satellites in the same halo) |
| \(f\) | f | The growth rate at \(z\): \(f = d\mathrm{ln}D/d\mathrm{ln}a\) |
| \(f_{1h, s_B s_B}\) | f1h_sBsB | An order unity amplitude value multiplying the 1-halo term, NsBsB |
| \(f_s\) | f_s | The satellite fraction, which is (total number of satellites / total number of galaxies) |
| \(f_{s_B}\) | f_sB | The type B satellites fraction, which is (total number of type B satellites / total number of satellites) |
| \(\gamma_{b_{1,s_A}}\) | gamma_b1sA | The relative fraction of b1_sA to b1_cA |
| \(\gamma_{b_{1,s_B}}\) | gamma_b1sB | The relative fraction of b1_sB to b1_cA |
| \(\sigma_8(z)\) | sigma8_z | The mass variance at \(r = 8 \ \mathrm{Mpc}/h\) at \(z\) |
| \(\sigma_c\) | sigma_c | The centrals FoG velocity dispersion, in units of \(\mathrm{Mpc}/h\) |
| \(\sigma_{s_A}\) | sigma_sA | The type A satellites FoG velocity dispersion, in units of \(\mathrm{Mpc}/h\) |
The Constrained Parameters¶
There are several constrained parameters, i.e., parameters whose values are solely determined by other parameters, in the default configuration. Note also that since these parameters are not freely varied, they do not require priors.
In [11]: for par in params.constrained:
....: print(par)
....:
---------------------------------------------------------------------------
NameError Traceback (most recent call last)
<ipython-input-11-0bf19a17b9e8> in <module>()
----> 1 for par in params.constrained:
2 print(par)
3
NameError: name 'params' is not defined
| Parameter | Name | Description |
| \(F_\mathrm{AP}\) | F_AP | The AP parameter, given by \(alpha_\parallel / \alpha_\perp\) |
| \(N_{c_B s}\) | N_cBs | The amplitude of the constant 1-halo term between type B centrals, [units: \((\mathrm{Mpc}/h)^3\)] |
| \(N_{s_B s_B}\) | N_sBsB | The amplitude of the constant 1-halo term between type B satellites, [units: \((\mathrm{Mpc}/h)^3\)] |
| \(\alpha\) | alpha | The isotropic AP dilation, given by \((\alpha_\perp^2 \alpha_\parallel)^{1/3}\) |
| \(b_1\) | b1 | The total galaxy linear bias |
| \(b_{1,c}\) | b1_c | The linear bias of the central sample |
| \(b_{1,c_B}\) | b1_cB | The linear bias of type B centrals (1 or more satellite(s) in the same halo) |
| \(b_{1,s}\) | b1_s | The linear bias of the satellite sample |
| \(b_{1,s_A}\) | b1_sA | The linear bias of the type A satellites sample |
| \(b_{1,s_B}\) | b1_sB | The linear bias of the type B satellites sample |
| \(b_1 \sigma_8\) | b1sigma8 | The value of \(b_1(z) \times \sigma_8(z)\) |
| \(\epsilon\) | epsilon | The anisotropic AP warping, given by \((\alpha_\perp / \alpha_\parallel)^{-1/3} - 1\) |
| \(f_{c_B}\) | f_cB | The type B centrals fraction, which is (total number of type B centrals / total number of centrals) |
| \(f \sigma_8\) | fsigma8 | The value of \(f(z) \times \sigma_8(z)\) |
| \(\sigma_{s_B}\) | sigma_sB | The type B satellites FoG velocity dispersion, in units of \(\mathrm{Mpc}/h\) |
The ParameterSet object handles constrained
parameters automatically. For example, in our default configuration, we have the
parameter fsigma8, which is the product of the growth rate f and
the mass variance sigma8_z. We can change the value of either f or
sigma8_z and the value of fsigma8_z will reflect those changes. For example,
In [12]: print(params['fsigma8'])
---------------------------------------------------------------------------
NameError Traceback (most recent call last)
<ipython-input-12-d6f6c6bb8ef8> in <module>()
----> 1 print(params['fsigma8'])
NameError: name 'params' is not defined
In [13]: print(params['f']*params['sigma8_z'])
---------------------------------------------------------------------------
NameError Traceback (most recent call last)
<ipython-input-13-3c4254d13be2> in <module>()
----> 1 print(params['f']*params['sigma8_z'])
NameError: name 'params' is not defined
In [14]: params['f'].value = 0.75
---------------------------------------------------------------------------
NameError Traceback (most recent call last)
<ipython-input-14-afcbaefd60f2> in <module>()
----> 1 params['f'].value = 0.75
NameError: name 'params' is not defined
In [15]: print(params['fsigma8'])
---------------------------------------------------------------------------
NameError Traceback (most recent call last)
<ipython-input-15-d6f6c6bb8ef8> in <module>()
----> 1 print(params['fsigma8'])
NameError: name 'params' is not defined
In [16]: print(params['f']*params['sigma8_z'])
---------------------------------------------------------------------------
NameError Traceback (most recent call last)
<ipython-input-16-3c4254d13be2> in <module>()
----> 1 print(params['f']*params['sigma8_z'])
NameError: name 'params' is not defined