7.4. Statistical analysis: \(\tt -s\)

Run on a file containing a list of likely halo parameters (obtained from a statistical analysis). The statistics mode -s deals with the results of a Jeans + MCMC analysis run on a set of dSph kinematic data. It allows the reconstruction of parameter correlations and confidence intervals of any quantities.

Note

All default parameter files from the following run examples are generated with the -D flag.

$ clumpy -sX -D

Examples below are constructed using the fake MCMC chain in the example file data/stat_example.dat.

7.4.1. \(\tt -s0\): CLs on \(M(r)\)

Median values, 68% and 95% confidence intervals of the reconstructed DM halo mass as a function of the distance to the halo centre.

$ clumpy -s0 -i clumpy_params_s0.txt
_images/s0D.png

Fig. 7.28 -s0 output ROOT figure


7.4.2. \(\tt -s1\): PDF on \(\log{\cal L}\) or \(\chi^2\)

$ clumpy -s1 -i clumpy_params_s1.txt
_images/s1D.png

Fig. 7.29 -s1 output ROOT figure


7.4.3. \(\tt -s2\): PDF correlations plots (parasm)

Triangle plot showing correlations and marginalised posterior distributions for the mass and DM profile parameters. See also Fig. 2.10 in the Picture gallery.

$ clumpy -s2 -i clumpy_params_s2.txt
_images/s2D.png

Fig. 7.30 -s2 output ROOT figure


7.4.4. \(\tt -s3\): best-fit parameters

$ clumpy -s3 -i clumpy_params_s3.txt
....

>>>>> Best-fit parameters (best chi2 or log likelihood) from a list of stat. analysis files
   [N.B.: a stat. analysis file must be formatted as described in stat_load_list()]

Name = dSph01
     DMprofile           EINASTO
     Rhos                4.38166e+08
     Rscale              0.0933164
     Rvir                10
     alpha               0.34653
     beta                3
     gamma               1
     Lightprofile        PLUMMER2D
     L                   1
     RLight              0.021
     alpha*              1
     beta*               3
     gamma*              0
     Anisoprofile        CONSTANT
     Beta_Aniso_0        0.738798
     Beta_Aniso_Inf      0
     RAniso              1
     AnisoShapeParam     2
     Log likelihood      -5.24362

   [Best fit params]  clumpy -s3(stat_files switch_stat)

7.4.5. \(\tt -s4\): CLs on parameters

is interactive:

$ clumpy -s4 -i clumpy_params_s4.txt
....

>>>>> CL lower and upper value (first and second line below) from a list of stat. analysis files
   [N.B.: a stat. analysis file must be formatted as described in stat_load_list()]

 Select a parameter (from which the CL is calculated):
       rhos (kpc)                            [0]
       rs (kpc)                              [1]
       Rvir (kpc)                            [2]
       alpha                                 [3]
       beta (outer)                          [4]
       gamma (inner)                         [5]
       rho(r)                                [6]
       L  (L_sol)                            [7]
       rL (kpc)                              [8]
       alpha*                                [9]
       beta* (outer)                         [10]
       gamma* (inner)                        [11]
       nu(r) (Lsol/kpc^3)                    [12]
       I(R) (Lsol/kpc^2)                     [13]
       beta_0                                [14]
       beta_infty                            [15]
       ra (kpc)                              [16]
       eta                                   [17]
       beta(r)                               [18]
       M(r) (Msol)                           [19]
       J(alpha_int) (smooth)                 [20]
       sigma_p(R)(km/s) (projected)          [21]
       vr^2(r)(km^2/s^2) (unprojected)       [22]
 .......your choice:

7.4.6. \(\tt -s5\): CLs on \(\rho(r)\)

Same as -s0 for the density.

$ clumpy -s5 -i clumpy_params_s5.txt
_images/s5D.png

Fig. 7.31 -s5 output ROOT figure


7.4.7. \(\tt -s6\): CLs on \(J(\alpha_{\rm int})\)

Same as above for the J-factors (D-factors depending on the chosen option).

$ clumpy -s6 -i clumpy_params_s6.txt
_images/s6D.png

Fig. 7.32 -s6 output ROOT figure


7.4.8. \(\tt -s7\): CLs on \(J(\theta)\)

$ clumpy -s7 -i clumpy_params_s7.txt
_images/s7D.png

Fig. 7.33 -s7 output ROOT figure


7.4.9. \(\tt -s8\): CLs on \(\sigma_p(R)\)

Same as above for the dSph galaxy velocity dispersion \(\sigma_{\rm p}\). This is compared to the kinematic data points used to run the Jeans + MCMC analysis.

$ clumpy -s8 -i clumpy_params_s8.txt
_images/s8D.png

Fig. 7.34 -s8 output ROOT figure


7.4.10. \(\tt -s9\): CLs on \(v_r^2(r)\)

$ clumpy -s9 -i clumpy_params_s9.txt
_images/s9D.png

Fig. 7.35 -s9 output ROOT figure


7.4.11. \(\tt -s10\): CLs on \(\beta_{\rm ani}(r)\)

$ clumpy -s10 -i clumpy_params_s10.txt
_images/s10D.png

Fig. 7.36 -s10 output ROOT figure


7.4.12. \(\tt -s11\): CLs on \(\nu(r)\)

$ clumpy -s11 -i clumpy_params_s11.txt
_images/s11D.png

Fig. 7.37 -s11 output ROOT figure


7.4.13. \(\tt -s12\): CLs on \(I(R)\)

$ clumpy -s12 -i clumpy_params_s12.txt
_images/s12D.png

Fig. 7.38 -s12 output ROOT figure