Equation of State Fitting

Here I fit the phase diagram to the model:

$$T(\Delta) = T_0 \Delta ^\gamma$$

First I do it by minimizing $- \sum log[ P(\Delta, T) ]$ with the help of scipy, this is the result:

Now, I run an MCMC to sample the space of parameters {$T_0$, $\gamma$} and maximize the probability $\sum log[ P(\Delta, T) ]$, I use the pymc package to do so and from the sampling I get the posterior distribution for the parameters:

Sampling for $T_0$:

Sampling for $\gamma$:

From the distributions I can get the mean and the standard deviation for the parameters:

$$T_0 = 3.96875 \pm 0.00016$$ $$\gamma = 0.44024 \pm 0.00017$$