minor edits.

statinf.tex

-Here we solve the curve fitting problem presented in Sec.~\ref{sec:curve_fitting} using of Bayesian statistical inference. Given some data $d$ and a model $\mathcal{M}$, Bayesian parameter estimation involves computing the posterior distribution of the parameters $\theta$ describing the model. Using Bayes theorem, we can write 
+Given some data $d$ and a model $\mathcal{M}$, Bayesian parameter estimation involves computing the posterior distribution of the parameters $\theta$ describing the model. Using Bayes theorem, we can write 
 \begin{equation}
 \begin{equation}
 p(\theta | d, \mathcal{M}) = \frac{p(\theta | \mathcal{M}) ~ p(d | \theta , \mathcal{M})}{p(d | \mathcal{M})}, 
 p(\theta | d, \mathcal{M}) = \frac{p(\theta | \mathcal{M}) ~ p(d | \theta , \mathcal{M})}{p(d | \mathcal{M})}, 
 \end{equation}
 \end{equation}
@@ -13,6 +13,8 @@ is the evidence of the model $\mathcal{M}$. Bayesian model selection involves co
 \end{equation}
 \end{equation}
 
 
 \subsubsection{Problems}
 \subsubsection{Problems}
+Here we solve the curve fitting problem presented in Sec.~\ref{sec:curve_fitting} using of Bayesian statistical inference. 
+
 \begin{enumerate}
 \begin{enumerate}
 \item Compute the posterior distribution $p(H_0 | d, \mathcal{M}_1)$ of the Hubble constant $H_0$ using the Supernova Cosmology project data $z \leq 0.1$. Assume the Hubble's law [Eq.~\eqref{eq:Hubble_law}] as the model $\mathcal{M}_1$. Assume uniform prior for $H_0$ in the interval $(10, 100)$ km/s/Mpc. You can use a Gaussian likelihood with $\sigma = 1$.  That is, 
 \item Compute the posterior distribution $p(H_0 | d, \mathcal{M}_1)$ of the Hubble constant $H_0$ using the Supernova Cosmology project data $z \leq 0.1$. Assume the Hubble's law [Eq.~\eqref{eq:Hubble_law}] as the model $\mathcal{M}_1$. Assume uniform prior for $H_0$ in the interval $(10, 100)$ km/s/Mpc. You can use a Gaussian likelihood with $\sigma = 1$.  That is, 
 \begin{equation}
 \begin{equation}