minor edit in statinf

statinf.tex

@@ -16,9 +16,9 @@ is the evidence of the model $\mathcal{M}$. Bayesian model selection involves co
 Here we solve the curve fitting problem presented in Sec.~\ref{sec:curve_fitting} using of Bayesian statistical inference. 
 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.~\ref{eq:Hubble's Law}] as the model $\mathcal{M}_1$. Assume uniform prior for $H_0$ in the interval $(10, 100)$ km/s/Mpc. You can either use a Gaussian likelihood with $\sigma_{i} = 1$ or calculate the standard deviations (${\sigma_{i}}$) of $d_{L}$ from the data.  In any case, the likelihood of data is:   
 \begin{equation}
 \begin{equation}
-p(d | H_0, \mathcal{M}_1) = \exp \left( - \sum_i \big |d_i - d_L(z_i, \mathcal{M}_1) \big |^2 \right), 
+p(d | H_0, \mathcal{M}_1) = \exp \left( - \sum_i \Big |\dfrac{d_i - d_L(z_i, \mathcal{M}_1)}{\sigma_{i}} \Big |^2 \right), 
 \end{equation}
 \end{equation}
 where $d_i$ and $z_i$ are the samples of the luminosity distance and redshift from the data and $d_L(z_i, \mathcal{M}_1)$ is the relation between luminosity distance and redshift predicted by model $\mathcal{M}_1$ evaluated at redshift $z_i$. 
 where $d_i$ and $z_i$ are the samples of the luminosity distance and redshift from the data and $d_L(z_i, \mathcal{M}_1)$ is the relation between luminosity distance and redshift predicted by model $\mathcal{M}_1$ evaluated at redshift $z_i$. 
 \item Repeat the analysis using the full data set. What are the differences that you see in the posterior?
 \item Repeat the analysis using the full data set. What are the differences that you see in the posterior?