small test

doc/src/Bayesian/Bayesian.do.txt

@@ -6,34 +6,11 @@ DATE: today
 !split
 ===== What is Bayesian Statistics  =====
 !bblock
-Say something general here. Reminder about probabilities from the statistics section
+Say something more general here. Reminder about probabilities from the statistics section
 o Product rule
 o Binomial distribution
 o Gaussian PDF
 o other PDFs
-!eblock
-
-!split
-===== Bayesian regression analysis =====
-!bblock
-!bt
-\[
-mathbf {y} -\mathbf {X} {\boldsymbol {\beta }})\right).} \rho(\mathbf{y}|\mathbf{X},\boldsymbol\beta,\sigma^{2}) \propto (\sigma^{2})^{-n/2} \exp\left(-\frac{1}{2{\sigma}^{2}}(\mathbf{y}- \mathbf{X} \boldsymbol\beta)^{\rm T}(\mathbf{y}- \mathbf{X} \boldsymbol\beta)\right).
-\]
-!et
-The ordinary least squares solution is to estimate the coefficient vector using the Moore-Penrose pseudoinverse:
-!bt
-\[
-{\hat {\boldsymbol {\beta }}=(\mathbf {X} ^{\rm {T}}\mathbf {X} )^{-1}\mathbf {X} ^{\rm {T}}\mathbf {y} }  \hat{\boldsymbol\beta} = (\mathbf{X}^{\rm T}\mathbf{X})^{-1}\mathbf{X}^{\rm T}\mathbf{y}
-\]
-!et
-where 
-!bt
-\[
-{\displaystyle \mathbf {X} } \mathbf {X}  
-\]
-!et
-is the ${n\times k n \times k$ design matrix, each row of which is a predictor vector $\mathbf {x} _{i}^{\rm {T}} \mathbf{x}_{i}^{\rm T}$ and $\mathbf {y}  \mathbf {y}$  is the column $n$-vector $[y_{1}\;\cdots \;y_{n}]^{\rm {T}} [y_1 \; \cdots \; y_n]^{\rm T}$.
-
+o Bayesian regression analysis
 !eblock