Changes between Version 13 and Version 14 of OfficialTolArchiveNetworkGrzLinModel

Timestamp:

Mar 30, 2011, 3:47:25 PM (14 years ago)

Author:

Víctor de Buen Remiro

Comment:

--

OfficialTolArchiveNetworkGrzLinModel

@@ -44 +44 @@
 
 Each particular distribution may have its own additional parameters which will be treated 
-as a different Gibbs block and should implement
+as a different Gibbs block and should implement next methods in order to be able of build
+both bayesian and max-likelihood estimations
 
  * the mean function: [[BR]] [[BR]] 
@@ -50 +51 @@
  * the log-density function: [[BR]] [[BR]] 
    [[LatexEquation( \ln f)]] [[BR]][[BR]]
- * the partial derivative of log-density function respect to the linear prediction [[BR]] [[BR]] 
-   [[LatexEquation( \frac{\partial\ln f}{\partial\eta})]] 
+ * the first and second partial derivatives of log-density function respect to the linear prediction [[BR]] [[BR]] 
+   [[LatexEquation( \frac{\partial\ln f}{\partial\eta},\frac{\partial^{2}\ln f}{\partial\eta^{2}} )]] 
 
 This class also implements these common features
@@ -69 +70 @@
  * the density function has the variance as extra parameter[[BR]] [[BR]] 
    [[LatexEquation( f\left(y;\mu,\sigma^{2}\right)=\frac{1}{\sqrt{2\pi\sigma^{2}}}e^{^{-\frac{1}{2}\frac{\left(y-\mu\right)^{2}}{\sigma^{2}}}} )]][[BR]] [[BR]] 
+ * the density function will be then [[BR]] [[BR]] 
+   [[LatexEquation( f\left(y;\mu,\sigma^{2}\right)=\frac{1}{\sqrt{2\pi\sigma^{2}}}e^{^{-\frac{1}{2}\frac{\left(y-\mu\right)^{2}}{\sigma^{2}}}} )]][[BR]] [[BR]]
  * the log-density function will be then [[BR]] [[BR]] 
-   [[LatexEquation( \ln f\left(y;\mu,\sigma^{2}\right)= -\frac{1}{2}\ln\left(2\pi\sigma^{2}\right)-\frac{1}{2\sigma^{2}}\left(y}-\mu\right)^{2} )]]
-
+   [[LatexEquation( \ln f\left(y;\mu,\sigma^{2}\right)= -\frac{1}{2}\ln\left(2\pi\sigma^{2}\right)-\frac{1}{2\sigma^{2}}\left(y}-\mu\right)^{2} )]][[BR]] [[BR]]
+ * the partial derivative of log-density function respect to the linear prediction is [[BR]] [[BR]]
+   [[LatexEquation( \frac{\partial\ln f}{\partial\eta}=\frac{1}{\sigma^{2}}\left(y-\eta\right) )]] [[BR]] [[BR]]
 
 === Weighted Poisson Regresion ===
@@ -87 +91 @@
  * and its logarithm will be [[BR]] [[BR]] 
    [[LatexEquation( \ln f\left(y;\mu\right)=-\ln\left(y!\right)+y\ln\left(\mu\right)-\mu = -\ln\left(y!\right)+y\eta-e^{\eta} )]]
+ * the partial derivative of log-density function respect to the linear prediction is [[BR]] [[BR]]
+   [[LatexEquation( \frac{\partial\ln f}{\partial\eta}=y-e^{\eta} )]] [[BR]] [[BR]]