Changes between Version 15 and Version 16 of UWSummerStatsWorkshop

Timestamp:

Jul 24, 2015, 11:35:54 AM (10 years ago)

Author:

iovercast

Comment:

--

UWSummerStatsWorkshop

@@ -178 +178 @@
  * CI - cost of type I error, CII - cost of type II error
 * Monte Carlo approximation (backtracking to yesterday)
- * 
+=== Thursday PM1 ===
+* Linear regression models
+ * y = a0 + a1Xa + e (e=random variation between individuals)
+ * linear in the parameters
+ * I = covariance of outcomes. In the simple case you assume there is no covariance, so I is the identity matrix, but if there is covariance between the data or the animals or experiments then it can be incorporated with this variable.
+* Ordinary least squares estimation
+ * SSR(Beta) sum of squared residuals
+  * Find values for Beta such that sum of squared residuals is small to increase the likelihood value
+ * R - solve(), lm() "linear model"
+* Bayesian regression
+ * You can make probability statements
+  * probability some beta value >0 given 
+ * OLS overfits when # of predictors is large
+ * can do model selection and averaging
+ * Beta is a vector
+ * If prior variance is very small, then posterior mean will concentrate around your prior mean.
+ * If you have a lot of data, as sample size grows mean will concentrate on OLS estimate.
+ * Similar logic to Bayesian inference
+* How to select prior for a vector of parameters
+ * g-prior
+ * Uncertainty in my prior is the same as uncertainy from n/g observations.
+ * Posterior calculations are relatively similar
+  * Posterior mean estimate is OLS estimate shrunken a little bit toward zero
+* "It's bad form not to have a picture at the end."
+=== Thursday PM2 ===
+* Changing significance level as a function of ''n''
+* a/(1-b) * prior odds of H0/H1
+ * a = alpha level, significance
+ * b = power
+* R is the ratio of costs
+* Significance level should decrease as n increases.
+* False discovery rate B/K
+* Bayesian False Discoveries
+ * Posterior odds = bayes factor * prior odds < R
+ * '''Depends on the sample size, but not on the number of test'''
+* '''Don't use bonferroni, use false discovery rate, but better still use bayesian methods.'''
+* Bayesian approaches in GWAS (Stephens & Balding 2009)
 
 ==== quotes ====
@@ -191 +227 @@
 * "Improper posteriors are a no-no, that's just anarchy."
 * "The only way to do this is to do it."
+* "... Nutritional epidemiology being the poster child for spurious results."