Changes between Version 13 and Version 14 of UWSummerStatsWorkshop

Timestamp:

Jul 23, 2015, 1:02:18 PM (9 years ago)

Author:

iovercast

Comment:

--

UWSummerStatsWorkshop

@@ -133 +133 @@
  * ML tends to overfit to the data when you have a large parameter space relative to the sample size... 
 === Wednesday PM2 ===
-* 
+* "You've got your data, it's not random anymore.... You've run your experiment, your data certainly aren't random."
+* Partition is a collection of sets. 
+* Axioms
+ * Total probability - Sum of all events in a partition = 1
+ * Marginal probability - Sum of probability of event E intersected with all possible events in the partition. 
+* Likelihood ratio x prior odds = posterior odds
+* Standard distributions
+ * Discrete random variable
+ * Pr(Y=y) = p(y) probability density function, must be 0 <= p(y) <= 1 & sum of all p(y) = 1
+ * Probability densities
+  * Always >=0, sum of all area under curve = 1
+* Binary distribution
+ * Y={1,0}
+ * Pr(Y=y|θ) = p(y|θ) = θ^y(1-θ)^(1-y)
+* Binomial distribution
+* Likelihood inference
+* Poisson distribution
+* Why use gamma vs beta?
+
+=== Thursday AM1 ===
+* Posterior is proportional to the likelihood times the prior (colloquial).
+* Estimation, hypothesis testing, prediction.
+* Beta distribution as a prior:
+ * Mean of beta is a/(a+b)
+ * Beta is flexible, to a degree
+* Uniform prior is tricky, even though its "uninformative", its not uniform on all scales.
+* Conjugate: posterior is the same form as the prior.
+ * Theta^(y+a-1) * (1-Theta)^(N-y+b-1)
+ * Posterior mean: (y+a)/(N+a+b)
+ * Weighted estimator of sample mean and prior mean
+  * As sample size increases sample mean weight increases
+  * With fixed sample size increasing a+b (beta parameters) increases weight on prior.
+  * Nonsymmetric vs asymmetric?
+ * Averaging out over all the possible values theta could takeweighted by the posterior (Averaging out the uncertainty).
+* Hypothesis testing:
+ * Ratio of probabilities of data given model 1 vs model 2 or null.
+* "Bayesian modelling can be very intoxicating."
+=== Thursday AM2 ===
 
 ==== quotes ====
@@ -144 +181 @@
 * "You're going to be wrong whatever you do. These are cartoons of reality, none of these models are right."
 * "There's only one tomorrow, or maybe there are many tomorrows... Every day is a new tomorrow."
+* "Improper posteriors are a no-no, that's just anarchy."
+* "The only way to do this is to do it."