Changes between Version 2 and Version 3 of UWSummerStatsWorkshop


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Timestamp:
Jul 20, 2015, 3:04:34 PM (10 years ago)
Author:
iovercast
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  • UWSummerStatsWorkshop

    v2 v3  
    1414 
    1515Taught by Eric Anderson and Matthew Stephens 
     16* Monday AM 
     17 * Probability as representation of uncertainty vs long range frequency. 
     18 * Expectation of mean of beta distribution is alpha/(alpha+beta) 
     19 * Jeffreys Prior - a=b=0.5 
     20 * Marginal distribution of y integrating out over theta 
     21 * "Propagating uncertainly" - Take uncertainty into account down the line. 
     22* Monday AM II 
     23 * Monte Carlo Method - "In search of a definition..." - Approximate '''expectation based on sample mean''' of simulated random variables. 
     24  * "Simple sample mean..." 
     25 * Wright-Fisher Model 
     26  * Sampling with replacement between generations 
     27 * Markov Chains 
     28  * Transition probability matrices. Do they have to be symmetric? 
     29  * Limiting distribution (''ergodic Markov chain''), regardless of where you start, as t->inf the probability of being in any state will be the same. 
     30  * Time averaging over the chain converges to the limiting distribution. 
     31  * "known only up to scale" - shape but not normalizing constant? 
     32  * Reversible jump mcmc? Bridge sampling? Importance sampling? 
     33 * Ergodicity 
     34  * No transient states - No states you can't reach in a finite number of steps. 
     35  * Irreducible - any state is reachable from any other state in a finite number of steps 
     36  * Aperiodic - Can't get stuck in a loop 
     37 * Stationary distribution of Markov chain 
     38  * General balance equation: πP = π, where P is a transition probability matrix and π is the stationary distribution. 
     39 * Time-reversible Markov chains is required to for detailed balance to satisfy general balance 
     40 * Metropolis-Hastincs Algorithm 
     41  * Take state i, propose state j, accept the proposed move with probability min {1, some probability Hastings ratio} 
     42  * f(j)/f(i) x q(i|j)/q(j|i) 
     43   * Ratio of target densites x ratio of proposal densities 
     44  * f(j) is more likely then it increases probablity 
     45 
     46==== quotes ==== 
     47* "Out of all the tomorrows we might experience...." 
     48* "Uncertainty is, intrinsically, personal."