303 class 4.1

.github/workflows/deploy.yml

@@ -1,7 +1,7 @@
 name: Build and deploy mdBook site
 on:
   push:
-    branches: ['main']
+    branches: ["main"]
   pull_request:
   workflow_dispatch:
 
@@ -10,16 +10,16 @@ jobs:
     name: Build with mdBook
     runs-on: ubuntu-latest
     steps:
-    - uses: actions/checkout@v4
-      with:
-        lfs: true
-    - uses: cargo-bins/cargo-binstall@main
-    - name: Install mdBook, mdBook-KaTeX, and mdBook-ToC
-      run: cargo binstall -y mdbook mdbook-katex mdbook-toc
-    - name: Build
-      run: mdbook build
-    - name: Upload artifact
-      uses: actions/upload-pages-artifact@v3
+      - uses: actions/checkout@v4
+        with:
+          lfs: true
+      - uses: cargo-bins/cargo-binstall@main
+      - name: Install mdBook, mdBook-KaTeX, and mdBook-ToC
+        run: cargo binstall -y mdbook mdbook-katex mdbook-toc
+      - name: Build
+        run: mdbook build
+      - name: Upload artifact
+        uses: actions/upload-pages-artifact@v3
 
   deploy:
     name: Deploy the site to GitHub Pages

src/notes/class_notes/stats303.md

@@ -229,7 +229,8 @@ $$
 
 ### importance sampling
 
-for value $f$ following distribution with PDF $p$, do not know CDF
+for value $f$ following distribution with PDF $p$, do not know CDF,
+want expectation
 
 define distribution $q(z)$ with known CDF
 
@@ -250,7 +251,8 @@ $$
 
 ### simulated annealing
 
-to avoid trapped in local minimum
+- to avoid trapped in local minimum
+- still need to try multiple time
 
 when seeking minimum, accept increase in $f$ with probability
 
@@ -300,16 +302,19 @@ design Markov chain w/ stationary distribution $\pi=p$:
     \right)$
     - $⇒ p(x)Q_{x,x^*}α(x,x^*)=p(x^*)Q_{x^*,x}α(x^*,x)$
 1. use new Markov chain w/ $Q'_{x,x^*}:=α(x,x^*)Q_{x,x^*},\quad x^*≠x$
-    - $Q_{x,x}$ take the rest of probability
+    - $Q_{x,x}$ take the rest of probability s.t. $∑_yQ_{x,y}=1$
 
-- do not know when stationary
+- drawback: do not know when stationary/converge. sample may be dependent
 
 ### Gibbs sampling
 
 want to sample variable $x_i$ following different distribution
 
 fix $x_{-i}:=\{x_1\ldots x_{i-1},x_{i+1}\ldots\}$ to previous value
-    when sampling $x_i$
+    when sampling $x_i$:
+$$
+Q_{x,x^*}:=p(x_i^*|x_{-1})
+$$
 
 a special case for metropolis hasting method $\Leftarrow$