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<!DOCTYPE html>
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<title>Introduction to Markov Chains</title>
<meta charset="utf-8" />
<meta name="author" content="Stat 340: Bayesian Statistics" />
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<textarea id="source">
class: middle, clear
class: title-slide, left, middle
# Introduction to Markov Chains
### Stat 340: Bayesian Statistics
---
class: inverse
## Your turn
<img src="figs/graduation_mc.jpg" width="75%" style="display: block; margin: auto;" />
1. What's the probability that a student who drops out will re-enroll?
1. What's the probability that a senior will graduate?
1. Does that probability depend on how many years it took them to achieve senior class standing?
---
class: middle
# Concepts
## 1. Markov chains
## 2. Transition matrices
---
class: inverse
## Your turn
<img src="figs/graduation_mc.jpg" width="70%" style="display: block; margin: auto;" />
.Large[
Write down the `\(6 \times 6\)` transition matrix for the university graduation rate Markov chain model.
1. Should the probabilities within each .bold[row] sum to 1?
1. Should the probabilities within each .bold[column] sum to 1?
]
---
class: middle
# Concepts
## 3. Calculating probabilities using the transition matrix
## 4. Marginal distribution of `\(\bf X_n\)`
---
class: inverse
## Your turn
Read over state/chain classifications and apply these labels to the following Markov chains:
.pull-left[
<img src="figs/mc1.png" width="85%" /><img src="figs/mc2.png" width="85%" />
]
.pull-right[
<img src="figs/mc3.png" width="85%" /><img src="figs/mc4.png" width="85%" />
]
---
class: middle
<img src="figs/mc1.png" width="809" style="display: block; margin: auto;" />
---
class: middle
<img src="figs/mc2.png" width="931" style="display: block; margin: auto;" />
---
class: middle
<img src="figs/mc3.png" width="1076" style="display: block; margin: auto;" />
---
class: middle
<img src="figs/mc4.png" width="647" style="display: block; margin: auto;" />
---
class: middle
# Concepts
## 5. Long-run behavior
## 6. Ergodic Markov chains
</textarea>
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