---
# System prepended metadata

title: Bayesian methods for Hackers ch1-2
tags: [d3, ' meeting']

---

---
title: "Bayesian methods for Hackers ch1-2"
tags: d3, meeting

slideOptions:
  theme: serif
  transition: slide
---

## Let's Bayesian thinking

---

##  Bayesian Methods for Hackers ch1-2

- Present: Dragon Chen
- Date: 09/18

---

## Intro

- Title: Bayesian Methods for Hackers
- Github: [這](https://github.com/CamDavidsonPilon/Probabilistic-Programming-and-Bayesian-Methods-for-Hackers)(qsirch 上也有 pdf)

![](https://i.imgur.com/YPqAwBk.png)    

----

- You are a **skilled programmer**, but bugs still slip into your code.
- After a particularly difficult implementation of an algorithm, you decide to **test your code** on a trivial example.

----

- It passes. You test the code on a harder problem.
- It passes once again. And it passes the next, even more difficult, test too!
- You are **starting to believe** that there may be no bugs in this code. . .

----

## You already are thinking Bayesian!

Bayesian inference is simply **updating your beliefs** after considering new **evidence**

---

## Bayesian Worldview

----

- Bayesian worldview interprets probability as measure of believability in an event

<span><!-- .element: class="fragment" -->==How confident we are in an event occurring==</span>

----

### versus Frequentists

- Frequentist assume probability is the long-run frequency of events
- *Probability of plane accidents* under a frequentist philosophy is interpreted as the *long-term frequency of plane accidents*

----

### Belief

- Bayesians interpret a probability as the measure of belief, or confidence, in an event occurring.
- An individual assigns belief of p(probability) to an event
- The definition leaves room for conflicting **beliefs between individuals**

----

### Different Belief

- Different individuals have different beliefs of events occurring because they possess different information about the world.
- The existence of different beliefs does not imply that anyone is wrong.

---

## Procedure
### Coin Example

- I flip a coin. We assume the coin is fair, that the probability of heads is 0.5. Assume, then, that I peek at the coin. Now I know for certain what the result is.
- Now what is your belief that the coin is heads?

----

- Assume the coin is fair, prob is 0.5
- We denote our belief about event A as P(A)
- We call this quantity the **prior probability**

"When the facts change, I change my mind. What do you do, sir?", John Maynard Keynes

----

- Bayesian updates his/her beliefs after seeing evidence
- We denote our updated belief as P(A|X)
- Prob of A given the evidence X
- We call the updated belief the **posterior probability**

----

- If you flip 1/3/5 coins keep showing head-up, do you still believe the coin is fair?

----

![](https://i.imgur.com/SHzgAzR.png)

----

The posterior probabilities are represented by the curves, and our uncertainty is proportional to the <font color="red">width of the curve</font>.

----

- We did not **completely discard the prior belief** after seeing new evidence X, but we **re-weighted the prior** to incorporate the **new evidence**

---

## Else Detail

- N → ∞, our Bayesian results (often) align with frequentist results
- For small N, inference is much more unstable

---

## Some Detail of PyMC

![](https://i.imgur.com/FwxOAcz.png)

----

![](https://i.imgur.com/4D5Yvys.png)

----

![](https://i.imgur.com/EimyIz7.png)

---

### Thank you for listening! :dragon: 