Practical 1

class: center, middle, title-slide

.title[
# Practical 1
]
.author[
### Olivier Gimenez
]
.date[
### last updated: 2024-10-17
]

---

## Setting the scene

* The chance of the  test being positive given you are a vampire is `\(\Pr(+|\text{vampire}) = 0.90\)` (**sensitivity**).

* The chance of a negative test given you are mortal is `\(\Pr(-|\text{mortal}) = 0.95\)` (**specificity**).

---

## Question

* Suppose the diagnostic test has the same sensitivity and specificity but vampirism is more common: `\(10\%\)` of the population is vampire.

* What is the probability that a person is a vampire, given that the test is positive?

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## Solution

The probability that a person is a vampire, given that the test is positive

- `\(\Pr(+ | \text{vampire}) = 0.9\)`
- `\(\Pr(- | \text{mortal}) = 0.95\)`
- `\(\Pr(\text{vampire}) = 0.1\)`

`\begin{align}
 \Pr(+) &= \Pr(+ | \text{vampire}) \Pr(\text{vampire}) + \Pr(+ | \text{mortal}) \Pr(\text{mortal}) \\
  &= 0.9*0.1 + 0.05*0.9 \\
  &=0.135
\end{align}`

`\begin{align}
 \Pr(\text{vampire} | +) &= \Pr(+ | \text{vampire}) \Pr(\text{vampire}) / \Pr(+) \\
  &= 0.9*0.1 / 0.135\\
  &= 0.666 \text{ (no comment)}
\end{align}`