add classification notes #265

d-morrison · 2025-11-14T06:12:05Z

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d-morrison · 2025-11-14T06:12:44Z

@copilot complete and polish the introduction to classification section

Copilot · 2025-11-14T06:12:51Z

@d-morrison I've opened a new pull request, #266, to work on those changes. Once the pull request is ready, I'll request review from you.

Copilot

Pull Request Overview

This PR adds a new section on classification to the probability document, introducing concepts related to positive predictive value through a COVID-19 testing example. The changes include a new classification chapter file, a macro definition for probability mass functions, and an update to gitignore.

Adds new classification.qmd file with positive predictive value calculations
Defines \pmf macro in macros.qmd for probability mass function notation
Updates .gitignore to exclude Quarto IPython notebook files

Reviewed Changes

Copilot reviewed 3 out of 4 changed files in this pull request and generated 14 comments.

File	Description
classification.qmd	New file containing classification introduction and positive predictive value example with Bayesian calculations
probability.qmd	Includes the new classification section in the probability document
macros.qmd	Adds `\pmf` macro definition for probability mass function notation
.gitignore	Adds pattern to ignore Quarto IPython notebook cache files

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classification.qmd

Copilot · 2025-11-14T06:16:06Z

classification.qmd

+$$\mass(A) = 0.07$$ 
+
+$$\mass(\neg A) = .93$$
+
+
+
+$p\left( negative \middle| no\ covid \right) = .99$:
+$p\left( B \middle| !A \right)$
+
+$$p\left( Covid \middle| positive \right) = ?$$
+
+$$p\left( A \middle| B \right) = \frac{p\left( B \middle| A \right)p(A)}{p(B)}$$
+
+$$p(B) = p\left( B \middle| A \right)p(A) + p\left( B \middle| !A \right)p(!A)$$
+
+$$p\left( B \middle| A \right)p(A) = .99*\ .07 = .0693$$
+
+$$\ p\left( B \middle| !A \right)p(!A) = .01*.93 = .0093$$
+
+$$p(B) = .0693 + .0093 = .0786$$
+
+$$p\left( A \middle| B \right) = .0693/.0786$$
+
+$$= .88$$
+
+$${p\left( A \middle| B \right) = \frac{p\left( B \middle| A \right)p(A)}{p(B)}
+}{= p\left( B \middle| A \right)\frac{p(A)}{p(B)}
+}{= p\left( B \middle| A \right)\frac{p(A)}{p\left( B \middle| A \right)p(A) + p\left( B \middle| !A \right)p(!A)}}$$
+
+$$= \frac{p(A)}{p(A) + \frac{p\left( B \middle| !A \right)}{p\left( B \middle| A \right)}p(!A)}$$
+
+$$= \frac{1}{1 + \frac{p\left( B \middle| !A \right)}{p\left( B \middle| A \right)}\frac{p(!A)}{p(A)}}


Inconsistent notation. Earlier in the document, disease is represented as D (line 12), but here it's represented as A. The notation should be consistent throughout the document.

Suggested change

$$\mass(A) = 0.07$$

$$\mass(\neg A) = .93$$

$p\left( negative \middle| no\ covid \right) = .99$:

$p\left( B \middle| !A \right)$

$$p\left( Covid \middle| positive \right) = ?$$

$$p\left( A \middle| B \right) = \frac{p\left( B \middle| A \right)p(A)}{p(B)}$$

$$p(B) = p\left( B \middle| A \right)p(A) + p\left( B \middle| !A \right)p(!A)$$

$$p\left( B \middle| A \right)p(A) = .99*\ .07 = .0693$$

$$\ p\left( B \middle| !A \right)p(!A) = .01*.93 = .0093$$

$$p(B) = .0693 + .0093 = .0786$$

$$p\left( A \middle| B \right) = .0693/.0786$$

$$= .88$$

$${p\left( A \middle| B \right) = \frac{p\left( B \middle| A \right)p(A)}{p(B)}

}{= p\left( B \middle| A \right)\frac{p(A)}{p(B)}

}{= p\left( B \middle| A \right)\frac{p(A)}{p\left( B \middle| A \right)p(A) + p\left( B \middle| !A \right)p(!A)}}$$

$$= \frac{p(A)}{p(A) + \frac{p\left( B \middle| !A \right)}{p\left( B \middle| A \right)}p(!A)}$$

$$= \frac{1}{1 + \frac{p\left( B \middle| !A \right)}{p\left( B \middle| A \right)}\frac{p(!A)}{p(A)}}

$$\mass(D) = 0.07$$

$$\mass(\neg D) = .93$$

$p\left( negative \middle| no\ covid \right) = .99$:

$p\left( B \middle| \neg D \right)$

$$p\left( Covid \middle| positive \right) = ?$$

$$p\left( D \middle| B \right) = \frac{p\left( B \middle| D \right)p(D)}{p(B)}$$

$$p(B) = p\left( B \middle| D \right)p(D) + p\left( B \middle| \neg D \right)p(\neg D)$$

$$p\left( B \middle| D \right)p(D) = .99*\ .07 = .0693$$

$$\ p\left( B \middle| \neg D \right)p(\neg D) = .01*.93 = .0093$$

$$p(B) = .0693 + .0093 = .0786$$

$$p\left( D \middle| B \right) = .0693/.0786$$

$$= .88$$

$${p\left( D \middle| B \right) = \frac{p\left( B \middle| D \right)p(D)}{p(B)}

}{= p\left( B \middle| D \right)\frac{p(D)}{p(B)}

}{= p\left( B \middle| D \right)\frac{p(D)}{p\left( B \middle| D \right)p(D) + p\left( B \middle| \neg D \right)p(\neg D)}}$$

$$= \frac{p(D)}{p(D) + \frac{p\left( B \middle| \neg D \right)}{p\left( B \middle| D \right)}p(\neg D)}$$

$$= \frac{1}{1 + \frac{p\left( B \middle| \neg D \right)}{p\left( B \middle| D \right)}\frac{p(\neg D)}{p(D)}}

Copilot · 2025-11-14T06:16:07Z

classification.qmd

+$p\left( negative \middle| no\ covid \right) = .99$:
+$p\left( B \middle| !A \right)$
+
+$$p\left( Covid \middle| positive \right) = ?$$


Inconsistent notation. Line 25 uses no\ covid (with escaped space), line 26 uses !A, and line 28 uses Covid. The notation should be consistent - either use the symbolic notation consistently (like \neg A or !A) or use descriptive text consistently.

Suggested change

$p\left( negative \middle| no\ covid \right) = .99$:

$p\left( B \middle| !A \right)$

$$p\left( Covid \middle| positive \right) = ?$$

$p\left( B \middle| \neg A \right) = .99$:

$p\left( B \middle| \neg A \right)$

$$p\left( A \middle| B \right) = ?$$

Copilot · 2025-11-14T06:16:07Z

classification.qmd

+
+$$p(B) = p\left( B \middle| A \right)p(A) + p\left( B \middle| !A \right)p(!A)$$
+
+$$p\left( B \middle| A \right)p(A) = .99*\ .07 = .0693$$


Space before multiplication operator. Remove the space after the asterisk: should be .99 * .07 instead of .99*\ .07.

Suggested change

$$p\left( B \middle| A \right)p(A) = .99*\ .07 = .0693$$

$$p\left( B \middle| A \right)p(A) = .99 * .07 = .0693$$

Copilot · 2025-11-14T06:16:08Z

classification.qmd

+$p\left( negative \middle| no\ covid \right) = .99$:
+$p\left( B \middle| !A \right)$
+
+$$p\left( Covid \middle| positive \right) = ?$$


Inconsistent disease reference. Line 17 mentions "covid" but line 28 switches to "Covid" (capitalized). The disease name should be consistently capitalized (typically "COVID-19" or just "disease" if keeping it generic).

Copilot · 2025-11-14T06:16:09Z

classification.qmd

+$$\mass(A) = 0.07$$ 
+
+$$\mass(\neg A) = .93$$


Undefined notation \mass. This macro is used but not defined in macros.qmd, which could cause compilation errors. Consider using \pmf or defining the \mass macro.

Copilot · 2025-11-14T06:16:09Z

classification.qmd

+
+$$p\left( B \middle| A \right)p(A) = .99*\ .07 = .0693$$
+
+$$\ p\left( B \middle| !A \right)p(!A) = .01*.93 = .0093$$


Leading space before equation. Remove the leading backslash-space: should be p\left( instead of \ p\left(.

Suggested change

$$\ p\left( B \middle| !A \right)p(!A) = .01*.93 = .0093$$

$$p\left( B \middle| !A \right)p(!A) = .01*.93 = .0093$$

Copilot · 2025-11-14T06:16:09Z

classification.qmd

+$${p\left( A \middle| B \right) = \frac{p\left( B \middle| A \right)p(A)}{p(B)}
+}{= p\left( B \middle| A \right)\frac{p(A)}{p(B)}
+}{= p\left( B \middle| A \right)\frac{p(A)}{p\left( B \middle| A \right)p(A) + p\left( B \middle| !A \right)p(!A)}}$$


Malformed LaTeX equation. Lines 44-46 appear to be a single equation split incorrectly with multiple $$ delimiters. This should use proper multi-line equation formatting like \begin{align} or separate the steps into individual equations with text between them.

Suggested change

$${p\left( A \middle| B \right) = \frac{p\left( B \middle| A \right)p(A)}{p(B)}

}{= p\left( B \middle| A \right)\frac{p(A)}{p(B)}

}{= p\left( B \middle| A \right)\frac{p(A)}{p\left( B \middle| A \right)p(A) + p\left( B \middle| !A \right)p(!A)}}$$

$$

\begin{align*}

p\left( A \middle| B \right) &= \frac{p\left( B \middle| A \right)p(A)}{p(B)} \\

&= p\left( B \middle| A \right)\frac{p(A)}{p(B)} \\

&= p\left( B \middle| A \right)\frac{p(A)}{p\left( B \middle| A \right)p(A) + p\left( B \middle| !A \right)p(!A)}

\end{align*}

$$

Copilot · 2025-11-14T06:16:09Z

classification.qmd

+$$\pmf{ + | D} = .99$$
+
+99% specific means if they don't have covid, the test says no covid, 99%
+time
+
+7% of people actually have covid: 
+
+$$\mass(A) = 0.07$$ 
+
+$$\mass(\neg A) = .93$$
+
+
+
+$p\left( negative \middle| no\ covid \right) = .99$:
+$p\left( B \middle| !A \right)$
+
+$$p\left( Covid \middle| positive \right) = ?$$
+
+$$p\left( A \middle| B \right) = \frac{p\left( B \middle| A \right)p(A)}{p(B)}$$
+
+$$p(B) = p\left( B \middle| A \right)p(A) + p\left( B \middle| !A \right)p(!A)$$
+
+$$p\left( B \middle| A \right)p(A) = .99*\ .07 = .0693$$
+
+$$\ p\left( B \middle| !A \right)p(!A) = .01*.93 = .0093$$
+
+$$p(B) = .0693 + .0093 = .0786$$
+
+$$p\left( A \middle| B \right) = .0693/.0786$$
+
+$$= .88$$
+
+$${p\left( A \middle| B \right) = \frac{p\left( B \middle| A \right)p(A)}{p(B)}
+}{= p\left( B \middle| A \right)\frac{p(A)}{p(B)}
+}{= p\left( B \middle| A \right)\frac{p(A)}{p\left( B \middle| A \right)p(A) + p\left( B \middle| !A \right)p(!A)}}$$
+
+$$= \frac{p(A)}{p(A) + \frac{p\left( B \middle| !A \right)}{p\left( B \middle| A \right)}p(!A)}$$
+
+$$= \frac{1}{1 + \frac{p\left( B \middle| !A \right)}{p\left( B \middle| A \right)}\frac{p(!A)}{p(A)}}


[nitpick] Inconsistent decimal notation. Throughout the document, probabilities are written as .99, .07, .93, etc. (without leading zero), but it would be clearer and more standard to use 0.99, 0.07, 0.93 for readability.

Co-authored-by: d-morrison <2474437+d-morrison@users.noreply.github.com>

github-actions · 2025-11-14T06:31:48Z

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…ated notation Co-authored-by: d-morrison <2474437+d-morrison@users.noreply.github.com>

Co-authored-by: d-morrison <2474437+d-morrison@users.noreply.github.com>

Create classification appendix chapter with polished content

add classification notes

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Create classification appendix chapter with polished content #266

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Complete and polish classification section introduction

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d-morrison and others added 11 commits November 13, 2025 23:54

Update classification.qmd

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Update classification.qmd

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Update classification.qmd

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Merge classification branch keeping polished version

9c4b4d2

Add newlines after sentences and use custom macros

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Simplify sentence structure and add formal classification definition

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Add slide breaks and speaker notes for RevealJS format

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Fix LaTeX equation nesting error: use aligned instead of align

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Add definition blocks for diagnostic test characteristics and abbrevi…

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…ated notation Co-authored-by: d-morrison <2474437+d-morrison@users.noreply.github.com>

Move classification section to appendix chapter

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Co-authored-by: d-morrison <2474437+d-morrison@users.noreply.github.com>

Merge pull request #266 from d-morrison/copilot/sub-pr-265

890fca9

Create classification appendix chapter with polished content


		$$p(B) = p\left( B \middle\| A \right)p(A) + p\left( B \middle\| !A \right)p(!A)$$

		$$p\left( B \middle\| A \right)p(A) = .99*\ .07 = .0693$$


		$$p\left( B \middle\| A \right)p(A) = .99*\ .07 = .0693$$

		$$\ p\left( B \middle\| !A \right)p(!A) = .01*.93 = .0093$$

	$$\ p\left( B \middle\| !A \right)p(!A) = .01*.93 = .0093$$
	$$p\left( B \middle\| !A \right)p(!A) = .01*.93 = .0093$$

-$${p\left( A \middle| B \right) = \frac{p\left( B \middle| A \right)p(A)}{p(B)}
-}{= p\left( B \middle| A \right)\frac{p(A)}{p(B)}
-}{= p\left( B \middle| A \right)\frac{p(A)}{p\left( B \middle| A \right)p(A) + p\left( B \middle| !A \right)p(!A)}}$$
+$$
+\begin{align*}
+p\left( A \middle| B \right) &= \frac{p\left( B \middle| A \right)p(A)}{p(B)} \\
+&= p\left( B \middle| A \right)\frac{p(A)}{p(B)} \\
+&= p\left( B \middle| A \right)\frac{p(A)}{p\left( B \middle| A \right)p(A) + p\left( B \middle| !A \right)p(!A)}
+\end{align*}
+$$

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