This appendix provides a quick reference for mathematical notation used throughout the course. You do not need to memorise these — use this page as a lookup when you encounter unfamiliar symbols.
B.1 Basic notation
Symbol
Meaning
Example
\(x\)
A variable (lowercase)
Blood pressure measurement
\(X\)
A random variable (uppercase)
Blood pressure in the population
\(\bar{x}\)
Sample mean
Mean blood pressure in your study
\(\mu\)
Population mean
True mean blood pressure
\(s\) or \(\hat{\sigma}\)
Sample standard deviation
SD of blood pressures in your data
\(\sigma\)
Population standard deviation
True SD of blood pressures
\(n\)
Sample size
Number of patients
\(p\)
Probability or proportion
Prevalence of a disease
\(\hat{p}\)
Estimated proportion
Observed prevalence in your sample
B.2 Probability
Symbol
Meaning
\(P(A)\)
Probability of event A
\(P(A \mid B)\)
Probability of A given B (conditional probability)
Or in words: Posterior \(\propto\) Likelihood \(\times\) Prior
B.8 Model performance
Symbol
Meaning
TP, FP, TN, FN
True/false positives/negatives
Se = TP / (TP + FN)
Sensitivity (recall)
Sp = TN / (TN + FP)
Specificity
PPV = TP / (TP + FP)
Positive predictive value (precision)
NPV = TN / (TN + FN)
Negative predictive value
AUC
Area under the ROC curve
NB
Net benefit (from decision curve analysis)
B.9 Subscripts and superscripts
Notation
Meaning
\(x_i\)
Value for individual \(i\)
\(x_{ij}\)
Value of variable \(j\) for individual \(i\)
\(\hat{\theta}\)
Estimated value of \(\theta\)
\(\theta^*\)
Bootstrap replicate of \(\theta\)
\(x^2\)
\(x\) squared
\(\sqrt{x}\)
Square root of \(x\)
B.10 Greek letters commonly used in statistics
Letter
Name
Common use
\(\alpha\)
Alpha
Significance level, elastic net mixing
\(\beta\)
Beta
Regression coefficients, Type II error rate
\(\gamma\)
Gamma
Effect modifier, shape parameter
\(\delta\)
Delta
Difference, effect size
\(\epsilon\)
Epsilon
Error term, small quantity
\(\lambda\)
Lambda
Rate parameter, penalty parameter
\(\mu\)
Mu
Population mean
\(\pi\)
Pi
Proportion, prior
\(\sigma\)
Sigma
Standard deviation
\(\tau\)
Tau
Between-study variance (meta-analysis)
\(\chi^2\)
Chi-squared
Chi-squared test statistic
By Mark Khurana and Neil Scheidwasser
Reference
Khurana, M., & Scheidwasser, N. (2026). Advanced Statistics and Machine Learning for Health Research. https://mlhealthcourse.github.io/
BibTeX
@book{khurana2026statml,
title = {Advanced Statistics and Machine Learning for Health Research},
author = {Khurana, Mark and Scheidwasser, Neil},
year = {2026},
url = {https://mlhealthcourse.github.io/}
}
Source Code
---title: "Mathematical Notation Reference"---# Mathematical Notation Reference {#sec-math-notation .unnumbered}This appendix provides a quick reference for mathematical notation used throughout the course. You do not need to memorise these --- use this page as a lookup when you encounter unfamiliar symbols.## Basic notation| Symbol | Meaning | Example ||--------|---------|---------|| $x$ | A variable (lowercase) | Blood pressure measurement || $X$ | A random variable (uppercase) | Blood pressure in the population || $\bar{x}$ | Sample mean | Mean blood pressure in your study || $\mu$ | Population mean | True mean blood pressure || $s$ or $\hat{\sigma}$ | Sample standard deviation | SD of blood pressures in your data || $\sigma$ | Population standard deviation | True SD of blood pressures || $n$ | Sample size | Number of patients || $p$ | Probability or proportion | Prevalence of a disease || $\hat{p}$ | Estimated proportion | Observed prevalence in your sample |## Probability| Symbol | Meaning ||--------|---------|| $P(A)$ | Probability of event A || $P(A \mid B)$ | Probability of A given B (conditional probability) || $P(A \cap B)$ | Probability of both A and B || $P(A \cup B)$ | Probability of A or B (or both) |## Distributions| Notation | Distribution | Parameters ||----------|-------------|------------|| $X \sim N(\mu, \sigma^2)$ | Normal | Mean $\mu$, variance $\sigma^2$ || $X \sim \text{Bin}(n, p)$ | Binomial | Trials $n$, success probability $p$ || $X \sim \text{Pois}(\lambda)$ | Poisson | Rate $\lambda$ || $X \sim \text{Beta}(\alpha, \beta)$ | Beta | Shape parameters $\alpha$, $\beta$ |## Regression| Symbol | Meaning ||--------|---------|| $y_i$ | Outcome for patient $i$ || $x_i$ | Predictor value for patient $i$ || $\beta_0$ | Intercept || $\beta_1, \beta_2, \ldots$ | Regression coefficients || $\hat{y}_i$ | Predicted value for patient $i$ || $\epsilon_i$ | Residual (error) for patient $i$ || $\hat{\beta}$ | Estimated coefficient |**Linear regression:** $y_i = \beta_0 + \beta_1 x_{1i} + \beta_2 x_{2i} + \cdots + \epsilon_i$**Logistic regression:** $\log\left(\frac{p_i}{1 - p_i}\right) = \beta_0 + \beta_1 x_{1i} + \beta_2 x_{2i} + \cdots$## Penalised regression| Symbol | Meaning ||--------|---------|| $\lambda$ | Penalty strength (regularisation parameter) || $\alpha$ | Elastic net mixing parameter (0 = ridge, 1 = LASSO) || $\|\boldsymbol{\beta}\|_1 = \sum |\beta_j|$ | L1 norm (sum of absolute values) || $\|\boldsymbol{\beta}\|_2^2 = \sum \beta_j^2$ | L2 norm squared (sum of squares) |## Survival analysis| Symbol | Meaning ||--------|---------|| $T$ | Survival time (random variable) || $t$ | A specific time point || $S(t) = P(T > t)$ | Survival function || $h(t)$ | Hazard function (instantaneous risk) || $H(t)$ | Cumulative hazard || $\text{HR}$ | Hazard ratio (from Cox model) |**Cox model:** $h(t \mid \mathbf{x}) = h_0(t) \exp(\beta_1 x_1 + \beta_2 x_2 + \cdots)$## Bayesian statistics| Symbol | Meaning ||--------|---------|| $\theta$ | Parameter of interest || $P(\theta)$ or $\pi(\theta)$ | Prior distribution || $P(D \mid \theta)$ or $L(\theta \mid D)$ | Likelihood || $P(\theta \mid D)$ | Posterior distribution || $P(D)$ | Marginal likelihood (evidence) |**Bayes' theorem:** $P(\theta \mid D) = \frac{P(D \mid \theta) \, P(\theta)}{P(D)}$Or in words: Posterior $\propto$ Likelihood $\times$ Prior## Model performance| Symbol | Meaning ||--------|---------|| TP, FP, TN, FN | True/false positives/negatives || Se = TP / (TP + FN) | Sensitivity (recall) || Sp = TN / (TN + FP) | Specificity || PPV = TP / (TP + FP) | Positive predictive value (precision) || NPV = TN / (TN + FN) | Negative predictive value || AUC | Area under the ROC curve || NB | Net benefit (from decision curve analysis) |## Subscripts and superscripts| Notation | Meaning ||----------|---------|| $x_i$ | Value for individual $i$ || $x_{ij}$ | Value of variable $j$ for individual $i$ || $\hat{\theta}$ | Estimated value of $\theta$ || $\theta^*$ | Bootstrap replicate of $\theta$ || $x^2$ | $x$ squared || $\sqrt{x}$ | Square root of $x$ |## Greek letters commonly used in statistics| Letter | Name | Common use ||--------|------|-----------|| $\alpha$ | Alpha | Significance level, elastic net mixing || $\beta$ | Beta | Regression coefficients, Type II error rate || $\gamma$ | Gamma | Effect modifier, shape parameter || $\delta$ | Delta | Difference, effect size || $\epsilon$ | Epsilon | Error term, small quantity || $\lambda$ | Lambda | Rate parameter, penalty parameter || $\mu$ | Mu | Population mean || $\pi$ | Pi | Proportion, prior || $\sigma$ | Sigma | Standard deviation || $\tau$ | Tau | Between-study variance (meta-analysis) || $\chi^2$ | Chi-squared | Chi-squared test statistic |