Statistics

Thu, 12 Mar 2026 00:00:00 +0000

Statistics #

Statistical methods help you turn raw data into reliable conclusions, while understanding uncertainty, variability, and confidence.

Statistics provides the language and tools for reasoning about data, uncertainty, and inference.

ML needs understanding data behaviour, drawing conclusions, and validating machine learning models.

Collect Data
Present & Organise Data (in a systematic manner)
Alalyse Data
Infer about the Data
Take Decision from the Data

Statistics Topic	What you learn (plain English)	ML Connection
1. Basic Probability & Statistics	Summarise data; understand spread; basic probability rules	Data understanding (EDA), feature sanity checks, detecting outliers, interpreting “average behaviour”
2. Conditional Probability & Bayes	Update probability using new information; Bayes’ rule	Naïve Bayes, Bayesian thinking, posterior probabilities, probabilistic classification
3. Probability Distributions	Model randomness with distributions; expectation/variance/covariance	Likelihood models, noise assumptions (Gaussian), sampling, probabilistic modelling foundations
4. Hypothesis Testing	Sampling, CLT, confidence intervals, significance tests, ANOVA, MLE	A/B testing, evaluating model improvements, significance vs noise, parameter estimation (MLE)
5. Prediction & Forecasting	Correlation, regression, time series (AR/MA/ARIMA/SARIMA etc.)	Linear regression, forecasting, sequential data modelling, baseline predictive modelling
6. GMM & EM	Mixtures of Gaussians; iterative estimation with EM	Unsupervised learning (soft clustering), density estimation, latent-variable models

flowchart TD
 A["Statistical Methods<br/>AIML ZC418"] --> B["1. Basic Probability and Statistics"]
 A --> C["2. Conditional Probability and Bayes"]
 A --> D["3. Probability Distributions"]
 A --> E["4. Hypothesis Testing"]
 A --> F["5. Prediction and Forecasting"]
 A --> G["6. Gaussian Mixture Model and EM"]

 B --> B1["Central Tendency<br/>Mean - Median - Mode"]
 B --> B2["Variability<br/>Range - Variance - SD - Quartiles"]
 B --> B3["Basic Probability Concepts"]
 B3 --> B31["Axioms of Probability"]
 B3 --> B32["Definition of Probability"]
 B3 --> B33["Mutually Exclusive vs Independent"]

 C --> C1["Conditional Probability"]
 C --> C2["Independence (conditional)"]
 C --> C3["Bayes Theorem"]
 C --> C4["Naive Bayes (intro)"]

 D --> D1["Random Variables<br/>Discrete and Continuous"]
 D --> D2["Expectation - Variance - Covariance"]
 D --> D3["Transformations of RVs"]
 D --> D4["Key Distributions"]
 D4 --> D41["Bernoulli"]
 D4 --> D42["Binomial"]
 D4 --> D43["Poisson"]
 D4 --> D44["Normal (Gaussian)"]
 D4 --> D45["t - Chi-square - F (intro)"]

 E --> E1["Sampling<br/>Random and Stratified"]
 E --> E2["Sampling Distributions<br/>CLT"]
 E --> E3["Estimation<br/>Confidence Intervals"]
 E --> E4["Hypothesis Tests<br/>Means and Proportions"]
 E --> E5["ANOVA<br/>Single and Dual factor"]
 E --> E6["Maximum Likelihood"]

 F --> F1["Correlation"]
 F --> F2["Regression"]
 F --> F3["Time Series Basics<br/>Components"]
 F --> F4["Moving Averages<br/>Simple and Weighted"]
 F --> F5["Time Series Models"]
 F5 --> F51["AR"]
 F5 --> F52["ARMA / ARIMA"]
 F5 --> F53["SARIMA / SARIMAX"]
 F5 --> F54["VAR / VARMAX"]
 F --> F6["Exponential Smoothing"]

 G --> G1["GMM<br/>Mixture of Gaussians"]
 G --> G2["EM Algorithm<br/>E-step - M-step"]

 B -.-> C
 C -.-> D
 D -.-> E
 E -.-> F
 F -.-> G

Data - Types #

flowchart TD
	A[(Data)] --> B["Categorical (Qualitative)"]
 A --> C["Numerical (Quantitative)"]

 B --> B1[Nominal]
 B --> B2[Ordinal]

 C --> C1[Discrete]
 C --> C2[Continuous]

 C2 --> C21[Interval]
 C2 --> C22[Ratio]

 %% Styling
 style A fill:#E1F5FE,stroke:#333
 style B fill:#90CAF9,stroke:#333
 style B1 fill:#90CAF9,stroke:#333
 style B2 fill:#90CAF9,stroke:#333
 style C fill:#FFF9C4,stroke:#333
 style C1 fill:#FFF9C4,stroke:#333
 style C2 fill:#FFF9C4,stroke:#333
 style C21 fill:#FFF9C4,stroke:#333
 style C22 fill:#FFF9C4,stroke:#333

Categorical (Qualitative) #

express a qualitative attribute e.g. hair color, eye color

Data Analysis on Arshad Siddiqui

Statistics

Statistics #

Data - Types #

Categorical (Qualitative) #