Statistics for ML #11 — PDF: Probability Density Function

PDF: Probability Density Function

This is post #11 in the Statistics for ML series by Md Salek Miah, covering the essential statistical foundations for machine learning and epidemiology research.

📌 This series covers 100 topics from basic data types to advanced Bayesian ML. Tailored for public health researchers and data scientists working with DHS surveys, health data, and predictive modeling.

Core Concept

The PDF: Probability Density Function is a fundamental concept in probability and statistics. Understanding it deeply enables correct model selection, valid inference, and meaningful interpretation in both classical statistics and modern machine learning.

Mathematical Foundation

Each distribution, theorem, or concept in this series is presented with:

• Formal mathematical definition
• Intuitive explanation
• Real-world public health examples (DHS data, maternal health, child health)
• Python and R code for implementation
• Connection to ML algorithms and applications

Why This Matters for ML & Public Health

In my research on maternal health across Bangladesh, Nepal, Zambia, and Burkina Faso using DHS survey data, these statistical foundations appear constantly:

• Choosing correct probability distributions for count outcomes (Poisson, Negative Binomial)
• Handling imbalanced binary outcomes (Bernoulli, SMOTE)
• Valid inference under complex survey design (CLT, sampling theory)
• Interpreting SHAP values correctly (requires understanding expectations and conditional distributions)
• Model calibration: predicted probabilities must match true event frequencies

Code Example

# Template for post #11: PDF: Probability Density Function
import numpy as np
import pandas as pd
from scipy import stats
import matplotlib.pyplot as plt

# Load your dataset
# df = pd.read_csv('dhs_data.csv')

# Explore the relevant distribution/concept
# See full worked example in the complete post
print("Statistics for ML #11: PDF: Probability Density Function")
print("Author: Md Salek Miah | SUST | saleksta@gmail.com")

# R equivalent
# library(tidyverse)
# library(survey)
# Full R code for PDF: Probability Density Function
# Author: Md Salek Miah

Further Reading

• Full series index
• My research publications

• Connect: saleksta@gmail.com

  ResearchGate

Part of the Statistics for ML series — post #11 of 100.