Maximum Likelihood - Explained

2026-03-07 · Source: DataMListic · Field: Technology & Digital — Artificial Intelligence & Machine Learning, Data Science & Analytics · Depth: Intermediate, quick

Summary

Maximum Likelihood Estimation (MLE) is a statistical method used to determine the parameters of a probability distribution that best fit a given set of observed data. The normal distribution, characterized by its mean (mu) and standard deviation (sigma), serves as a primary example. MLE operates by constructing a likelihood function, which quantifies how plausible specific distribution parameters are given the observed data. This function is derived by multiplying the probability densities of each data point under a hypothesized distribution. The parameters (mu and sigma) that maximize this likelihood function are chosen as the maximum likelihood estimates. To mitigate the issue of multiplying many small numbers, the log-likelihood function is often used, which converts products into sums without altering the location of the maximum.

Key takeaway

For Data Scientists and Machine Learning Engineers seeking to model data distributions, understanding Maximum Likelihood Estimation is crucial. It provides a robust framework for estimating unknown parameters (like mean and standard deviation) from observed data. You should apply MLE when fitting parametric models to ensure your chosen parameters best reflect the underlying data generation process, particularly when dealing with continuous data assumed to be normally distributed.

Key insights

Maximum Likelihood Estimation identifies distribution parameters that maximize the probability of observing given data.

Principles

• Normal distributions are defined by mean (mu) and standard deviation (sigma).
• Log-likelihood simplifies calculations without changing the maximum.

Method

To find maximum likelihood estimates, calculate the product of individual data point densities for various parameter sets, then identify the parameters yielding the highest product.

In practice

• Use MLE to estimate parameters for normal distributions.
• Apply log-likelihood for numerical stability with many data points.

Topics

• Maximum Likelihood Estimation
• Normal Distribution
• Likelihood Function
• Parameter Estimation
• Statistical Inference

Best for: Data Scientist, Machine Learning Engineer, AI Student

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Editorial summary, takeaway, and curation by AIssential. Original article published by DataMListic.