Maximum LikelihoodThe estimation method behind most of statistics, in five steps.MathematicsChoose the parameter making the observed data most probable.1Write the likelihoodL(θ) is the joint density of the data, read as a function of θ.2Take logarithmsProducts become sums, and the maximising θ is unchanged.3DifferentiateSet the derivative of the log-likelihood to zero for the scoreequation.4Solve for θAnalytically where possible, numerically where it is not.5Confirm it is a maximumThe second derivative must be negative, and check the boundarytoo.MLE is consistent and asymptotically efficient, but can be biased insmall samples: the MLE of a variance divides by n, not n − 1.Maximum Likelihoodlearnposters.com
Maximum Likelihood — printable math wall chart from LearnPosters. Free vector PDF, US Letter and A4.

Maximum Likelihood, step by step

Choose the parameter making the observed data most probable.

  1. Write the likelihoodL(θ) is the joint density of the data, read as a function of θ.
  2. Take logarithmsProducts become sums, and the maximising θ is unchanged.
  3. DifferentiateSet the derivative of the log-likelihood to zero for the score equation.
  4. Solve for θAnalytically where possible, numerically where it is not.
  5. Confirm it is a maximumThe second derivative must be negative, and check the boundary too.

MLE is consistent and asymptotically efficient, but can be biased in small samples: the MLE of a variance divides by n, not n − 1.

Questions about the Maximum Likelihood poster

What’s on the Maximum Likelihood poster?
5 numbered steps. Choose the parameter making the observed data most probable. Write the likelihood — L(θ) is the joint density of the data, read as a function of θ.; Take logarithms — Products become sums, and the maximising θ is unchanged.; Differentiate — Set the derivative of the log-likelihood to zero for the score equation.; Solve for θ — Analytically where possible, numerically where it is not.; Confirm it is a maximum — The second derivative must be negative, and check the bound…. MLE is consistent and asymptotically efficient, but can be biased in small samples: the MLE of a variance divides by n, not n − 1.
Who is the Maximum Likelihood poster for?
Maximum Likelihood belongs to the Mathematics section rather than to a school year, because math is not something one grade owns. Anyone learning probability & statistics can pin it up — a beginner, a student mid-course, or someone revising years later.
When should you use the Maximum Likelihood poster?
When a model has parameters and you need the values the data best support. A wall chart earns its place by being glanceable from where the work is happening, so Maximum Likelihood belongs on the wall where that math work actually happens, within glancing distance, rather than filed away.
What other posters go with Maximum Likelihood?
Bayes' Theorem, Central Limit Theorem and Conditional Probability sit alongside Maximum Likelihood in the Mathematics section. Printed together they make a wall rather than a single sheet, which is how a reference set actually gets used.Bayes' TheoremCentral Limit TheoremConditional Probability
Is the Maximum Likelihood poster free to download and print?
Yes. Maximum Likelihood downloads as a free PDF with no account, no email and no watermark, like everything else in the Mathematics section. Print as many copies as you like for a home, a classroom, a library or a tutoring group; reselling the file is the only thing the licence rules out.Read the licence
What size does the Maximum Likelihood poster print at?
Maximum Likelihood is a vector PDF laid out for US Letter, and prints on A4 with Fit to page — the same file, no separate download. Because every mark on it is drawn rather than photographed, it stays sharp enlarged to A3, A2 or A1 at a copy shop. Colour carries emphasis only, so a greyscale print of Maximum Likelihood loses nothing.Printing guide

Related posters

Charts that sit alongside Maximum Likelihood on the same wall.

Browse every Mathematics poster, or start from the full catalogue.