Likelihood Principle

TL;DR

• Inference should be based only on the observed data and the assumed data distribution.
• The fit of a model or hypothesis is judged solely by how well it explains the observed data, not by prior assumptions about the model.
• Applying this principle aims to reduce bias and make probability assessments objective.

Definition

The likelihood principle states that the probability of an observed data set should not depend on the particular model or hypothesis being tested, but only on the data itself and the assumed distribution of the data. In other words, the likelihood of a model or hypothesis should only be based on how well it fits the observed data, not on any preconceived notions or assumptions about the model or hypothesis.

Explanation

The principle requires that evaluations of models or hypotheses rely exclusively on the observed data and the assumed statistical distribution for that data. It emphasizes that prior beliefs or assumptions about models should not influence the computed likelihood of those models beyond how they account for the observed outcomes. As a result, applying the likelihood principle aims to ensure that probability assessments reflect only the empirical evidence provided by the sample.

The likelihood principle is a key concept in statistical inference, the process of using statistical techniques to make inferences about a population from a sample. By adhering to the principle, inferences drawn from sample data are intended to be objective and unbiased.

Examples

Clinical trial example

In a clinical trial, a group of patients is randomly assigned to receive either a new drug or a placebo, and the outcomes of the two groups are compared. The hypothesis being tested is whether the new drug is more effective than the placebo. The likelihood of this hypothesis should only be based on how well the data from the clinical trial fits the assumed distribution, not on any preconceived notions about the drug or the placebo.

Election poll example

In an election, a group of voters is randomly selected and asked whom they plan to vote for. The hypothesis being tested is whether a particular candidate will win the election. The likelihood of this hypothesis should only be based on how well the poll data fits the assumed distribution, not on any preconceived notions about the candidate or the election.

Use cases

• Economics
• Biology
• Psychology

Notes or pitfalls

• The likelihood principle is important because it ensures that probability assessments for models or hypotheses are based solely on observed data, helping to eliminate bias and promote objectivity in statistical conclusions.

Related terms

• Statistical inference