Likelihood

TL;DR

Measures how compatible observed data are with a particular hypothesis or model.
Quantifies the probability of an event given available evidence or data.
Used to evaluate hypotheses and support decision-making from empirical observations.

Definition

Likelihood is a statistical concept that measures the probability of an event occurring given certain evidence or data. It is a measure of the compatibility of the data with a specific hypothesis or model.

Explanation

Likelihood expresses how well observed data support a particular hypothesis or model by quantifying the probability of the observed outcomes under that hypothesis. It is applied by comparing evidence (data) against hypotheses or models to assess which hypotheses are more compatible with the data. Practically, likelihoods are used to evaluate the plausibility of events or outcomes based on available evidence and to inform inferences and decisions.

Examples

Clinical trial example

Suppose you are conducting a study on the effectiveness of a new drug for treating a particular disease. You randomly assign 100 patients to receive the drug and 100 patients to receive a placebo. After a certain period of time, you collect data on the number of patients who showed improvement in their condition. Based on this data, you calculate the likelihood that the drug is effective in treating the disease.

In this example, the likelihood of the drug being effective is determined by comparing the number of patients who showed improvement to the total number of patients in the study. This calculation can help researchers determine the efficacy of the drug and make decisions about its use in clinical practice.

Forensic DNA example

Suppose a crime has been committed and the investigators have collected DNA samples from the crime scene. They also have DNA samples from potential suspects. The likelihood of a suspect being the perpetrator of the crime is calculated by comparing the DNA samples and determining the probability of a match.

In this example, comparing the DNA samples helps investigators narrow down their list of suspects and ultimately identify the perpetrator.

Use cases

Evaluating the efficacy of a drug and informing decisions about its use in clinical practice.
Comparing forensic evidence (such as DNA) to potential suspects to narrow suspects and identify a perpetrator.
Making inferences and decisions based on how well data support particular hypotheses or models.

Hypothesis
Model
Probability
Evidence
Data
Inference