# What's the difference between likelihood and confidence in claim being true

I'm reading the IPCC report on climate change from 2007. In their uncertainity guide they make a distinction between likelihood and levels of confidence. What's the difference between the terms?

http://www.ipcc.ch/pdf/assessment-report/ar4/wg1/ar4-uncertaintyguidancenote.pdf

## 2 Answers

Likelihood, as M. Chernick wrote, has a very standard statistical meaning. "Levels of confidence" suggest a number of statistical concepts, but are somewhat ambiguous. Reading the relevant sections in the linked article, it seems that "levels of confidence" are a subjective survey measurement taken from experts whereas Likelihood is a measure taken from a statistical model.

Likelihood is, at large, a random function telling you the probability of a particular choice of your model parameters given the data (which in a Frequentist setting is where the randomness comes from---we think of the likelihood as something that exists for all possible experiments and sets of observations). It's useful because it is instrumental in building Bayesian and Likelihoodist estimation procedures.

The paper seems to define Likelihood differently, more like the posterior predictive probability in a Bayesian setting.

So beware of confusing the paper's likelihood with classical statistical Likelihood and consider that the paper's likelihood may be a mathematical measure and "Levels of confidence" a surveyed value.

• Good answer, but a likelihood is not a "random function" at all, but a "measurable function" telling you not the probability of anything, but only relative probabilities. May 28, 2012 at 18:42
• I agree that the likelihood doesn't need to be normalized, but for a particular data set the likelihood function is considered a measurable mapping from parameter space to R. You can use that construction to build a function from the sample space to the space of likelihood functions and see it as a random function. May 28, 2012 at 22:52
• Or, I guess in other words, the likelihood function cannot be fixed without knowledge of the data, so if you consider the data generating process to be a random process then the likelihood function is going to inherit that randomness. That was all I was trying to get across. May 28, 2012 at 22:53
• That makes sense. May 28, 2012 at 23:02

In statistics these terms have formal meanings. Likelihood is the function of the unknown parameters that represents the probability of the observed data given the parameters. Confidence refers to the level of coverage for a confidence interval/region as a 95% confidence level means that the prescription for constructing the confidence region would include the true parameter(s) 95% of the time in repeated sampling. After reading the linked document it seems that the authors do not clearly define either term. Their meaning of level of confidence has to do with expert agreement and objective evidence. The greater each is the more confidence you have. Likelihood seems to be related to the formal statistical term but is not defined clearly enough to be sure whether or not they are one in the same. I have to agree with tel about being careful not to confuse the authors terms with the standard statistical terms.

• Please, take a look at the paper posted by the OP. These terms are interpreted differently there. But I agree with definitions you are giving in the Statistics argot.
– user10525
May 28, 2012 at 16:03