# What is the difference between confidence intervals and confidence bands?

On Wikipedia it mentions states that a confidence band is:

$$\Pr(\hat{f}(x) - w(x) < f(x) < \hat{f}(x) + w(x), \text{ for all }x) = 1-\alpha$$

Where where $$\hat{f}(x)$$ is the point estimate of $$f(x)$$.

and it states that a confidence interval is:

Let X be a random sample from a probability distribution with statistical parameters θ, which is a quantity to be estimated, and φ, representing quantities that are not of immediate interest. A confidence interval for the parameter θ, with confidence level or confidence coefficient γ, is an interval with random endpoints (u(X), v(X)), determined by the pair of random variables u(X) and v(X), with the property:

$${\Pr }_{\theta ,\varphi }(u(X)<\theta

Is the only difference in the point estimate vs. the random variables for the upper and lower intervals/bands? A.K.A bands are symmetric and intervals don't have to be?

What are the advantages of one over the other?

When would you use one over the other?

Thanks!

Actually it is very simple. For a one dimensional variable there is a confidence interval, e.g., like $$\pm1.5$$. For a two dimensional plot, there is a confidence band, which are functions above and below the estimates, e.g., from regression.