For evenly spaced intervals, this process can be done using the (*) Newton-Cotes rules, whose closed type of degree two is equivalent to Simpson's rule.
This task is performed by using a Chebyshev expansion of the relevant function in the Clenshaw- Curtis method. It's not parameter or posterior distribution estimation, but accomplishing this task by averaging across samples from updating conditional distributions is known as Gibbs sampling, which is an application of Markov Chain Monte Carlo methods for accomplishing this task. For evenly spaced intervals, this process can be done using the (*) Newton-Cotes rules, whose closed type of degree two is equivalent to Simpson's rule. For uncomplicated functions, this can be done precisely by hand using the Fundamental Theorem of Calculus. For 10 points, identify this procedure that can approximate the area under a curve.
This task is performed by using a Chebyshev expansion of the relevant function in the Clenshaw- Curtis method.
numerical integration [or numerical quadrature; anti-prompt on "automatic integration"; prompt on "integration"]