Some Examples of Untraditional Statistical Computing

In many cases, finding a maximum likelihood estimator or a Generalized Likelihood Ratio Test estimate becomes an optimization problem. The challenges come when the problem is not formulated as what we usually see, or the size of the problem is too large to be manageable by conventional methods. We present three examples that have this flavor. They are (1) finding the maximum likelihood estimate of a curve embedded in a noisy picture, (2) finding a penalized maximum likelihood estimate for embedded linear features, and (3) computing an M-estimate. We present that they can be solved by applying (a) network flow algorithms from Operation Research, (b) a “best basis” algorithm from Computational Harmonic Analysis, and (c) methods from nonlinear optimization. We present some computational results. The philosophical point that we advocate is that incorporating optimization techniques from fields other than statistics enables us to solve some “hard” problems in statistical estimation.