Constrained Maximum Likelihood (CML) is a new software module developed at Aptech Systems for the generation of maximum likelihood estimates of statistical models with general constraints on parameters. These constraints can be linear or nonlinear, equality or inequality. The software uses the Sequential Quadratic Programming method with various descent algorithms to iterate from a given starti...

Maximum likelihood estimation in statistics leads to the problem of maximizing a product of powers of polynomials. We study the algebraic degree of the critical equations of this optimization problem. This degree is related to the number of bounded regions in the corresponding arrangement of hypersurfaces, and to the Euler characteristic of the complexified complement. Under suitable hypotheses...

Two new approaches to multivariate calibration are described that, for the first time, allow information on measurement uncertainties to be included in the calibration process in a statistically meaningful way. The new methods, referred to as maximum likelihood principal components regression (MLPCR) and maximum likelihood latent root regression (MLLRR), are based on principles of maximum likel...

This paper surveys the theoretical and computational development of the restricted maximum likelihood (REML) approach for the estimation of covariance matrices in linear stochastic models. A new derivation of this approach is given, valid under very weak conditions on the noise. Then the calculation of the gradient of restricted loglikelihood functions is discussed , with special emphasis on th...

A likelihood-based approach to density modification is developed that can be applied to a wide variety of cases where some information about the electron density at various points in the unit cell is available. The key to the approach consists of developing likelihood functions that represent the probability that a particular value of electron density is consistent with prior expectations for t...

Whole genome shotgun assembly is the process of taking many short sequenced segments (reads) and reconstructing the genome from which they originated. We demonstrate how the technique of bidirected network flow can be used to explicitly model the double-stranded nature of DNA for genome assembly. By combining an algorithm for the Chinese Postman Problem on bidirected graphs with the constructio...

We analyze a maximum likelihood approach for combining phylogenetic trees into a larger "supertree." This is based on a simple exponential model of phylogenetic error, which ensures that ML supertrees have a simple combinatorial description (as a median tree, minimizing a weighted sum of distances to the input trees). We show that this approach to ML supertree reconstruction is statistically co...

where p above is the density function if X is continuous and the mass function if X is discrete. The MLE is denoted θ̂ or θ̂n if we wish to emphasize the sample size. Above, we suppress the dependency of L on X1, . . . , X (n) to emphasize that we are treating the likelihood as a function of θ. Note that both X and θ may be scalars or vectors (not necessarily of the same dimension) and that L may...

Many visual matching algorithms can be described in terms of the features and the inter-feature distance or metric. The most commonly used metric is the sum of squared differences (SSD), which is valid from a maximum likelihood perspective when the real noise distribution is Gaussian. However, we have found experimentally that the Gaussian noise distribution assumption is often invalid. This im...

This paper addresses the problem of autocalibration, which is a critical step in existing uncalibrated structure from motion algorithms that utilize an initialization to avoid the local minima in metric bundle adjustment. Currently, all known direct (not non-linear) solutions to the uncalibrated structure from motion problem solve for a projective reconstruction that is related to metric by som...