Joint Maximum Likelihood of Phylogeny and Ancestral States Is Not Consistent.

Maximum likelihood estimation in phylogenetics requires a means of handling unknown ancestral states. Classical maximum likelihood averages over these unknown intermediate states, leading to provably consistent estimation of the topology and continuous model parameters. Recently, a computationally efficient approach has been proposed to jointly maximize over these unknown states and phylogenetic parameters. Although this method of joint maximum likelihood estimation can obtain estimates more quickly, its properties as an estimator are not yet clear. In this article, we show that this method of jointly estimating phylogenetic parameters along with ancestral states is not consistent in general. We find a sizeable region of parameter space that generates data on a four-taxon tree for which this joint method estimates the internal branch length to be exactly zero, even in the limit of infinite-length sequences. More generally, we show that this joint method only estimates branch lengths correctly on a set of measure zero. We show empirically that branch length estimates are systematically biased downward, even for short branches.

Binary Complementary Filters for Compressive Raman Spectroscopy.

The previously described optimized binary compressive detection (OB-CD) strategy enables fast hyperspectral Raman (and fluorescence) spectroscopic analysis of systems containing two or more chemical components. However, each OB-CD filter collects only a fraction of the scattered photons and the remainder of the photons are lost. Here, we present a refinement of OB-CD, the OB-CD2 strategy, in which all of the collected Raman photons are detected using a pair of complementary binary optical filters that direct photons of different colors to two photon counting detectors. The OB-CD2 filters are generated using a new optimization algorithm described in this work and implemented using a holographic volume diffraction grating and a digital micromirror device (DMD) whose mirrors are programed to selectively direct photons of different colors either to one or the other photon-counting detector. When applied to pairs of pure liquids or two-component solid powder mixtures, the resulting OB-CD2 strategy is shown to more accurately estimate Raman scattering rates of each chemical component, when compared to the original OB-CD, thus facilitating chemical classification at speeds as fast as 3 µs per measurement and the collection of Raman images in under a second.