Implications of uniformly distributed, empirically informed priors for phylogeographical model selection: A reply to Hickerson et al

Establishing that a set of population-splitting events occurred at the same time can be a potentially persuasive argument that a common process affected the populations. Oaks et al. (2013) assessed the ability of an approximate-Bayesian method (msBayes) to estimate such a pattern of simultaneous divergence across taxa, to which Hickerson et al. (2014) responded. Both papers agree the method is sensitive to prior assumptions and often erroneously supports shared divergences; the papers differ about the explanation and solution. Oaks et al. (2013) suggested the method's behavior is caused by the strong weight of uniform priors on divergence times leading to smaller marginal likelihoods of models with more divergence-time parameters (Hypothesis 1); they proposed alternative priors to avoid strongly weighted posteriors. Hickerson et al. (2014) suggested numerical approximation error causes msBayes analyses to be biased toward models of clustered divergences (Hypothesis 2); they proposed using narrow, empirical uniform priors. Here, we demonstrate that the approach of Hickerson et al. (2014) does not mitigate the method's tendency to erroneously support models of clustered divergences, and often excludes the true parameter values. Our results also show that the tendency of msBayes analyses to support models of shared divergences is primarily due to Hypothesis 1. This series of papers demonstrate that if our prior assumptions place too much weight in unlikely regions of parameter space such that the exact posterior supports the wrong model of evolutionary history, no amount of computation can rescue our inference. Fortunately, more flexible distributions that accommodate prior uncertainty about parameters without placing excessive weight in vast regions of parameter space with low likelihood increase the method's robustness and power to detect temporal variation in divergences.Comment: 24 pages, 4 figures, 1 table, 14 pages of supporting information with 10 supporting figure

A Bayesian Solution to the Conflict of Narrowness and Precision in Direct Inference

The conflict of narrowness and precision in direct inference occurs if a body of evidence contains estimates for frequencies in a certain reference class and less precise estimates for frequencies in a narrower reference class. To develop a solution to this conflict, I draw on ideas developed by Paul Thorn and John Pollock. First, I argue that Kyburg and Teng’s solution to the conflict of narrowness and precision leads to unreasonable direct inference probabilities. I then show that Thorn’s recent solution to the conflict leads to unreasonable direct inference probabilities. Based on my analysis of Thorn’s approach, I propose a natural distribution for a Bayesian analysis of the data directly obtained from studying members of the narrowest reference class

Passive mode-locking in semiconductor lasers with saturable absorbers bandgap shifted through quantum well intermixing

Passive mode-locking in semiconductor lasers in a Fabry–Perot configuration with a bandgap blueshift applied to the saturable absorber (SA) section has been experimentally characterized. For the first time a fully post-growth technique, quantum well intermixing, was adopted to modify the material bandgap in the SA section. The measurements showed not only an expected narrowing of the pulse width but also a significant expansion of the range of bias conditions generating a stable train of optical pulses. Moreover, the pulses from lasers with bandgap shifted absorbers presented reduced chirp and increased peak power with respect to the nonshifted case

Guaranteed state estimation using a bundle of interval observers with adaptive gains applied to the induction machine

he scope of this paper is the design of an interval observer bundle for the guaranteed state estimation of an uncertain induction machine with linear, time-varying dynamics. These guarantees are of particular interest in the case of safety-critical systems. In many cases, interval observers provide large intervals for which the usability becomes impractical. Hence, based on a reduced-order hybrid interval observer structure, the guaranteed enclosure within intervals of the magnetizing current’s estimates is improved using a bundle of interval observers. One advantage of such an interval observer bundle is the possibility to reinitialize the interval observers at specified timesteps during runtime with smaller initial intervals, based on previously observed system states, resulting in decreasing interval widths. Thus, unstable observer dynamics are considered so as to take advantage of their transient behavior, whereby the overall stability of the interval estimation is maintained. An algorithm is presented to determine the parametrization of reduced-order interval observers. To this, an adaptive observer gain is introduced with which the system states are observed optimally by considering a minimal interval width at variable operating points. Furthermore, real-time capability and validation of the proposed methods are shown. The results are discussed with simulations as well as experimental data obtained with a test bench

Narrowest Significance Pursuit: inference for multiple change-points in linear models

We propose Narrowest Significance Pursuit (NSP), a general and flexible methodology for automatically detecting localised regions in data sequences which each must contain a change-point, at a prescribed global significance level. Here, change-points are understood as abrupt changes in the parameters of an underlying linear model. NSP works by fitting the postulated linear model over many regions of the data, using a certain multiresolution sup-norm loss, and identifying the shortest interval on which the linearity is significantly violated. The procedure then continues recursively to the left and to the right until no further intervals of significance can be found. The use of the multiresolution sup-norm loss is a key feature of NSP, as it enables the transfer of significance considerations to the domain of the unobserved true residuals, a substantial simplification. It also guarantees important stochastic bounds which directly yield exact desired coverage probabilities, regardless of the form or number of the regressors. NSP works with a wide range of distributional assumptions on the errors, including Gaussian with known or unknown variance, some light-tailed distributions, and some heavy-tailed, possibly heterogeneous distributions via self-normalisation. It also works in the presence of autoregression. The mathematics of NSP is, by construction, uncomplicated, and its key computational component uses simple linear programming. In contrast to the widely studied "post-selection inference" approach, NSP enables the opposite viewpoint and paves the way for the concept of "post-inference selection". Pre-CRAN R code implementing NSP is available at https://github.com/pfryz/nsp

Robust Control of Quantum Information

Errors in the control of quantum systems may be classified as unitary, decoherent and incoherent. Unitary errors are systematic, and result in a density matrix that differs from the desired one by a unitary operation. Decoherent errors correspond to general completely positive superoperators, and can only be corrected using methods such as quantum error correction. Incoherent errors can also be described, on average, by completely positive superoperators, but can nevertheless be corrected by the application of a locally unitary operation that ``refocuses'' them. They are due to reproducible spatial or temporal variations in the system's Hamiltonian, so that information on the variations is encoded in the system's spatiotemporal state and can be used to correct them. In this paper liquid-state nuclear magnetic resonance (NMR) is used to demonstrate that such refocusing effects can be built directly into the control fields, where the incoherence arises from spatial inhomogeneities in the quantizing static magnetic field as well as the radio-frequency control fields themselves. Using perturbation theory, it is further shown that the eigenvalue spectrum of the completely positive superoperator exhibits a characteristic spread that contains information on the Hamiltonians' underlying distribution.Comment: 14 pages, 6 figure

Does the Housing Market React to New Information on School Quality?

This paper analyzes housing market reactions to the release of previously unpublished information on school quality. Using the sharp discontinuity in the information environment allows us to study price changes within school catchment areas, thus controlling for neighborhood unobservables. We find a substantial housing market reaction to publication of school quality indicators, suggesting that households care about school quality, and may be willing to pay for better schools. The publication effect is robust to a number of sensitivity checks, but does not seem to be permanent as prices revert to prepublication levels after two to three months. We discuss this reversion in relation to the literature on behavioral finance and the concept of limited attention.valuation of school quality, hedonic methods, price reversion