Determining Structurally Identifiable Parameter Combinations Using Subset Profiling

Identifiability is a necessary condition for successful parameter estimation of dynamic system models. A major component of identifiability analysis is determining the identifiable parameter combinations, the functional forms for the dependencies between unidentifiable parameters. Identifiable combinations can help in model reparameterization and also in determining which parameters may be experimentally measured to recover model identifiability. Several numerical approaches to determining identifiability of differential equation models have been developed, however the question of determining identifiable combinations remains incompletely addressed. In this paper, we present a new approach which uses parameter subset selection methods based on the Fisher Information Matrix, together with the profile likelihood, to effectively estimate identifiable combinations. We demonstrate this approach on several example models in pharmacokinetics, cellular biology, and physiology

Trans-dimensional inversion of modal dispersion data on the New England Mud Patch

© The Author(s), 2020. This article is distributed under the terms of the Creative Commons Attribution License. The definitive version was published in Bonnel, J., Dosso, S. E., Eleftherakis, D., & Chapman, N. R. Trans-dimensional inversion of modal dispersion data on the New England Mud Patch. IEEE Journal of Oceanic Engineering, 45(1), (2020): 116-130, doi:10.1109/JOE.2019.2896389.This paper presents single receiver geoacoustic inversion of two independent data sets recorded during the 2017 seabed characterization experiment on the New England Mud Patch. In the experimental area, the water depth is around 70 m, and the seabed is characterized by an upper layer of fine grained sediments with clay (i.e., mud). The first data set considered in this paper is a combustive sound source signal, and the second is a chirp emitted by a J15 source. These two data sets provide differing information on the geoacoustic properties of the seabed, as a result of their differing frequency content, and the dispersion properties of the environment. For both data sets, source/receiver range is about 7 km, and modal time-frequency dispersion curves are estimated using warping. Estimated dispersion curves are then used as input data for a Bayesian trans-dimensional inversion algorithm. Subbottom layering and geoacoustic parameters (sound speed and density) are thus inferred from the data. This paper highlights important properties of the mud, consistent with independent in situ measurements. It also demonstrates how information content differs for two data sets collected on reciprocal tracks, but with different acoustic sources and modal content.10.13039/100000006-Office of Naval Research 10.13039/100007297-Office of Naval Research Globa

Bayesian inference for pulsar timing models

The extremely regular, periodic radio emission from millisecond pulsars makes them useful tools for studying neutron star astrophysics, general relativity, and low-frequency gravitational waves. These studies require that the observed pulse times of arrival be fit to complex timing models that describe numerous effects such as the astrometry of the source, the evolution of the pulsar's spin, the presence of a binary companion, and the propagation of the pulses through the interstellar medium. In this paper, we discuss the benefits of using Bayesian inference to obtain pulsar timing solutions. These benefits include the validation of linearized least-squares model fits when they are correct, and the proper characterization of parameter uncertainties when they are not; the incorporation of prior parameter information and of models of correlated noise; and the Bayesian comparison of alternative timing models. We describe our computational setup, which combines the timing models of Tempo2 with the nested-sampling integrator MultiNest. We compare the timing solutions generated using Bayesian inference and linearized least-squares for three pulsars: B1953+29, J2317+1439, and J1640+2224, which demonstrate a variety of the benefits that we posit.Comment: 13 pages, 4 figures, RevTeX 4.1. Revised in response to referee's suggestions; contains a broader discussion of model comparison, revised Monte Carlo runs, improved figure

Simultaneous inference for misaligned multivariate functional data

We consider inference for misaligned multivariate functional data that represents the same underlying curve, but where the functional samples have systematic differences in shape. In this paper we introduce a new class of generally applicable models where warping effects are modeled through nonlinear transformation of latent Gaussian variables and systematic shape differences are modeled by Gaussian processes. To model cross-covariance between sample coordinates we introduce a class of low-dimensional cross-covariance structures suitable for modeling multivariate functional data. We present a method for doing maximum-likelihood estimation in the models and apply the method to three data sets. The first data set is from a motion tracking system where the spatial positions of a large number of body-markers are tracked in three-dimensions over time. The second data set consists of height and weight measurements for Danish boys. The third data set consists of three-dimensional spatial hand paths from a controlled obstacle-avoidance experiment. We use the developed method to estimate the cross-covariance structure, and use a classification setup to demonstrate that the method outperforms state-of-the-art methods for handling misaligned curve data.Comment: 44 pages in total including tables and figures. Additional 9 pages of supplementary material and reference