Understanding predictive uncertainty in hydrologic modeling: The challenge of identifying input and structural errors

Meaningful quantification of data and structural uncertainties in conceptual rainfall-runoff modeling is a major scientific and engineering challenge. This paper focuses on the total predictive uncertainty and its decomposition into input and structural components under different inference scenarios. Several Bayesian inference schemes are investigated, differing in the treatment of rainfall and structural uncertainties, and in the precision of the priors describing rainfall uncertainty. Compared with traditional lumped additive error approaches, the quantification of the total predictive uncertainty in the runoff is improved when rainfall and/or structural errors are characterized explicitly. However, the decomposition of the total uncertainty into individual sources is more challenging. In particular, poor identifiability may arise when the inference scheme represents rainfall and structural errors using separate probabilistic models. The inference becomes ill‐posed unless sufficiently precise prior knowledge of data uncertainty is supplied; this ill‐posedness can often be detected from the behavior of the Monte Carlo sampling algorithm. Moreover, the priors on the data quality must also be sufficiently accurate if the inference is to be reliable and support meaningful uncertainty decomposition. Our findings highlight the inherent limitations of inferring inaccurate hydrologic models using rainfall‐runoff data with large unknown errors. Bayesian total error analysis can overcome these problems using independent prior information. The need for deriving independent descriptions of the uncertainties in the input and output data is clearly demonstrated.Benjamin Renard, Dmitri Kavetski, George Kuczera, Mark Thyer, and Stewart W. Frank

Inferring Latent States and Refining Force Estimates via Hierarchical Dirichlet Process Modeling in Single Particle Tracking Experiments

Optical microscopy provides rich spatio-temporal information characterizing in vivo molecular motion. However, effective forces and other parameters used to summarize molecular motion change over time in live cells due to latent state changes, e.g., changes induced by dynamic micro-environments, photobleaching, and other heterogeneity inherent in biological processes. This study focuses on techniques for analyzing Single Particle Tracking (SPT) data experiencing abrupt state changes. We demonstrate the approach on GFP tagged chromatids experiencing metaphase in yeast cells and probe the effective forces resulting from dynamic interactions that reflect the sum of a number of physical phenomena. State changes are induced by factors such as microtubule dynamics exerting force through the centromere, thermal polymer fluctuations, etc. Simulations are used to demonstrate the relevance of the approach in more general SPT data analyses. Refined force estimates are obtained by adopting and modifying a nonparametric Bayesian modeling technique, the Hierarchical Dirichlet Process Switching Linear Dynamical System (HDP-SLDS), for SPT applications. The HDP-SLDS method shows promise in systematically identifying dynamical regime changes induced by unobserved state changes when the number of underlying states is unknown in advance (a common problem in SPT applications). We expand on the relevance of the HDP-SLDS approach, review the relevant background of Hierarchical Dirichlet Processes, show how to map discrete time HDP-SLDS models to classic SPT models, and discuss limitations of the approach. In addition, we demonstrate new computational techniques for tuning hyperparameters and for checking the statistical consistency of model assumptions directly against individual experimental trajectories; the techniques circumvent the need for "ground-truth" and subjective information.Comment: 25 pages, 6 figures. Differs only typographically from PLoS One publication available freely as an open-access article at http://journals.plos.org/plosone/article?id=10.1371/journal.pone.013763

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

Estimating the p-mode frequencies of the solar twin 18 Sco

Solar twins have been a focus of attention for more than a decade, because their structure is extremely close to that of the Sun. Today, thanks to high-precision spectrometers, it is possible to use asteroseismology to probe their interiors. Our goal is to use time series obtained from the HARPS spectrometer to extract the oscillation frequencies of 18 Sco, the brightest solar twin. We used the tools of spectral analysis to estimate these quantities. We estimate 52 frequencies using an MCMC algorithm. After examination of their probability densities and comparison with results from direct MAP optimization, we obtain a minimal set of 21 reliable modes. The identification of each pulsation mode is straightforwardly accomplished by comparing to the well-established solar pulsation modes. We also derived some basic seismic indicators using these values. These results offer a good basis to start a detailed seismic analysis of 18 Sco using stellar models.Comment: 12 pages, 6 figures, to be published in A&