[1] With growing interest in understanding the magnitudes and sources of uncertainty in hydrological modeling, the difficult problem of characterizing model structure adequacy is now attracting considerable attention. Here, we examine this problem via a model-structureindependent approach based in information theory. In particular, we (a) discuss how to assess and compute the information content in multivariate hydrological data, (b) present practical methods for quantifying the uncertainty and shared information in data while accounting for heteroscedasticity, (c) show how these tools can be used to estimate the best achievable predictive performance of a model (for a system given the available data), and (d) show how model adequacy can be characterized in terms of the magnitude and nature of its aleatory uncertainty that cannot be diminished (and is resolvable only up to specification of its density), and its epistemic uncertainty that can, in principle, be suitably resolved by improving the model. An illustrative modeling example is provided using catchment-scale data from three river basins, the Leaf and Chunky River basins in the United States and the Chuzhou basin in China. Our analysis shows that the aleatory uncertainty associated with making catchment simulations using this data set is significant ($50%). Further, estimated epistemic uncertainties of the HyMod, SAC-SMA, and Xinanjiang model hypotheses indicate that considerable room for model structural improvements remain.

The problem of estimation of density functionals like entropy and mutual information has received much attention in the statistics and information theory communities. A large class of estimators of functionals of the probability density suffer from the curse of dimensionality, wherein the mean squared error (MSE) decays increasingly slowly as a function of the sample size T as the dimension d of the samples increases. In particular, the rate is often glacially slow of order O(T−γ/d), where γ > 0 is a rate parameter. Examples of such estimators include kernel density estimators, k-nearest neighbor (k-NN) density estimators, k-NN entropy estimators, intrinsic dimension estimators and other examples. In this paper, we propose a weighted affine combination of an ensemble of such estimators, where optimal weights can be chosen such that the weighted estimator converges at a much faster dimension invariant rate of O(T−1). Furthermore, we show that these optimal weights can be determined by solving a convex optimization problem which can be performed offline and does not require training data. We illustrate the superior performance of our weighted estimator for two important applications: (i) estimating the Panter-Dite distortion-rate factor and (ii) estimating the Shannon entropy for testing the probability distribution of a random sample.

Although nociceptin/orphanin FQ (N/OFQ) influences dopamine (DA) neuronal activity, it is not known whether N/OFQ acts directly on DA neurons, indirectly by means of local circuitry, or both. We used two parallel approaches, dual in situ hybridization (ISH) and neurotoxic lesions of DA neurons by using 6-hydroxydopamine (6-OHDA), to ascertain whether N/OFQ and the N/OFQ receptor (NOP) mRNA are expressed in DA neurons in the ventral tegmental area (VTA) and substantia nigra compacta (SNc). In the VTA and SNc, small populations (approximately 6-10%) of N/OFQ-containing neurons coexpressed mRNA for tyrosine hydroxylase (TH), the rate-limiting enzyme for DA synthesis. Similarly, very few (1-2%) TH-positive neurons contained N/OFQ mRNA signal. A majority of NOP-positive neurons (approximately 75%) expressed TH mRNA and roughly half of the TH-containing neurons expressed NOP mRNA. Many N/OFQ neurons (approximately 50-60%) expressed glutamic acid decarboxylase 65 and 67 mRNAs, markers for gamma-aminobutyric acid (GABA) neurons. In the 6-OHDA lesion studies, NOP mRNA levels were nearly 80 and 85% lower in the VTA and SNc, respectively, on the lesioned side. These lesions appear to lead to compensatory changes, with N/OFQ mRNA levels approximately 60% and 300% higher in the VTA and SNc, respectively, after 6-OHDA lesions. Finally, N/OFQ-stimulated [(35)S]guanylyl-5'-O-(gamma-thio)-triphosphate levels were decreased in the VTA and SNc but not the prefrontal cortex after 6-OHDA lesions. Accordingly, it appears that N/OFQ mRNA was found largely on nondopaminergic (i.e., GABA) neurons, whereas NOP mRNA was located on DA neurons. N/OFQ is in a position to influence DA neuronal activity by means of the NOP located on DA neurons.

This paper introduces a class of k-nearest neighbor (k-NN) estimators called bipartite plug-in (BPI) estimators for estimating integrals of non-linear functions of a probability density, such as Shannon entropy and Rényi entropy. The density is assumed to be smooth, have bounded support, and be uniformly bounded from below on this set. Unlike previous k-NN estimators of non-linear density functionals, the proposed estimator uses data-splitting and boundary correction to achieve lower mean square error. Specifically, we assume that T i.i.d. samples Xi ∈ R d from the density are split into two pieces of cardinality M and N respectively, with M samples used for computing a k-nearest-neighbor density estimate and the remaining N samples used for empirical estimation of the integral of the density functional.By studying the statistical properties of k-NN balls, explicit rates for the bias and variance of the BPI estimator are derived in terms of the sample size, the dimension of the samples and the underlying probability distribution. Based on these results, it is possible to specify optimal choice of tuning parameters M/T , k for maximizing the rate of decrease of the mean square error (MSE). The resultant optimized BPI estimator converges faster and achieves lower mean squared error than previous k-NN entropy estimators. In addition, a central limit theorem is established for the BPI estimator that allows us to specify tight asymptotic confidence intervals.

We describe the development of an algorithm for the automatic classification of heart sound phonocardiogram waveforms as normal, abnormal or uncertain. Our approach consists of three major components: 1) Heart sound segmentation, 2) Transformation of one-dimensional waveforms into two-dimensional timefrequency heat map representations using Mel-frequency cepstral coefficients and 3) Classification of MFCC heat maps using deep convolutional neural networks. We applied the above approach to produce submissions for the 2016 PhysioNet Computing in Cardiology Challenge. We present results from the challenge, as well as describe in detail the resulting neural network architecture produced and design decisions made. IntroductionThe goal of the 2016 PhysioNet Computing in Cardiology Challenge was to accurately classify normal and abnormal heart sounds from phonocardiogram (PCG) waveforms. A particular aim was to identify from a single short recording whether a subject should be referred on for expert diagnosis. Accurate and robust algorithms were required that could deal with heart sounds that exhibit very poor signal quality.The challenge training set consisted of 3,240 heart sound recordings, lasting from 5 seconds to just over 120 seconds. Recordings were collected from nine different locations on the body (including aortic area, pulmonic area, tricuspid area and mitral area, among others). Recordings from healthy subjects were labeled as normal. Recordings from subjects with a confirmed cardiac diagnosis were labeled as abnormal. Abnormal recordings were collected from patients who suffered from a variety of illnesses, including heart valve defects (mitral valve prolapse, mitral regurgitation, aortic stenosis, valvular surgery) and coronary artery disease. An in depth description of the challenge and the dataset is provided in [1], as well as a thorough review of the field of cardiac auscultation.We present an algorithm that computes heat maps of the time-frequency distribution of signal energy and uses a deep convolutional neural network to automatically classify normal versus abnormal heart sound recordings. Logistic regression hidden semi-Markov model-based heart sound segmentation is first performed on the PCG waveform. Spectrograms (energy maps) consisting of 6 cepstral coefficients that capture Mel-frequencies varying over time are derived for overlapping sliding windows of threesecond duration, beginning at the first heart sound, S 1 . A deep convolutional neural network consisting of two alternating convolution and max pooling layers is trained to perform automatic feature extraction. A final multilayer perceptron, consisting of two fully connected layers, distinguishes between normal and abnormal spectrograms. Heart sound recordings of variable length are dealt with by computing an ensemble of logit scores for all overlapping three-second segments contained within a recording and maximizing the average scores computed for all classes. ApproachOur approach consists of three major components: 1. Segme...