Implicit Copulas from Bayesian Regularized Regression Smoothers

We show how to extract the implicit copula of a response vector from a Bayesian regularized regression smoother with Gaussian disturbances. The copula can be used to compare smoothers that employ different shrinkage priors and function bases. We illustrate with three popular choices of shrinkage priors --- a pairwise prior, the horseshoe prior and a g prior augmented with a point mass as employed for Bayesian variable selection --- and both univariate and multivariate function bases. The implicit copulas are high-dimensional, have flexible dependence structures that are far from that of a Gaussian copula, and are unavailable in closed form. However, we show how they can be evaluated by first constructing a Gaussian copula conditional on the regularization parameters, and then integrating over these. Combined with non-parametric margins the regularized smoothers can be used to model the distribution of non-Gaussian univariate responses conditional on the covariates. Efficient Markov chain Monte Carlo schemes for evaluating the copula are given for this case. Using both simulated and real data, we show how such copula smoothing models can improve the quality of resulting function estimates and predictive distributions

Variational Bayes Estimation of Discrete-Margined Copula Models with Application to Time Series

We propose a new variational Bayes estimator for high-dimensional copulas with discrete, or a combination of discrete and continuous, margins. The method is based on a variational approximation to a tractable augmented posterior, and is faster than previous likelihood-based approaches. We use it to estimate drawable vine copulas for univariate and multivariate Markov ordinal and mixed time series. These have dimension $rT$, where $T$ is the number of observations and $r$ is the number of series, and are difficult to estimate using previous methods. The vine pair-copulas are carefully selected to allow for heteroskedasticity, which is a feature of most ordinal time series data. When combined with flexible margins, the resulting time series models also allow for other common features of ordinal data, such as zero inflation, multiple modes and under- or over-dispersion. Using six example series, we illustrate both the flexibility of the time series copula models, and the efficacy of the variational Bayes estimator for copulas of up to 792 dimensions and 60 parameters. This far exceeds the size and complexity of copula models for discrete data that can be estimated using previous methods

Clearing Alaskan water supply impoundments: management, laboratory study, and literature review

The literature review prepared in conjunction with this study is contained in IWR-67-A, published separately as "Clearing Alaskan Water Supply Impoundments: Literature Review" by the Institute of Water Resources, University of Alaska, Fairbanks, Alaska. The data developed in the laboratory portion of the study are contained in IWR-67-B. Contact the Institute of Water Resources for access to this material. IWR-67-A and IWR-67-B are available on microfiche.Water supply impoundments in northern regions have seen only limited application. Reasons for the lack of use of such impoundments include the following: 1) little demand for water due to the low population densities and rustic life styles; 2) a lack of conventional distribution systems in many communities; 3) poorly developed technology for construction of dams on permafrost; 4) adequacy of existing river, lake, ice, and lagoon water supplies; 5) shortage of capital to finance the high cost of construction in remote regions.The work upon which this report is based was supported by funds provided by the United States Department of the Interior, Office of Water Research and Technology, as authorized by the Water Resources Research Act of 1964, Public Law 88-379, as amended (Project A-043-ALAS)

Partition and composition matrices

This paper introduces two matrix analogues for set partitions. A composition matrix on a finite set X is an upper triangular matrix whose entries partition X, and for which there are no rows or columns containing only empty sets. A partition matrix is a composition matrix in which an order is placed on where entries may appear relative to one-another. We show that partition matrices are in one-to-one correspondence with inversion tables. Non-decreasing inversion tables are shown to correspond to partition matrices with a row ordering relation. Partition matrices which are s-diagonal are classified in terms of inversion tables. Bidiagonal partition matrices are enumerated using the transfer-matrix method and are equinumerous with permutations which are sortable by two pop-stacks in parallel. We show that composition matrices on X are in one-to-one correspondence with (2+2)-free posets on X. Also, composition matrices whose rows satisfy a column-ordering relation are shown to be in one-to-one correspondence with parking functions. Finally, we show that pairs of ascent sequences and permutations are in one-to-one correspondence with (2+2)-free posets whose elements are the cycles of a permutation, and use this relation to give an expression for the number of (2+2)-free posets on {1,...,n}.Comment: 14 page

The Effect of the Tax Reform Act of 1986 and Regional Economies on Apartment Values

The theoretical effects of the Tax Reform Act of 1986 on commercial real estate have been widely written about; however, little empirical work has been done that actually measures the hypothesized effects. We find that, after controlling for general national economic conditions and regional effects, the effect of the Tax Act of 1986 was negatively related to apartment values. The magnitude of the effect was a function of the local vacancy rates and economic growth where those regions with slow economic growth and high vacancy rates were strongly affected.

Real Business Cycle Realizations

Much recent business cycle research focuses on moments of macroeconomic aggregates. We construct examples of real business cycle sample paths for output, consumption, and employment for the U.S. economy. Annual sample paths are generated from an initial condition in 1925, measured technology and government spending shocks since then, and a standard, calibrated, one-sector model of the business cycle. Quarterly sample paths are generated similarly, from an initial condition in 1955. The law of motion for shocks is not parametrized and so decision-rules are estimated by GMM. We compare the paths with actual history graphically and by spectral methods.real business cycles, Solow residuals, US business cycle history

Testing the Validity and Reliability of Electromyography Acquisition Capabilities of a Wearable EMG Device, Sense3, by Strive

There is a growing demand in the sports world for wearable technology, particularly those with electromyography acquisition capabilities. Electromyography (EMG) is technique for measuring the electrical activity that occurs during muscle contraction and relaxation. Basic practical applications of EMG use in sports include, but are not limited to: measuring activation timing of a muscle, measuring levels of activation, and detecting fatigue. The sports performance company Strive has designed an EMG wearable, called Sense3, that targets the following muscles of the lower limb: Quadriceps, Hamstrings, and Glutes. Sense3 must pass reliability assays to determine the validity of the EMG system in order for Sense3 to be accessible as a commercialized product. This study was designed to compare the EMG acquisition performance of Sense3 to the performance of a traditional EMG acquisition device, MA-300, during slow and controlled movements, simulated by use of a dynamometer, and during dynamic movements. Statistics from the reliability assays showed Sense3 to be reliable in the Rectus Femoris and Biceps Femoris during dynamometer trials. Sense3 was unable to consistently record useable EMG signals for analysis during dynamic exercise trials. The ability to record EMG signals during dynamic movement was the main determinant for validity of Sense3’s EMG acquisition system. The results suggest that Sense3 is not a valid EMG acquisition system for sports-based, dynamic use