A new Bayesian approach to the reconstruction of spectral functions

We present a novel approach for the reconstruction of spectra from Euclidean correlator data that makes close contact to modern Bayesian concepts. It is based upon an axiomatically justified dimensionless prior distribution, which in the case of constant prior function m(ω) only imprints smoothness on the reconstructed spectrum. In addition we are able to analytically integrate out the only relevant overall hyper-parameter α in the prior, removing the necessity for Gaussian approximations found e.g. in the Maximum Entropy Method. Using a quasi-Newton minimizer and high-precision arithmetic, we are then able to find the unique global extremum of P[ρ|D] in the full Nω » Nτ dimensional search space. The method actually yields gradually improving reconstruction results if the quality of the supplied input data increases, without introducing artificial peak structures, often encountered in the MEM. To support these statements we present mock data analyses for the case of zero width delta peaks and more realistic scenarios, based on the perturbative Euclidean Wilson Loop as well as the Wilson Line correlator in Coulomb gauge.

Benchmarking the Bayesian reconstruction of the non-perturbative heavy ǪǬ potential

The extraction of the finite temperature heavy quark potential from lattice QCD relies on a spectral analysis of the real-time Wilson loop. Through its position and shape, the lowest lying spectral peak encodes the real and imaginary part of this complex potential. We benchmark this extraction strategy using leading order hard-thermal loop (HTL) calculations. I.e. we analytically calculate the Wilson loop and determine the corresponding spectrum. By fitting its lowest lying peak we obtain the real- and imaginary part and confirm that the knowledge of the lowest peak alone is sufficient for obtaining the potential. We deploy a novel Bayesian approach to the reconstruction of spectral functions to HTL correlators in Euclidean time and observe how well the known spectral function and values for the real and imaginary part are reproduced. Finally we apply the method to quenched lattice QCD data and perform an improved estimate of both real and imaginary part of the non-perturbative heavy ǪǬ potential.

Association of optical tracklets from a geosynchronous belt survey via the direct Bayesian admissible region approach

The direct Bayesian admissible region approach is an a priori state free measurement association and initial orbit determination technique for optical tracks. In this paper, we test a hybrid approach that appends a least squares estimator to the direct Bayesian method on measurements taken at the Zimmerwald Observatory of the Astronomical Institute at the University of Bern. Over half of the association pairs agreed with conventional geometric track correlation and least squares techniques. The remaining pairs cast light on the fundamental limits of conducting tracklet association based solely on dynamical and geometrical information.

Introduction to Bayesian Data Analysis

A workshop providing an introduction to Bayesian data analysis and hypothesis testing using R, Jags and the BayesFactor package.

Application of Local Rank Tests for Nonparametric Regression

Let Y_i = f(x_i) + E_i\ (1\le i\le n) with given covariates x_1\lt x_2\lt \cdots\lt x_n , an unknown regression function f and independent random errors E_i with median zero. It is shown how to apply several linear rank test statistics simultaneously in order to test monotonicity of f in various regions and to identify its local extrema.

Nonparametric location estimators in the randomized complete block design

Several tests for the comparison of different groups in the randomized complete block design exist. However, there is a lack of robust estimators for the location difference between one group and all the others on the original scale. The relative marginal effects are commonly used in this situation, but they are more difficult to interpret and use by less experienced people because of the different scale. In this paper two nonparametric estimators for the comparison of one group against the others in the randomized complete block design will be presented. Theoretical results such as asymptotic normality, consistency, translation invariance, scale preservation, unbiasedness, and median unbiasedness are derived. The finite sample behavior of these estimators is derived by simulations of different scenarios. In addition, possible confidence intervals with these estimators are discussed and their behavior derived also by simulations.

Some Identification Issues in Nonparametric Linear Models with Endogenous Regressors

In applied work economists often seek to relate a given response variable y to some causal parameter mu* associated with it. This parameter usually represents a summarization based on some explanatory variables of the distribution of y, such as a regression function, and treating it as a conditional expectation is central to its identification and estimation. However, the interpretation of mu* as a conditional expectation breaks down if some or all of the explanatory variables are endogenous. This is not a problem when mu* is modelled as a parametric function of explanatory variables because it is well known how instrumental variables techniques can be used to identify and estimate mu*. In contrast, handling endogenous regressors in nonparametric models, where mu* is regarded as fully unknown, presents di±cult theoretical and practical challenges. In this paper we consider an endogenous nonparametric model based on a conditional moment restriction. We investigate identification related properties of this model when the unknown function mu* belongs to a linear space. We also investigate underidentification of mu* along with the identification of its linear functionals. Several examples are provided in order to develop intuition about identification and estimation for endogenous nonparametric regression and related models.

Direct and Indirect Measures of Capacity Utilization: A Nonparametric Analysis of U.S. Manufacturing

We measure the capacity output of a firm as the maximum amount producible by a firm given a specific quantity of the quasi-fixed input and an overall expenditure constraint for its choice of variable inputs. We compute this indirect capacity utilization measure for the total manufacturing sector in the US as well as for a number of disaggregated industries, for the period 1970-2001. We find considerable variation in capacity utilization rates both across industries and over years within industries. Our results suggest that the expenditure constraint was binding, especially in periods of high interest rates.

Bayesian models for the analysis of genetic structure when populations are correlated

Motivation: Population allele frequencies are correlated when populations have a shared history or when they exchange genes. Unfortunately, most models for allele frequency and inference about population structure ignore this correlation. Recent analytical results show that among populations, correlations can be very high, which could affect estimates of population genetic structure. In this study, we propose a mixture beta model to characterize the allele frequency distribution among populations. This formulation incorporates the correlation among populations as well as extending the model to data with different clusters of populations. Results: Using simulated data, we show that in general, the mixture model provides a good approximation of the among-population allele frequency distribution and a good estimate of correlation among populations. Results from fitting the mixture model to a dataset of genotypes at 377 autosomal microsatellite loci from human populations indicate high correlation among populations, which may not be appropriate to neglect. Traditional measures of population structure tend to over-estimate the amount of genetic differentiation when correlation is neglected. Inference is performed in a Bayesian framework.

Efficiency Bounds for Estimating Linear Functionals of Nonparametric Regression Models with Endogenous Regressors

Consider a nonparametric regression model Y=mu*(X) + e, where the explanatory variables X are endogenous and e satisfies the conditional moment restriction E[e|W]=0 w.p.1 for instrumental variables W. It is well known that in these models the structural parameter mu* is 'ill-posed' in the sense that the function mapping the data to mu* is not continuous. In this paper, we derive the efficiency bounds for estimating linear functionals E[p(X)mu*(X)] and int_{supp(X)}p(x)mu*(x)dx, where p is a known weight function and supp(X) the support of X, without assuming mu* to be well-posed or even identified.

Liberalization, Ownership, and Efficiency in Indian Banking: A Nonparametric Approach

This paper empirically estimates and analyzes various efficiency scores of Indian banks during 1997-2003 using data envelopment analysis (DEA). During the 1990s India's financial sector underwent a process of gradual liberalization aimed at strengthening and improving the operational efficiency of the financial system. It is observed, none the less, that Indian banks are still not much differentiated in terms of input or output oriented technical efficiency and cost efficiency. However, they differ sharply in respect of revenue and profit efficiencies. The results provide interesting insight into the empirical correlates of efficiency scores of Indian banks. Bank size, ownership, and the fact of its being listed on the stock exchange are some of the factors that are found to have positive impact on the average profit efficiency and to some extent revenue efficiency scores are. Finally, we observe that the median efficiency scores of Indian banks in general and of bigger banks in particular have improved considerably during the post-reform period.

Are Indian Firms too Small? A Nonparametric Analysis of Cost Efficiency and Industry Structure of Indian Manufacturing

In this paper we use the 2004-05 Annual Survey of Industries data to estimate the levels of cost efficiency of Indian manufacturing firms in the various states and also get state level measures of industrial organization (IO) efficiency. The empirical results show the presence of considerable cost inefficiency in a majority of the states. Further, we also find that, on average, Indian firms are too small. Consolidating them to attain the optimal scale would further enhance efficiency and lower average cost.

Technical Efficiency in the Indian Textiles Industry: A Nonparametric Analysis of Firm-Level Data

The Indian textiles industry is now at the crossroads with the phasing out of quota regime that prevailed under the Multi-Fiber Agreement (MFA) until the end of 2004. In the face of a full integration of the textiles sector in the WTO, maintaining and enhancing productive efficiency is a precondition for competitiveness of the Indian firms in the new liberalized world market. In this paper we use data obtained from the Annual Survey of Industries for a number of years to measure the levels of technical efficiency in the Indian textiles industry at the firm level. We use both a grand frontier applicable to all firms and a group frontier specific to firms from any individual state, ownership, or organization type in order to evaluate their efficiencies. This permits us to separately identify how locational, proprietary, and organizational characteristics of a firm affect its performance.