Auxiliary Distribution Research Articles

Experimental Data Modeling: Issues in Empirical Identification of Distribution

Identification of distribution underlying experimental data sets, lacking established mechanistic models, calls for an inferential process involving necessarily uncertainty of some sort. While components pertaining to parameter estimation are routinely tak en into account, those related to selection of distribution form often are not; their awkward theoretical evaluation may explain why the issue tends to be conveniently ignored. Such an attitude may however lead to severe underestimation of overall uncertainty, s ince the component accounting for identification of distribution form often exceeds those concerning estimates of parameters. A pragmatic approach is presented, relying upon numerical simulation, allowing realistic evaluation of uncertainty inherent in empirical identification of form in a straightforward way. Application to an actual case is presented, and issues concerning identification procedure for parameters of auxiliary empirical distributions are discussed.

Another generalization of the bivariate FGM distribution with two-dimensional extensions

The Farlie–Gumbel–Morgenstern family of bivariate distributions with given marginals is frequently used in theory and applications and has been generalized in many ways. With the help of two auxiliary distributions, we propose another generalization and study its properties. After defining the dimension of a distribution as the cardinal of the set of canonical correlations, we prove that some well-known distributions are practically two-dimensional. Then we introduce an extended FGM family in two dimensions and study how to approximate any distribution to this family.

Investigation on the performance of the single-phase LSPM motor for variable capacity type compressor

This paper investigates the performance of the line start permanent magnet (LSPM) motor which needs a high efficiency characteristic in a wide operation region. LSPM motor's performance indexes, such as efficiency, motor current, load angle and synchronous torque, have complex relationship with each other according to the main and auxiliary windings distribution, and the selection of running capacitor. The output characteristics can be defined by the winding structure which is calculated by d-q equivalent circuit and finite element method. The efficiency characteristic is verified by simulation as well as by experiment on the designed LSPM motor. From the results, we show that the redesigned model considering the winding structure and capacitor matching has a wide operating region.

Extreme quantile estimation with nonparametric adaptive importance sampling

In this article, we propose a nonparametric adaptive importance sampling (NAIS) algorithm to estimate rare event quantile. Indeed, Importance Sampling (IS) is a well-known adapted random simulation technique. It consists in generating random weighted samples from an auxiliary distribution rather than the distribution of interest. The optimization of this auxiliary distribution is often very difficult in practice. First, we review how to define the optimal auxiliary density of IS for quantile estimation in the general case and then propose a nonparametric method based on Gaussian kernel density estimator to approach the optimal auxiliary density that does not assume an initial PDF guess. This method is then finally applied to theoretical cases to demonstrate the efficiency of the proposed NAIS algorithm and on the quantile estimation of the temperature of a forest fire detection simulator.

Efficient Simulation and Likelihood Methods for Non-Neutral Multi-Allele Models

Throughout the 1980s, Simon Tavaré made numerous significant contributions to population genetics theory. As genetic data, in particular DNA sequence, became more readily available, a need to connect population-genetic models to data became the central issue. The seminal work of Griffiths and Tavaré (1994a , 1994b , 1994c) was among the first to develop a likelihood method to estimate the population-genetic parameters using full DNA sequences. Now, we are in the genomics era where methods need to scale-up to handle massive data sets, and Tavaré has led the way to new approaches. However, performing statistical inference under non-neutral models has proved elusive. In tribute to Simon Tavaré, we present an article in spirit of his work that provides a computationally tractable method for simulating and analyzing data under a class of non-neutral population-genetic models. Computational methods for approximating likelihood functions and generating samples under a class of allele-frequency based non-neutral parent-independent mutation models were proposed by Donnelly, Nordborg, and Joyce (DNJ) (Donnelly et al., 2001). DNJ (2001) simulated samples of allele frequencies from non-neutral models using neutral models as auxiliary distribution in a rejection algorithm. However, patterns of allele frequencies produced by neutral models are dissimilar to patterns of allele frequencies produced by non-neutral models, making the rejection method inefficient. For example, in some cases the methods in DNJ (2001) require 10(9) rejections before a sample from the non-neutral model is accepted. Our method simulates samples directly from the distribution of non-neutral models, making simulation methods a practical tool to study the behavior of the likelihood and to perform inference on the strength of selection.

Global sensitivity analysis for stochastic ground motion modeling in seismic-risk assessment

Seismic risk assessment requires adoption of appropriate models for the earthquake hazard, the structural system and for its performance, and quantification of the uncertainties involved in these models through appropriate probability distributions. Characterization of the seismic hazard comprises undoubtedly the most critical component of this process, the one associated with the largest amount of uncertainty. For applications involving dynamic analysis this hazard is frequently characterized through stochastic ground motion models. This paper discusses a novel, global sensitivity analysis for the seismic risk with emphasis on such a stochastic ground motion modeling. This analysis aims to identify the overall (i.e. global) importance of each of the uncertain model parameters, or of groups of them, towards the total risk. The methodology is based on definition of an auxiliary density (distribution) function, proportional to the integrand of the integral quantifying seismic risk, and on comparison of this density to the initial probability distribution for the model parameters of interest. Uncertainty in the rest of the model parameters is explicitly addressed through integration of their joint auxiliary distribution to calculate the corresponding marginal distributions. The relative information entropy is used to quantify the difference between the compared density functions and an efficient approach based on stochastic sampling is introduced for estimating this entropy for all quantities of interest. The framework is illustrated in an example that adopts a source-based stochastic ground motion model, and valuable insight is provided for its implementation within structural engineering applications.

Partition function loop series for a general graphical model: free-energy corrections and message-passing equations

A loop series expansion for the partition function of a general statistical model on a graph is carried out. If the auxiliary probability distributions of the expansion are chosen to be a fixed point of the belief-propagation equation, the first term of the loop series gives the Bethe–Peierls (BP) free-energy functional at the replica-symmetric level of the mean-field spin-glass theory, and corrections are contributed only by subgraphs that are free of dangling edges. This result generalizes the early work of Chertkov and Chernyak on binary statistical models. If the belief-propagation equation has multiple fixed points, a loop series expansion is performed for the grand partition function. The first term of this series gives the BP free-energy functional at the first-step replica-symmetry-breaking (RSB) level of the mean-field spin-glass theory, and corrections again come only from subgraphs that are free of dangling edges, provided that the auxiliary probability distributions of the expansion are chosen to be a fixed point of the survey-propagation equation. The same loop series expansion can be performed for higher-level partition functions, obtaining the higher-level RSB BP free-energy functionals (and the correction terms) and message-passing equations without using the BP approximation.

Estimation of domain means on the basis of strategy dependent on depth function of auxiliary variables' distribution

The paper deals with the problem of estimation of a domain means in a finite and fixed population. We assume that observations of a multidimensional auxiliary variable are known in the population. The proposed estimation strategy consists of the well known Horvitz-Thompson estimator and the non-simple sampling design dependent on a synthetic auxiliary variable whose observations are equal to the values of a depth function of the auxiliary variable distribution. The well known spherical and Mahalanobis depth functions are considered. A sampling design is proportionate to the maximal order statistic determined on the basis of the synthetic auxiliary variable observations in a simple sample drawn without replacement. A computer simulation analysis leads to the conclusion that the proposed estimation strategy is more accurate for domain means than the well known simple sample means

A Grounded MoM-Based Spatial Green's Function Technique for the Analysis of Multilayered Circuits in Rectangular Shielded Enclosures

A continuous counterpart of the spatial images technique is proposed for the computation of the multilayered boxed Green's functions and their derivatives. The method employs a set of auxiliary linear distribution of sources to effectively impose the potential boundary conditions along the whole cavity contour. The imposition of these boundary conditions leads to a set of integral equations (IEs), on the unknown distributions of the auxiliary sources, which are solved by applying a method of moments approach. A convergence/efficiency study, related to the test and basis functions choice, is then presented and discussed. The technique is combined with the use of dynamic ground planes generating mirror basis functions, which completely remove any singular instability. Finally, the computed Green's functions are included into a mixed-potential IE formulation for the accurate and very fast analysis of practical multilayered shielded circuits. The proposed technique does not suffer from any convergence issue and it is extremely competitive in terms of accuracy and efficiency as compared to other methods known to the authors.

Cross-validation prior choice in Bayesian probit regression with many covariates

This paper examines prior choice in probit regression through a predictive cross-validation criterion. In particular, we focus on situations where the number of potential covariates is far larger than the number of observations, such as in gene expression data. Cross-validation avoids the tendency of such models to fit perfectly. We choose the scale parameter c in the standard variable selection prior as the minimizer of the log predictive score. Naive evaluation of the log predictive score requires substantial computational effort, and we investigate computationally cheaper methods using importance sampling. We find that K-fold importance densities perform best, in combination with either mixing over different values of c or with integrating over c through an auxiliary distribution.

Non-parametric adaptive importance sampling for the probability estimation of a launcher impact position

Importance sampling (IS) is a useful simulation technique to estimate critical probability with a better accuracy than Monte Carlo methods. It consists in generating random weighted samples from an auxiliary distribution rather than the distribution of interest. The crucial part of this algorithm is the choice of an efficient auxiliary PDF that has to be able to simulate more rare random events. The optimisation of this auxiliary distribution is often in practice very difficult. In this article, we propose to approach the IS optimal auxiliary density with non-parametric adaptive importance sampling (NAIS). We apply this technique for the probability estimation of spatial launcher impact position since it has currently become a more and more important issue in the field of aeronautics.

Double auxiliaries, anteriority and terminativity

In this work I analyze a construction containing an additional past participle auxiliary in Romance and German dialects and show that, although apparently similar, the semantic value of the additional auxiliary is different in the two sets of dialects: in German it is an index of terminativity, in Romance of anteriority. However, an implicational scale ruling the distribution of the additional auxiliary which goes from unergative to passive verbs (going through unaccusative verbs) is valid across all dialects shows that there is a strict relation between the two auxiliaries have and be which can be captured in terms of incorporation of a preposition/determiner as proposed by Kayne.

A Divergence Minimization Approach to Joint Multiuser Decoding for Coded CDMA

In this paper, a theoretical framework of divergence minimization (DM) is applied to derive iterative receiver algorithms for coded CDMA systems. The DM receiver obtained performs joint channel estimation, multiuser decoding, and noise- covariance estimation. While its structure is similar to that of many ad-hoc receivers in the literature, the DM receiver is the result of applying a formal framework for optimization without further simplifications, namely the DM approach with a factorizable auxiliary model distribution. The well-known expectation- maximization (EM) algorithm and space-alternating generalized expectation-maximization (SAGE) algorithm are special cases of degenerate model distributions within the DM framework. Furthermore, many ad-hoc receiver structures from literature are shown to represent approximations of the proposed DM receiver. The DM receiver has four interesting properties that all result directly from applying the formal framework: (i) The covariances of all estimates involved are taken into account, (ii) The residual interference after interference cancellation is handled by the noise-covariance estimation as opposed to by LMMSE filters in other receivers, (iii) Posterior probabilities of the code symbols are employed rather than extrinsic probabilities, (iv) The iterative receiver is guaranteed to converge in divergence. The theoretical insights are illustrated by simulation results.

Auxiliary fronting in Peranakan Javanese

Peranakan Javanese (PNJ) is a relatively undescribed variety of Javanese spoken primarily by ethnic Chinese native speakers of Javanese in the city of Semarang in Central Java (Indonesia). PNJ makes a structural distinction between auxiliaries and main verbs. Auxiliaries are unique in that they undergo optional head movement to C. Not only do single auxiliaries move to C, as in familiar languages, but sequences of two or three auxiliaries can move to C as well. Significantly, the order of the moved auxiliaries is always the same as the order in their unmoved position. The distribution of auxiliaries in PNJ is predicted if a ‘tucking in’ (Richards 1997) analysis of head movement similar to that of Collins (2002) is adopted. The PNJ facts are of special interest not only because they are an example of an additional language/construction that shows the distribution expected on the basis of ‘tucking in’, but also because PNJ provides evidence that helps to distinguish between ahead movementanalysis and the ‘standard’ version of theremnant movementanalysis, in which adverbs occupy fixed positions in the clause. It is quite difficult to distinguish between these approaches empirically, so the PNJ auxiliary facts are important in this regard.

Implementing the wild bootstrap using a two-point distribution

We consider how to select the auxiliary distribution to implement the wild bootstrap for regressions featuring heteroscedasticity of unknown form. We propose a new class of two-point distributions and suggest using the Kolmogorov–Smirnov statistic as a selection criterion.

On Approximating the Individual Risk Model

Error bounds are developed for Kornya-Presman–type approximations to the individual risk model. In particular, error bounds are given for the compound Poisson approximation, with the Poisson parameter equal to the expected number of claims. The approximations considered are a modification by Hipp of an approximation originally developed by Kornya, as well as Kornya’s original approximation. The error bounds are similar in concept to Hipp’s original error bounds using concentration–functions, as refined by Čekanavičius, Roos, and others. Computation of the bounds, however, is considerably simplified. In particular, concentration function type bounds called width-norm bounds are calculated directly from the values of the approximation, avoiding completely the need for calculating a special auxiliary compound Poisson distribution. Two examples are given. Depending on the portfolio parameters, the width-norm error bounds may or may not be sharper than the Hipp-Roos error bounds. In any event, it is recommended that the simpler widthnorm calculation, possibly together with an increase in the order of the approximation, be considered in practical applications if the goal is to achieve a specified accuracy with the least amount of computation. For large portfolios, where the maximum claim on any one policy is relatively small compared to the expected aggregate claims, the width-norm error bounds compare quite favorably with error bounds developed by De Pril and by Dhaene.

A unified framework to exploit information in BCI data for continuous prediction

To develop effective learning algorithms for continuous prediction using Electro-encephalogram (EEG) signal is a challenging research issue in brain–computer interface (BCI). In this paper, we propose a unified framework based on variational Bayesian method to fully exploit information contained in BCI data. To make continuous prediction, trials in training data set are first divided into segments. There are two key issues here. The first is that the actual intention (label) at each time interval (segment) is unknown. The second is that the final decision of a whole trial has to be drawn based on the predictions at individual time intervals. To address these key issues together, we introduce two auxiliary distributions in the lower bound on the log posterior and maximize this lower bound based on variational Bayesian method. We evaluated the proposed method on three data sets of BCI competition 2003 and 2005. The experimental results show that the averaged accuracy of our method is among the best.

On the typology of auxiliary selection

This paper extends a previous claim that auxiliary selection in the present perfect of monadic verbs reflects a pattern grounded in lexico-aspectual properties of individual verbs though mediated through their syntax. A novel argument in support of this conclusion is made, based on the cross-contextual typology of auxiliaries, showing that the cross-linguistic distribution of auxiliaries in the present perfect cannot be understood in isolation of other constructions requiring an auxiliary. In particular, it is argued that two sets of constraints restrict the mapping from lexico-aspectual features to a particular auxiliary ( have or be). One set restricts the mapping from lexical-aspectual features to argument structure at the lexicon-syntax interface, the other restricts the mapping from argument structure to the marked member of the auxiliary pair ( have). The analysis succeeds in predicting exactly 15 possible languages or patterns of auxiliary selection with monadic verbs, a variety of which are discussed throughout the paper. While the fundamental syntactic distinction made by the Unaccusative Hypothesis is confirmed by the formal analysis, it is argued that the present perfect imposes restrictions of its own on the argumental status of any verb entering the construction, on a par with constructions such as passives and resultatives.

An auxiliary size distribution model for the ultrasonically produced water droplets

While searching for improved ways of aromatization processes applicable in tobacco industry we have developed an ultrasound sprayer of liquids operating at f = 40 kHz. Recently, we have suggested [D. Šarković, V. Babović, On the statistics of ultrasonically produced water droplets, Zeitschrift für Naturforschung, Tübingen, 60a (2005) 489–493] a practical model for the distribution of particle diameters in produced aerosols. In this paper we present experimental data which seem to confirm the elementary features of the density distribution function. Also, we have generalized the previous formulae in order to treat a class of water mixtures and low-viscosity liquids. The corresponding expressions are given and basic consequences analyzed.

Orthogonal Laurent polynomials and quadrature formulas for unbounded intervals: II. Interpolatory rules

We study the convergence of quadrature formulas for integrals over the positive real line with an arbitrary (possibly complex) distribution function. The nodes of the quadrature formulas are the zeros of orthogonal Laurent polynomials with respect to an auxiliary distribution function and a certain nesting. The quadratures are called interpolatory (product) formulas. The class of functions for which convergence holds is characterized in terms of the moments of the auxiliary distribution function. We also include the convergence analysis of related two-point Padé-type approximants to the Stieltjes transform of the given distribution function. Finally, some illustrative numerical examples are also given.