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A Bayesian formulation for inference of material properties from experimental signals is proposed with a normal likelihood quantifying noise and an inverse gamma prior expressing uncertainty about noise variance. Asymptotic analysis shows that, for large samples, the posterior distribution is maximized at the database signal that minimizes an L2 norm between the experimental data and database entries. The largest posterior probability tends to 1 as the number of data points on the signals tends to ∞. There exists a critical ratio between the mode of the inverse gamma prior and the true variance of the normally distributed noise. This ratio determines how the posterior probability varies with the shape parameter of the inverse gamma prior. Numerical results based on an analytical expression and simulations confirm the conclusions from the asymptotic analysis. These results show that posterior probabilities are insensitive to the choice of prior mode when the prior's shape parameter is taken to be small. In spite of the use of interpolation in database construction, the approach is limited to cases where a small number of parameters is to be identified. When multiple signal types are analyzed simultaneously, a method using a weighted average of posterior distributions from the different signal types is proposed. This method is compared with a classical Bayesian approach that uses a joint likelihood. Effective choices of prior parameters are recommended. [ABSTRACT FROM AUTHOR]

A new nonparametric test of equality of two densities is investigated. The test statistic is an average of log-Bayes factors, each of which is constructed from a kernel density estimate. Prior densities for the bandwidths of the kernel estimates are required, and it is shown how to choose priors so that the log-Bayes factors can be calculated exactly. Critical values of the test statistic are determined by a permutation distribution, conditional on the data. An attractive property of the methodology is that a critical value of 0 leads to a test for which both type I and II error probabilities tend to 0 as sample sizes tend to ∞. Existing results on Kullback–Leibler loss of kernel estimates are crucial to obtaining these asymptotic results, and also imply that the proposed test works best with heavy-tailed kernels. Finite sample characteristics of the test are studied via simulation, and extensions to multivariate data are straightforward, as illustrated by an application to bivariate connectionist data. [ABSTRACT FROM AUTHOR]

Summary: Bayes factors that do not require prior distributions are proposed for testing one parametric model versus another. These Bayes factors are relatively simple to compute, relying only on maximum likelihood estimates, and are Bayes consistent at an exponential rate for nested models even when the smaller model is true. These desirable properties derive from the use of data splitting. Large sample properties, including consistency, of the Bayes factors are derived, and a simulation study explores practical concerns. The methodology is illustrated with civil engineering data involving compressive strength of concrete. [ABSTRACT FROM AUTHOR]

The plastic properties that characterize the uniaxial stress-strain response of a plastically isotropic material are not uniquely related to the indentation force versus indentation depth response. We consider results for three sets of plastic material properties that give rise to essentially identical curves of indentation force versus indentation depth in conical indentation. The corresponding surface profiles after unloading are also calculated. These computed results are regarded as the "experimental" data. A simplified Bayesian-type statistical approach is used to identify the values of flow strength and strain hardening exponent for each of the three sets of material parameters. The effect of fluctuations ("noise") superposed on the "experimental" data is also considered. We build the database for the Bayesian-type analysis using finite element calculations for a relatively coarse set of parameter values and use interpolation to refine the database. A good estimate of the uniaxial stress-strain response is obtained for each material both in the absence of fluctuations and in the presence of sufficiently small fluctuations. Since the indentation force versus indentation depth response for the three materials is nearly identical, the predicted uniaxial stress-strain response obtained using only surface profile data differs little from what is obtained using both indentation force versus indentation depth and surface profile data. The sensitivity of the representation of the predicted uniaxial stress-strain response to fluctuations increases with increasing strain hardening. We also explore the sensitivity of the predictions to the degree of database refinement. [ABSTRACT FROM AUTHOR]

A nonparametric Bayes procedure is proposed for testing the fit of a parametric model for a distribution. Alternatives to the parametric model are kernel density estimates. Data splitting makes it possible to use kernel estimates for this purpose in a Bayesian setting. A kernel estimate indexed by bandwidth is computed from one part of the data, a training set, and then used as a model for the rest of the data, a validation set. A Bayes factor is calculated from the validation set by comparing the marginal for the kernel model with the marginal for the parametric model of interest. A simulation study is used to investigate how large the training set should be, and examples involving astronomy and wind data are provided. A proof of Bayes consistency of the proposed test is also provided. [ABSTRACT FROM AUTHOR]

The article focuses on a study related to use of Bayesian probabilistic methodology combined with Arps' decline-curve analysis shale well production forecasts. It states that the Bayesian methodology provides a means and a workflow to generate probabilistic decline-curve forecasts and quantify reserves uncertainty in shale plays quickly and reliably, and also mentions that Bayesian methodology can also be applied with other analytical decline-curve models.

The one-sided cross-validation (OSCV) method is shown to be robust to lack of smoothness in the regression function. Two corrections for the case where the regression function has a discontinuous first derivative are proposed. Simulation results suggest that proposed modifications of the OSCV method are efficient for regression functions whose first derivative is discontinuous at more than two points. The OSCV method and its modification outperform the cross-validation method and the Ruppert–Sheather–Wand plug-in method in a data example involving a function that, potentially, has one discontinuity in its derivative. [ABSTRACT FROM PUBLISHER]

In this paper, we propose a change-point estimator based on local Fourier series estimates. At each potential change point, two Fourier series estimates are computed, one using data to the left of the possible change point and the other using data to the right. The difference between these estimates is computed, and the change-point estimate is defined to be the point at which this absolute difference is maximised. Mean-squared error properties of our local series estimates are derived and the change-point estimator is shown to converege to the truth at rate n-1 (where n is the sample size). In a simulation study, the proposed change-point estimator has a better overall performance than a local linear method. A data-driven bandwidth selector is also proposed and applied to the classical Nile River data. [ABSTRACT FROM AUTHOR]

This article is concerned with testing multiple hypotheses, one for each of a large number of small data sets. Such data are sometimes referred to as high-dimensional, low-sample size data. Our model assumes that each observation within a randomly selected small data set follows a mixture of C shifted and rescaled versions of an arbitrary density f. A novel kernel density estimation scheme, in conjunction with clustering methods, is applied to estimate f. Bayes information criterion and a new criterion weighted mean of within-cluster variances are used to estimate C, which is the number of mixture components or clusters. These results are applied to the multiple testing problem. The null sampling distribution of each test statistic is determined by f, and hence a bootstrap procedure that resamples from an estimate of f is used to approximate this null distribution. [ABSTRACT FROM AUTHOR]

We report the results of a period change analysis of time series observations for 378 pulsating variable stars. The null hypothesis of no trend in expected periods is tested for each of the stars. The tests are non-parametric in that potential trends are estimated by local linear smoothers. Our testing methodology has some novel features. First, the null distribution of a test statistic is defined to be the distribution that results in repeated sampling from a population of stars. This distribution is estimated by means of a bootstrap algorithm that resamples from the collection of 378 stars. Bootstrapping in this way obviates the problem that the conditional sampling distribution of a statistic, given a particular star, may depend on unknown parameters of that star. Another novel feature of our test statistics is that one-sided cross-validation is used to choose the smoothing parameters of the local linear estimators on which they are based. It is shown that doing so results in tests that are tremendously more powerful than analogous tests that are based on the usual version of cross-validation. The positive false discovery rate method of Storey is used to account for the fact that we simultaneously test 378 hypotheses. We ultimately find that 56 of the 378 stars have changes in mean pulsation period that are significant when controlling the positive false discovery rate at the 5% level. [ABSTRACT FROM AUTHOR]

Detecting changes in the mean of a stochastic process is important in many areas, including quality control. We develop powerful omnibus tests for the null hypothesis that the underlying mean is constant. The proposed tests can be applied to test for any kind of change, whether it be abrupt, smooth or cyclical. Nonparametric function estimation techniques are used in deriving these tests. The test statistics are derived from a Fourier series smoother that minimizes an estimate of mean integrated squared error. An important example of correlated data is that arising from a stationary time series. To obtain a valid test of mean constancy, it is necessary to estimate the spectrum of the error process, and we consider various methods of doing this. We have found that, in the case of an AR(1) model, the spectrum is well estimated if local linear smoothing is used in conjunction with generalized least squares. A power study of the proposed tests is done by simulation when the errors follow an AR(1) model, and the tests are applied to a set of astronomy data. [ABSTRACT FROM AUTHOR]