21,818 research outputs found
Nonparametric Covariate Adjustment for Receiver Operating Characteristic Curves
The accuracy of a diagnostic test is typically characterised using the
receiver operating characteristic (ROC) curve. Summarising indexes such as the
area under the ROC curve (AUC) are used to compare different tests as well as
to measure the difference between two populations. Often additional information
is available on some of the covariates which are known to influence the
accuracy of such measures. We propose nonparametric methods for covariate
adjustment of the AUC. Models with normal errors and non-normal errors are
discussed and analysed separately. Nonparametric regression is used for
estimating mean and variance functions in both scenarios. In the general noise
case we propose a covariate-adjusted Mann-Whitney estimator for AUC estimation
which effectively uses available data to construct working samples at any
covariate value of interest and is computationally efficient for
implementation. This provides a generalisation of the Mann-Whitney approach for
comparing two populations by taking covariate effects into account. We derive
asymptotic properties for the AUC estimators in both settings, including
asymptotic normality, optimal strong uniform convergence rates and MSE
consistency. The usefulness of the proposed methods is demonstrated through
simulated and real data examples
Zero-variance zero-bias quantum Monte Carlo estimators of the spherically and system-averaged pair density
We construct improved quantum Monte Carlo estimators for the spherically- and
system-averaged electron pair density (i.e. the probability density of finding
two electrons separated by a relative distance u), also known as the
spherically-averaged electron position intracule density I(u), using the
general zero-variance zero-bias principle for observables, introduced by
Assaraf and Caffarel. The calculation of I(u) is made vastly more efficient by
replacing the average of the local delta-function operator by the average of a
smooth non-local operator that has several orders of magnitude smaller
variance. These new estimators also reduce the systematic error (or bias) of
the intracule density due to the approximate trial wave function. Used in
combination with the optimization of an increasing number of parameters in
trial Jastrow-Slater wave functions, they allow one to obtain well converged
correlated intracule densities for atoms and molecules. These ideas can be
applied to calculating any pair-correlation function in classical or quantum
Monte Carlo calculations.Comment: 13 pages, 9 figures, published versio
Advances in forecast evaluation
This paper surveys recent developments in the evaluation of point forecasts. Taking West's (2006) survey as a starting point, we briefly cover the state of the literature as of the time of West's writing. We then focus on recent developments, including advancements in the evaluation of forecasts at the population level (based on true, unknown model coefficients), the evaluation of forecasts in the finite sample (based on estimated model coefficients), and the evaluation of conditional versus unconditional forecasts. We present original results in a few subject areas: the optimization of power in determining the split of a sample into in-sample and out-of-sample portions; whether the accuracy of inference in evaluation of multi-step forecasts can be improved with judicious choice of HAC estimator (it can); and the extension of West's (1996) theory results for population-level, unconditional forecast evaluation to the case of conditional forecast evaluation.Forecasting
Advances in forecast evaluation
This paper surveys recent developments in the evaluation of point forecasts. Taking West’s (2006) survey as a starting point, we briefly cover the state of the literature as of the time of West’s writing. We then focus on recent developments, including advancements in the evaluation of forecasts at the population level (based on true, unknown model coefficients), the evaluation of forecasts in the finite sample (based on estimated model coefficients), and the evaluation of conditional versus unconditional forecasts. We present original results in a few subject areas: the optimization of power in determining the split of a sample into in-sample and out-of-sample portions; whether the accuracy of inference in evaluation of multistep forecasts can be improved with the judicious choice of HAC estimator (it can); and the extension of West’s (1996) theory results for population-level, unconditional forecast evaluation to the case of conditional forecast evaluation.Forecasting ; Time-series analysis
Revisiting the Gelman-Rubin Diagnostic
Gelman and Rubin's (1992) convergence diagnostic is one of the most popular
methods for terminating a Markov chain Monte Carlo (MCMC) sampler. Since the
seminal paper, researchers have developed sophisticated methods for estimating
variance of Monte Carlo averages. We show that these estimators find immediate
use in the Gelman-Rubin statistic, a connection not previously established in
the literature. We incorporate these estimators to upgrade both the univariate
and multivariate Gelman-Rubin statistics, leading to improved stability in MCMC
termination time. An immediate advantage is that our new Gelman-Rubin statistic
can be calculated for a single chain. In addition, we establish a one-to-one
relationship between the Gelman-Rubin statistic and effective sample size.
Leveraging this relationship, we develop a principled termination criterion for
the Gelman-Rubin statistic. Finally, we demonstrate the utility of our improved
diagnostic via examples
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