(a) (b) (c) Fig. 7. Models learned with fixed ¯ α from three different walking subjects. (a) The learned latent coordinates shown in blue. (b) − ln variance plot shows smooth high confidence regions, but the variance near data is larger than in Fig.5c, similar to B-GPDM. (c) Typical samples from the dynamic predictive distribution are shown in green, while the mean-prediction sample is shown in...

The existing optimal design of the fixed sampling interval S2-EWMA control chart to monitor the sample variance of a process is based on the average run length (ARL) criterion. Since the shape of the run length distribution changes with the magnitude of the shift in the variance, the median run length (MRL) gives a more meaningful explanation about the in-control and out-of-control performances...

We derive an unbiased variance estimator for re-sampling procedures using the fact that those procedures are incomplete U-statistics. Our approach is based on careful examination of the combinatorics governing the covariances between re-sampling iterations. We establish such an unbiased variance estimator for the special case of K-Fold cross-validation. This estimator exists as soon as new obse...

In multivariate normal dynamic and state-space linear models the observational variance matrix is usually assumed known. Apart from a handful of special cases, estimation procedures that allow for the variance of the observational errors to be left unspecified are not widely available. The foundation of this paper is the general multivariate normal dynamic linear model with unknown but fixed ob...

It has long been recognized that sensory systems adapt to their inputs. Here we formulate the problem of optimal variance estimation for a broad class of nonstationary signals. We show that under weak assumptions, the Bayesian optimal causal variance estimate shows asymmetric dynamics: an abrupt increase in variance is more readily detectable than an abrupt decrease. By contrast, optimal adapta...

Chen (1) simulated random samples of beta, lognormal, and Poisson distributions with varying parameters following the method that we (2) used for fixed parameters. Chen claimed that the relationship between the supporting rate of Taylor’s law (TL) and skewness is “complex and nonmonotonic,” as some random samples of some skewed distributions did not support TL. Chen did not consider two crucial...

A familiär relation links the densities that result for the intersection of a convex body and straight lines under uniform isotropic randomness with those that result under weighted randomness. An extension of this relation to the intersection of more general domains is utilized to obtain the variance of the n-dimensional measure of the intersection of two bodies under uniform isotropic randomn...

For nonparametric regression models with fixed and random design, two classes of estimators for the error variance have been introduced: second sample moments based on residuals from a nonparametric fit, and difference-based estimators. The former are asymptotically optimal but require estimating the regression function; the latter are simple but have larger asymptotic variance. For nonparametr...

Idealized explicit convection simulations of the Met Office Unified Model exhibit spontaneous selfaggregation in radiative-convective equilibrium, as seen in other models in previous studies. This selfaggregation is linked to feedbacks between radiation, surface fluxes, and convection, and the organization is intimately related to the evolution of the column water vapor field. Analysis of the b...

We study a model of learning on social networks in dynamic environments, describing a group of agents who are each trying to estimate an underlying state that varies over time, given access to weak signals and the estimates of their social network neighbors. We study three models of agent behavior. In the “fixed response” model agents use a fixed linear combination to incorporate information fr...