The quartz flexure accelerometer has been applied in many inertial systems, but the accelerometer signal may be infected by various noise components. In order to be sufficient for the precision requirement, a noise reduction method is designed and explored to meliorate the measurement signal. By constructing a Hankel matrix with the single channel collected signal, the singular value decomposit...

It is shown that the volume of trade can be decomposed into proportional proxies for stochastic flows of good news and bad news into the market. Positive (good) information flows are assumed to increase the price of a financial vehicle while negative (bad) information flows decrease the price. For the majority of a sample of ten split-stocks it is shown that the proposed decomposition explains ...

Bias variance decomposition of the expected error defined for regression and classification problems is an important tool to study and compare different algorithms, to find the best areas for their application. Here the decomposition is introduced for the survival analysis problem. In our experiments, we study bias -variance parts of the expected error for two algorithms: original Cox proportio...

We study orthogonal decomposition of symmetric statistics based on samples drawn without replacement from finite populations. Under very mild smoothness conditions the first k terms of the decomposition provide stochastic expansion with remainder O(N−k/2). Assuming that the linear part of the decomposition is nondegenerate we establish one term Edgeworth expansion of the distribution function o...

This paper applies the Sobol’ decomposition of a function of many random variables to a problem in structural mechanics, namely the collapse of a two story two bay frame under gravity load. Prior to introduction of this example application, the Sobol’ decomposition itself is reviewed and extended to cover the case in which the input random variables have Gaussian distribution. Then, an illustra...

We propose and study properties of several estimators of variance decomposition in the local-projections framework. We find for empirically relevant sample sizes that, after being bias corrected with bootstrap, our estimators perform well in simulations. We also illustrate the workings of our estimators empirically for monetary policy and productivity shocks.

We revisit the idea of using sequential Monte Carlo (SMC) for inference in general probabilistic graphical models. By constructing a sequence of auxiliary target distributions (also known as a sequential decomposition) based on the graph structure we can run a standard SMC sampler on the graph. In this paper we study the impact of the sequential decomposition on the accuracy of the SMC method b...

Smoothing Spline ANOVA is a statistical modeling algorithm based on a function decomposition similar to the classical analysis of variance (ANOVA) decomposition and the associated notions of main effect and interaction. It represents a suitable screening technique for detecting important variables (Variable Screening) in a given dataset. We present the mathematical background together with poss...

A method for simultaneous modelling of the Cholesky decomposition of several covariance matrices is presented. We highlight the conceptual and computational advantages of the unconstrained parameterization of the Cholesky decomposition and compare the results with those obtained using the classical spectral (eigenvalue) and variance-correlation decompositions. All these methods amount to decomp...

The bias/variance decomposition of mean-squared error is well understood and relatively straightforward. In this note, a similar simple decomposition is derived, valid for any kind of error measure that, when using the appropriate probability model, can be derived from a Kullback-Leibler divergence or log-likelihood.