simulation output assume simulation run length is known in advance. This paper proposes an implementable batch-size selection procedure for estimating the variance of the sample mean without requiring that the sample size or simulation run length a priori.

The extended Kalman filter (EKF) is probably the most widely used estimation algorithm for nonlinear systems. However, more than 35 years of experience in the estimation community has shown that is difficult to implement, difficult to tune, and only reliable for systems that are almost linear

the convergence of a recursive mean shift procedure to the nearest stationary point of the underlying density function and thus its utility in detecting the modes of the density. The equivalence of the mean shift procedure to the Nadaraya–Watson estimator from kernel regression and the robust M-estimators

We propose a method (the \Gap statistic") for estimating the number of clusters (groups) in a set of data. The technique uses the output of any clustering algorithm (e.g. k-means or hierarchical), comparing the change in within cluster dispersion to that expected under an appropriate reference

‖ˆx − x ‖ 2 ℓ2 ≤ C2 ( · 2 log p · σ 2 + ∑ min(x 2 i, σ 2) Our results are nonasymptotic and we give values for the constant C. In short, our estimator achieves a loss within a logarithmic factor of the ideal mean squared error one would achieve with an oracle which would supply perfect information

Two approximate methods are proposed for maximum likelihood phylogenetic estimation, which allow variable rates of substitution across nucleotide sites. Three data sets with quite different characteristics were analyzed to examine empirically the performance of these methods. The first, called

rigor. ii 1 Maximum-likelihood Recall the definition of the maximum-likelihood estimation problem. We have a density function ¢¡¤£¦ ¥ §© ¨ that is governed by the set of parameters § (e.g.,   might be a set of Gaussians and § could be the means and covariances). We also have a data set of size

, and it is a problem that one always encounters while collecting fre-quency statistics on words and word sequences (m-grams) from a text of finite size. This means that even for a very large data col-lection, the maximum likelihood estimation method does not allow Turing’s estimate PT for a probability of a

Motivation: Gene expression microarray experiments can generate data sets with multiple missing expression values. Unfortunately, many algorithms for gene expression analysis require a complete matrix of gene array values as input. For example, methods such as hierarchical clustering and K-means

that it is difficult to implement, difficult to tune, and only reliable for systems which are almost linear on the time scale of the update intervals. In this paper a new linear estimator is developed and demonstrated. Using the principle that a set of discretely sampled points can be used to parameterise mean