Search results for "A* algorithm"

Sample Size Requirements of a Mixture Analysis Method with Applications in Systematic Biology

1999

The available information on sample size requirements of mixture analysis methods is insufficient to permit a precise evaluation of the potential problems facing practical applications of mixture analysis. We use results from Monte Carlo simulation to assess the sample size requirements of a simple mixture analysis method under conditions relevant to biological applications of mixture analysis. The mixture model used includes two univariate normal components with equal variances but assumes that the researcher is ignorant as to the equality of the variances. The method used relies on the EM algorithm to compute the maximum likelihood estimates of the mixture parameters, and the likelihood r…

Influence of rounding errors on the quality of heuristic optimization algorithms

2011

Abstract Search space smoothing and related heuristic optimization algorithms provide an alternative approach to simulated annealing and its variants: while simulated annealing traverses barriers in the energy landscape at finite temperatures, search space smoothing intends to remove these barriers, so that a greedy algorithm is sufficient to find the global minimum. Several formulas for smoothing the energy landscape have already been applied, one of them making use of the finite numerical precision on a computer. In this paper, we thoroughly investigate the effect of finite numerical accuracy on the quality of results achieved with heuristic optimization algorithms. We present computation…

Bayesian Smoothing in the Estimation of the Pair Potential Function of Gibbs Point Processes

1999

A flexible Bayesian method is suggested for the pair potential estimation with a high-dimensional parameter space. The method is based on a Bayesian smoothing technique, commonly applied in statistical image analysis. For the calculation of the posterior mode estimator a new Monte Carlo algorithm is developed. The method is illustrated through examples with both real and simulated data, and its extension into truly nonparametric pair potential estimation is discussed.

Algorithm AS 105: Fitting a Covariance Selection Model to a Matrix

1977

Model selection in linear mixed-effect models

2019

Linear mixed-effects models are a class of models widely used for analyzing different types of data: longitudinal, clustered and panel data. Many fields, in which a statistical methodology is required, involve the employment of linear mixed models, such as biology, chemistry, medicine, finance and so forth. One of the most important processes, in a statistical analysis, is given by model selection. Hence, since there are a large number of linear mixed model selection procedures available in the literature, a pressing issue is how to identify the best approach to adopt in a specific case. We outline mainly all approaches focusing on the part of the model subject to selection (fixed and/or ra…

Multicanonical Monte Carlo simulations

1998

Canonical Monte Carlo simulations of disordered systems like spin glasses and systems undergoing first-order phase transitions are severely hampered by rare event states which lead to exponentially diverging autocorrelation times with increasing system size and hence to exponentially large statistical errors. One possibility to overcome this problem is the multicanonical reweighting method. Using standard local update algorithms it could be demonstrated that the dependence of autocorrelation times on the system size V is well described by a less divergent power law, τ∝Vα, with 1<α<3, depending on the system. After a brief review of the basic ideas, combinations of multicanonical reweighting…

On stability issues in deriving multivariable regression models

2014

In many areas of science where empirical data are analyzed, a task is often to identify important variables with influence on an outcome. Most often this is done by using a variable selection strategy in the context of a multivariable regression model. Using a study on ozone effects in children (n = 496, 24 covariates), we will discuss aspects relevant for deriving a suitable model. With an emphasis on model stability, we will explore and illustrate differences between predictive models and explanatory models, the key role of stopping criteria, and the value of bootstrap resampling (with and without replacement). Bootstrap resampling will be used to assess variable selection stability, to d…

Affine-invariant rank tests for multivariate independence in independent component models

2016

We consider the problem of testing for multivariate independence in independent component (IC) models. Under a symmetry assumption, we develop parametric and nonparametric (signed-rank) tests. Unlike in independent component analysis (ICA), we allow for the singular cases involving more than one Gaussian independent component. The proposed rank tests are based on componentwise signed ranks, à la Puri and Sen. Unlike the Puri and Sen tests, however, our tests (i) are affine-invariant and (ii) are, for adequately chosen scores, locally and asymptotically optimal (in the Le Cam sense) at prespecified densities. Asymptotic local powers and asymptotic relative efficiencies with respect to Wilks’…

Parallel Construction and Query of Index Data Structures for Pattern Matching on Square Matrices

1999

AbstractWe describe fast parallel algorithms for building index data structures that can be used to gather various statistics on square matrices. The main data structure is the Lsuffix tree, which is a generalization of the classical suffix tree for strings. Given ann×ntext matrixA, we build our data structures inO(logn) time withn2processors on a CRCW PRAM, so that we can quickly processAin parallel as follows: (i) report some statistical information aboutA, e.g., find the largest repeated square submatrices that appear at least twice inAor determine, for each position inA, the smallest submatrix that occurs only there; (ii) given, on-line, anm×mpattern matrixPAT, check whether it occurs i…

Non-parametric Estimation of the Death Rate in Branching Diffusions

2002

We consider finite systems of diffusing particles in R with branching and immigration. Branching of particles occurs at position dependent rate. Under ergodicity assumptions, we estimate the position-dependent branching rate based on the observation of the particle process over a time interval [0, t]. Asymptotics are taken as t → ∞. We introduce a kernel-type procedure and discuss its asymptotic properties with the help of the local time for the particle configuration. We compute the minimax rate of convergence in squared-error loss over a range of Holder classes and show that our estimator is asymptotically optimal.