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### Report on the Last Work by Dr. Erich Nuding Rohn, Jiří 2016 - English This is a facsimile copy of a 1994 report on the unpublished last paper by Dr. Erich Nuding. It is being made public here in the hope that even after twenty-two years it may be of interest for researchers working in the area of interval computations because of the intriguing concept of the "fourth modality" which has not been rediscovered during a quarter of century which has elapsed since its original formulation. Keywords: set-valued mapping; interval linear equations; solution set; fourth modality Available in a digital repository NRGL Report on the Last Work by Dr. Erich Nuding

This is a facsimile copy of a 1994 report on the unpublished last paper by Dr. Erich Nuding. It is being made public here in the hope that even after twenty-two years it may be of interest for ...

Rohn, Jiří
Ústav informatiky, 2016

### Diagnostics for Robust Regression: Linear Versus Nonlinear Model Kalina, Jan 2016 - English Robust statistical methods represent important tools for estimating parameters in linear as well as nonlinear econometric models. In contrary to the least squares, they do not suffer from vulnerability to the presence of outlying measurements in the data. Nevertheless, they need to be accompanied by diagnostic tools for verifying their assumptions. In this paper, we propose the asymptotic Goldfeld-Quandt test for the regression median. It allows to formulate a natural procedure for models with heteroscedastic disturbances, which is again based on the regression median. Further, we pay attention to nonlinear regression model. We focus on the nonlinear least weighted squares estimator, which is one of recently proposed robust estimators of parameters in a nonlinear regression. We study residuals of the estimator and use a numerical simulation to reveal that they can be severely heteroscedastic also for data generated from a model with homoscedastic disturbances. Thus, we give a warning that standard residuals of the robust nonlinear estimator may produce misleading results if used for the standard diagnostic tools Keywords: robust estimation; outliers; diagnostic tools; nonlinear regression; residuals Fulltext is available at external website. Diagnostics for Robust Regression: Linear Versus Nonlinear Model

Robust statistical methods represent important tools for estimating parameters in linear as well as nonlinear econometric models. In contrary to the least squares, they do not suffer from ...

Kalina, Jan
Ústav informatiky, 2016

### Nonlinear Conjugate Gradient Methods Lukšan, Ladislav; Vlček, Jan 2015 - English Modifications of nonlinear conjugate gradient method are described and tested. Keywords: minimization; nonlinear conjugate gradient methods; comparison of methods; efficiency of methods Available in digital repository of the ASCR Nonlinear Conjugate Gradient Methods

Modifications of nonlinear conjugate gradient method are described and tested.

Ústav informatiky, 2015

### A Modified Limited-Memory BNS Method for Unconstrained Minimization Derived from the Conjugate Directions Idea Vlček, Jan; Lukšan, Ladislav 2015 - English A modification of the limited-memory variable metric BNS method for large scale unconstrained optimization of the differentiable function $f:{\cal R}^N\to\cal R$ is considered, which consists in corrections (based on the idea of conjugate directions) of difference vectors for better satisfaction of the previous quasi-Newton conditions. In comparison with [11], more previous iterations can be utilized here. For quadratic objective functions, the improvement of convergence is the best one in some sense, all stored corrected difference vectors are conjugate and the quasi-Newton conditions with these vectors are satisfied. The algorithm is globally convergent for convex sufficiently smooth functions and our numerical experiments indicate its efficiency. Keywords: large scale unconstrained optimization; numerical experiments; limited-memory variable metric method; BNS method; quasi-Newton method; convergence Available in digital repository of the ASCR A Modified Limited-Memory BNS Method for Unconstrained Minimization Derived from the Conjugate Directions Idea

A modification of the limited-memory variable metric BNS method for large scale unconstrained optimization of the differentiable function $f:{\cal R}^N\to\cal R$ is considered, which consists in ...

Ústav informatiky, 2015

### Some Robust Estimation Tools for Multivariate Models Kalina, Jan 2015 - English Standard procedures of multivariate statistics and data mining for the analysis of multivariate data are known to be vulnerable to the presence of outlying and/or highly influential observations. This paper has the aim to propose and investigate specific approaches for two situations. First, we consider clustering of categorical data. While attention has been paid to sensitivity of standard statistical and data mining methods for categorical data only recently, we aim at modifying standard distance measures between clusters of such data. This allows us to propose a hierarchical agglomerative cluster analysis for two-way contingency tables with a large number of categories, based on a regularized measure of distance between two contingency tables. Such proposal improves the robustness to the presence of measurement errors for categorical data. As a second problem, we investigate the nonlinear version of the least weighted squares regression for data with a continuous response. Our aim is to propose an efficient algorithm for the least weighted squares estimator, which is formulated in a general way applicable to both linear and nonlinear regression. Our numerical study reveals the computational aspects of the algorithm and brings arguments in favor of its credibility. Keywords: robust data mining; high-dimensional data; cluster analysis; outliers Fulltext is available at external website. Some Robust Estimation Tools for Multivariate Models

Standard procedures of multivariate statistics and data mining for the analysis of multivariate data are known to be vulnerable to the presence of outlying and/or highly influential observations. This ...

Kalina, Jan
Ústav informatiky, 2015

### Causation Entropy Principle and Bayesian Inference to Causal Networks Coufal, David; Hlinka, Jaroslav 2015 - English Keywords: causal links; causation entropy; Bayesian inference Available in a digital repository NRGL Causation Entropy Principle and Bayesian Inference to Causal Networks

Ústav informatiky, 2015

### Soupis publikovaných prací pana doc. RNDr. Ivana Kramosila, DrSc., zpracovaný ke dni 29. května 2015 knihovnou Ústavu informatiky AV ČR, v. v. i. Nývltová, Ludmila; Ramešová, Nina; Šírová, Tereza 2015 - Czech Keywords: bibliografie Available in a digital repository NRGL Soupis publikovaných prací pana doc. RNDr. Ivana Kramosila, DrSc., zpracovaný ke dni 29. května 2015 knihovnou Ústavu informatiky AV ČR, v. v. i.

Nývltová, Ludmila; Ramešová, Nina; Šírová, Tereza
Ústav informatiky, 2015

### Measures for Classification Results Evaluation Řezanková, Hana; Húsek, Dušan 2015 - English Keywords: similarity measures; measures of agreement; success rate of classification Available in a digital repository NRGL Measures for Classification Results Evaluation

Řezanková, Hana; Húsek, Dušan
Ústav informatiky, 2015

### Soupis publikovaných prací pana doc. Ing. Václava Šebesty, DrSc., zpracovaný v říjnu 2015 knihovnou Ústavu informatiky AV ČR, v. v. i. k příležitosti 70. narozenin autora Nývltová, Ludmila; Ramešová, Nina; Šírová, Tereza 2015 - Czech Keywords: bibliografie Available in a digital repository NRGL Soupis publikovaných prací pana doc. Ing. Václava Šebesty, DrSc., zpracovaný v říjnu 2015 knihovnou Ústavu informatiky AV ČR, v. v. i. k příležitosti 70. narozenin autora

Nývltová, Ludmila; Ramešová, Nina; Šírová, Tereza
Ústav informatiky, 2015

### On Two Methods for the Parameter Estimation Problem with Spatio-Temporal FRAP Data Papáček, Š.; Jablonský, J.; Matonoha, Ctirad 2015 - English FRAP (Fluorescence Recovery After Photobleaching) is a measurement technique for determination of the mobility of fluorescent molecules (presumably due to the diffusion process) within the living cells. While the experimental setup and protocol are usually fixed, the method used for the model parameter estimation, i.e. the data processing step, is not well established. In order to enhance the quantitative analysis of experimental (noisy) FRAP data, we firstly formulate the inverse problem of model parameter estimation and then we focus on how the different methods of data pre- processing influence the confidence interval of the estimated parameters, namely the diffusion constant $p$. Finally, we present a preliminary study of two methods for the computation of a least-squares estimate $\hat{p}$ and its confidence interval. Keywords: parameter estimation; fluorescence recovery after photobleaching; diffusion equation; Moullineaux method; Fisher information matrix; sensitivity analysis; confidence intervals; uncertainty quantification Available in digital repository of the ASCR On Two Methods for the Parameter Estimation Problem with Spatio-Temporal FRAP Data

FRAP (Fluorescence Recovery After Photobleaching) is a measurement technique for determination of the mobility of fluorescent molecules (presumably due to the diffusion process) within the living ...

Papáček, Š.; Jablonský, J.; Matonoha, Ctirad
Ústav informatiky, 2015