**1162**

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**Permutation Flip Processes**

Hladký, Jan; Řada, Hanka

2023 - English
We introduce a broad class of stochastic processes on permutations which we call flip processes. A single step in these processes is given by a local change on a randomly chosen fixed-sized tuple of the domain. We use the theory of permutons to describe the typical evolution of any such flip process started from any initial permutation. More specifically, we construct trajectories in the space of permutons with the property that if a finite permutation is close to a permuton then for any time it stays with high probability is close to this predicted trajectory. This view allows to study various questions inspired by dynamical systems.
Keywords:
*permutation; permuton; sorting dynamics; flip process*
Available in digital repository of the ASCR
Permutation Flip Processes

We introduce a broad class of stochastic processes on permutations which we call flip processes. A single step in these processes is given by a local change on a randomly chosen fixed-sized tuple of ...

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**Spatio-Spectral EEG Patterns in the Source-Reconstructed Space and Relation to Resting-State Networks: An EEG-fMRI Study**

Jiříček, Stanislav; Koudelka, V.; Mantini, D.; Mareček, R.; Hlinka, Jaroslav

2022 - English
In this work, we present and evaluate a novel EEG-fMRI integration approach combining a spatio-spectral decomposition method and a reliable source localization technique. On the large 72 subjects resting- state hdEEG-fMRI data set we tested the stability of the proposed method in terms of both extracted spatio-spectral patterns(SSPs) as well as their correspondence to the BOLD signal. We also compared the proposed method with the spatio-spectral decomposition in the electrode space as well as well-known occipital alpha correlate in terms of the explained variance of BOLD signal. We showed that the proposed method is stable in terms of extracted patterns and where they correlate with the BOLD signal. Furthermore, we show that the proposed method explains a very similar level of the BOLD signal with the other methods and that the BOLD signal in areas of typical BOLD functional networks is explained significantly more than by a chance. Nevertheless, we didn’t observe a significant relation between our source-space SSPs and the BOLD ICs when spatio-temporally comparing them. Finally, we report several the most stable source space EEG-fMRI patterns together with their interpretation and comparison to the electrode space patterns.
Keywords:
*EEG-fMRI Integration; EEG-informed fMRI; Spatio-spectral Decomposition; Electrical Source Imaging; Independent Component Analysis; Resting State Networks*
Available in digital repository of the ASCR
Spatio-Spectral EEG Patterns in the Source-Reconstructed Space and Relation to Resting-State Networks: An EEG-fMRI Study

In this work, we present and evaluate a novel EEG-fMRI integration approach combining a spatio-spectral decomposition method and a reliable source localization technique. On the large 72 subjects ...

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**Czech Gathering of Logicians 2022. Book of Abstracts**

Haniková, Zuzana; Švejdar, V.; Wannenburg, Johann Joubert

2022 - English
Fulltext is available at external website.
Czech Gathering of Logicians 2022. Book of Abstracts

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**A Bootstrap Comparison of Robust Regression Estimators**

Kalina, Jan; Janáček, Patrik

2022 - English
The ordinary least squares estimator in linear regression is well known to be highly vulnerable to the presence of outliers in the data and available robust statistical estimators represent more preferable alternatives. It has been repeatedly recommended to use the least squares together with a robust estimator, where the latter is understood as a diagnostic tool for the former. In other words, only if the robust estimator yields a very different result, the user should investigate the dataset closer and search for explanations. For this purpose, a hypothesis test of equality of the means of two alternative linear regression estimators is proposed here based on nonparametric bootstrap. The performance of the test is presented on three real economic datasets with small samples. Robust estimates turn out not to be significantly different from non-robust estimates in the selected datasets. Still, robust estimation is beneficial in these datasets and the experiments illustrate one of possible ways of exploiting the bootstrap methodology in regression modeling. The bootstrap test could be easily extended to nonlinear regression models.
Keywords:
*linear regression; robust estimation; nonparametric bootstrap; bootstrap hypothesis testing*
Fulltext is available at external website.
A Bootstrap Comparison of Robust Regression Estimators

The ordinary least squares estimator in linear regression is well known to be highly vulnerable to the presence of outliers in the data and available robust statistical estimators represent more ...

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**A Measure of Variability WIthin Parametric Families of Continuous Distributions**

Fabián, Zdeněk

2022 - English
A continuous probability measure on an open interval of the real line induces in it a unique geometry, "center of gravity" of which is the typical value of the distribution. In the paper is identified a score variance as a finite measure of variability of distributions with respect to the typical value and discussed its properties and methods of estimation. Itroducing a generalized Rao distance in the sample space one can appraise the precision of the estimate of the typical value.
Keywords:
*scalar-valued score; score mean; score variance; distance in the sample space*
Available at various institutes of the ASCR
A Measure of Variability WIthin Parametric Families of Continuous Distributions

A continuous probability measure on an open interval of the real line induces in it a unique geometry, "center of gravity" of which is the typical value of the distribution. In the paper is identified ...

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**Score correlation for skewed distributions**

Fabián, Zdeněk

2022 - English
Based on the new concept of the scalar-valued score function of continuous distributions we introduce the score correlation coeﬃcient ”tai-lored” to the assumed probabilistic model and study its properties by means of simulation experiments. It appeared that the new correlation method is useful for enormously skewed distributions.
Keywords:
*Scalar-valued score; score coeﬃcient of variation; Monte Carlo*
Available at various institutes of the ASCR
Score correlation for skewed distributions

Based on the new concept of the scalar-valued score function of continuous distributions we introduce the score correlation coeﬃcient ”tai-lored” to the assumed probabilistic model and study its ...

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**Introduction to statistical inference based on scalar-valued scores**

Fabián, Zdeněk

2022 - English
In the report we maintain consistently the following point of view: Given a continuous model, there are not the observed values, which are to be used in probabilistic and statistical considerations, but their ”treated forms”,the values of the scalar-valued score function corresponding to the model. Based on this modiﬁed concept of the score function, we develop theory of score random variables, study their geometry and deﬁne their new characteristics, ﬁnite even in cases of heavy-tailed models. A generalization for parametric families provides a new approach to parametric point estimation.
Keywords:
*continuous distributions; score mean; score variance; score moment estimation method; score distance*
Available at various institutes of the ASCR
Introduction to statistical inference based on scalar-valued scores

In the report we maintain consistently the following point of view: Given a continuous model, there are not the observed values, which are to be used in probabilistic and statistical considerations, ...

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**Scalar-Valued Score Functions and their use in Parametric Estimation**

Fabián, Zdeněk

2022 - English
In the paper we describe and explain a new direction in probabilistic and statistical reasoning, the approach based on scalar-valued score functions of continuous random variables. We show basic properties of score functions of standard distributions, generalize the approach for parametric families and show how to use them for solutions of problems of parametric statistics.
Keywords:
*core random variable; score mean; score variance; score distance; score correlation*
Available on request at various institutes of the ASCR
Scalar-Valued Score Functions and their use in Parametric Estimation

In the paper we describe and explain a new direction in probabilistic and statistical reasoning, the approach based on scalar-valued score functions of continuous random variables. We show basic ...

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**A New Look to Information and Uncertainty of Continuous Distributions**

Fabián, Zdeněk

2022 - English
We deﬁne information and uncertainty function of a family of continuous distributions. Their values are relative information and uncertainty of an observation from the given parametric family, their mean values are the generalized Fisher information and a new measure of variability, the score variance. In a series of examples we show why to use new concepts instead of the diﬀerential entropy.
Keywords:
*Diﬀerential entropy; information function; uncertainty function; mean information of distribution*
Available at various institutes of the ASCR
A New Look to Information and Uncertainty of Continuous Distributions

We deﬁne information and uncertainty function of a family of continuous distributions. Their values are relative information and uncertainty of an observation from the given parametric family, their ...

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**Large Perimeter Objects Surrounded by a 1.5D Terrain**

Keikha, Vahideh

2022 - English
Given is a 1.5D terrain T , i.e., an x-monotone polygonal chain in R2. Our objective is to approximate the largest area or perimeter convex polygon with at most k vertices inside T . For a constant k > 0, we design an FPTAS that efficiently approximates such polygons within a factor (1 − ǫ). For the special case of the´largest-perimeter contained triangle in T , we design an O(n log n) time exact algorithm that matches the same result for the area measure.
Available in digital repository of the ASCR
Large Perimeter Objects Surrounded by a 1.5D Terrain

Given is a 1.5D terrain T , i.e., an x-monotone polygonal chain in R2. Our objective is to approximate the largest area or perimeter convex polygon with at most k vertices inside T . For a constant k ...

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