**493**

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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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**City simulation software for modeling, planning, and strategic assessment of territorial city units**

Svítek, M.; Přibyl, O.; Vorel, J.; Garlík, B.; Resler, Jaroslav; Kozhevnikov, S.; Krč, Pavel; Geletič, Jan; Daniel, Milan; Dostál, R.; Janča, T.; Myška, V.; Aralkina, O.; Pereira, A. M.

2021 - English
SVÍTEK, M., PŘIBYL, O., VOREL, J., GARLÍK, B., RESLER, J., KOZHEVNIKOV, S., KRČ, P., GELETIČ, J., DANIEL, M., DOSTÁL, R., JANČA, T., MYŠKA, V., ARALKINA, O., PEREIRA, A. M. City simulation software for modeling, planning, and strategic assessment of territorial city units. 1.1. Prague: CTU & ICS CAS, 2021. Technical Report. ABSTRACT: The Smart Resilience City concept is a new vision of a city as a digital platform and eco-system of smart services where agents of people, things, documents, robots, and other entities can directly negotiate with each other on resource demand principals providing the best possible solution. It creates the smart environment making possible self-organization in sustainable or, when needed, resilient way of individuals, groups and the whole system objectives.
Keywords:
*Smart city; City simulation; Energy resource-demand modelling; Environmental modelling; Synthetic population; Transport modelling*
Available on request at various institutes of the ASCR
City simulation software for modeling, planning, and strategic assessment of territorial city units

SVÍTEK, M., PŘIBYL, O., VOREL, J., GARLÍK, B., RESLER, J., KOZHEVNIKOV, S., KRČ, P., GELETIČ, J., DANIEL, M., DOSTÁL, R., JANČA, T., MYŠKA, V., ARALKINA, O., PEREIRA, A. M. City simulation software ...

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**Score matching filters for Gaussian Markov random fields with a linear model of the precision matrix**

Turčičová, Marie; Mandel, J.; Eben, Kryštof

2021 - English
We present an ensemble filter that provides a rigorous covariance regularization when the underlying random field is Gaussian Markov. We use a linear model for the precision matrix (inverse of covariance) and estimate its parameters together with the analysis mean by the Score Matching method. This procedure provides an explicit expression for parameter estimators. The resulting analysis step formula is the same as in the traditional ensemble Kalman filter.
Keywords:
*Score matching; ensemble filter; Gaussian Markov random field; covariance modelling*
Available at various institutes of the ASCR
Score matching filters for Gaussian Markov random fields with a linear model of the precision matrix

We present an ensemble filter that provides a rigorous covariance regularization when the underlying random field is Gaussian Markov. We use a linear model for the precision matrix (inverse of ...

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**Assessment of Independent EEG Components Obtained by Different Methods for BCI Based on Motor Imagery**

Húsek, Dušan; Frolov, A. A.; Kerechanin, J. V.; Bobrov, P.D.

2021 - English
Eight methods of decomposition of a multichannel EEG signal are compared in terms of their ability to identify the most physiologically significant components. The criterion for the meaningfulness of a method is its ability to reduce mutual information between components; to create components that can be attributed to the activity of dipoles located in the cerebral cortex; find components that are provided by other methods and for this case; and at the same time, these components should most contribute to the accuracy of the BCI based on imaginary movement. Independent component analysis methods AMICA, RUNICA and FASTICA outperform others in the first three criteria and are second only to the Common Spatial Patterns method in the fourth criterion. The components created by all methods for 386 experimental sessions of 27 subjects were combined into more than 100 clusters containing more than 10 elements. Additionally, the components of the 12 largest clusters were analyzed. They have proven to be of great importance in controlling BCI, their origins can be modeled using dipoles in the brain, and they have been detected by several degradation methods. Five of the 12 selected components have been identified and described in our previous articles. Even if the physiological and functional origins of the rest of identified components’ are to be the subject of further research, we have shown that their physiological nature is at least highly probable.\n
Keywords:
*brain–computer interface; motor imagery; blind source separation; independent component analysis; common spatial patterns; cluster analysis; EEG pattern extraction; EEG analysis; ICA; CSP; BCI; motor imagery*
Available at various institutes of the ASCR
Assessment of Independent EEG Components Obtained by Different Methods for BCI Based on Motor Imagery

Eight methods of decomposition of a multichannel EEG signal are compared in terms of their ability to identify the most physiologically significant components. The criterion for the meaningfulness of ...

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**Visual Images Segmentation based on Uniform Textures Extraction**

Goltsev, A.; Gritsenko, V.; Húsek, Dušan

2020 - English
A new effective procedure for partial texture segmentation of visual images is proposed. The procedure segments any input image into a number of non-overlapping homogeneous ne-grained texture areas. The main advantages of the proposed procedure are as follows. It is completely unsupervised, that is, it processes the input image without any prior knowledge of either the type of textures or the number of texture segments in the image. In addition, the procedure segments arbitrary images of all types. This means that no changes to the procedure parameters are required to switch from one image type to another. Another major advantage of the procedure is that in most cases it extracts the uniform ne-grained texture segments present in the image, just as humans do. This result is supported by series of experiments that demonstrate the ability of the procedure to delineate uniform ne-grained texture segments over a wide range of images. At a minimum, image processing according to the proposed technique leads to a signficant reduction in the uncertainty of the internal structure of the analyzed image.
Keywords:
*Texture feature; Texture window; Homogeneous ne-grained texture segment; Texture segment extraction; Texture segmentation*
Available at various institutes of the ASCR
Visual Images Segmentation based on Uniform Textures Extraction

A new effective procedure for partial texture segmentation of visual images is proposed. The procedure segments any input image into a number of non-overlapping homogeneous ne-grained texture areas. ...

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**The scalar-valued score functions of continuous probability distribution**

Fabián, Zdeněk

2019 - English
In this report we give theoretical basis of probability theory of continuous random variables based on scalar valued score functions. We maintain consistently the following point of view: It is not the observed value, which is to be used in probabilistic and statistical considerations, but its 'treated form', the value of the scalar-valued score function of distribution of the assumed model. Actually, the opinion that an observed value of random variable should be 'treated' with respect to underlying model is one of main ideas of the inference based on likelihood in classical statistics. However, a vector nature of Fisher score functions of classical statistics does not enable a consistent use of this point of view. Instead, various inference functions are suggested and used in solutions of various statistical problems. Inference function of this report is the scalar-valued score function of distribution.
Keywords:
*Shortcomings of probability theory; Scalar-valued score functions; Characteristics of continous random variables; Parametric estimation; Transformed distributions; Skew-symmetric distributions*
Available at various institutes of the ASCR
The scalar-valued score functions of continuous probability distribution

In this report we give theoretical basis of probability theory of continuous random variables based on scalar valued score functions. We maintain consistently the following point of view: It is not ...

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