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Books on the topic 'Conditionally independent random variables'

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Published: 1 June 2024

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1

Braverman, Michael Sh. Independent random variables and rearrangement invariant spaces. Cambridge: Cambridge University Press, 1994.

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2

M, Lee Lawrence, Nicol David, and United States. National Aeronautics and Space Administration., eds. On the minimum of independent geometrically distributed random variables. Hampton, VA: Institute for Computer Applications in Science and Engineering, NASA Langley Research Center, 1994.

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3

Arak, T. V. Uniform limit theorems for sums of independent random variables. Providence, R.I: American Mathematical Society, 1988.

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4

Petrov, V. V. Limit theorems of probability theory: Sequences of independent random variables. Oxford: Clarendon Press, 1995.

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5

Meerschaert, Mark M. Limit Distributions for Sums of Independent Random Vectors: Heavy Tails in Theory and Practice. New York, USA: John Wiley & Sons, 2001.

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6

Lawler, Gregory F. Random walk and the heat equation. Providence, R.I: American Mathematical Society, 2010.

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7

Lemeshko, Boris, and Irina Veretel'nikova. Criteria for testing hypotheses about randomness and the absence of a trend. Application Guide. ru: INFRA-M Academic Publishing LLC., 2021. http://dx.doi.org/10.12737/1587437.

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The monograph discusses the application of statistical criteria aimed at testing hypotheses about the absence of a trend in the analyzed samples. The rejection of such a hypothesis gives grounds to consider the analyzed data as samples of independent equally distributed random variables. We consider a set of special criteria aimed at testing such hypotheses, as well as a set of criteria for the uniformity of laws, the uniformity of averages and the uniformity of variances, which can also be used for these purposes. The disadvantages and advantages of various criteria are emphasized, the application of criteria in conditions of violation of standard assumptions is considered. Estimates of the power of the criteria are given, which allows you to navigate when choosing the most preferred criteria. Following the recommendations will ensure the correctness and increase the validity of statistical conclusions when analyzing data. It is intended for specialists who are interested in the application of statistical methods for the analysis of various aspects and trends of the surrounding reality and who are in contact with the processing of experimental results, the need for data analysis in their activities. It will be useful for engineers, researchers, specialists of various profiles (doctors, biologists, sociologists, economists, etc.) who face the need for statistical analysis of experimental results in their activities. It will also be useful for university teachers, graduate students and students.

8

Schurz, Henri, Philip J. Feinsilver, Gregory Budzban, and Harry Randolph Hughes. Probability on algebraic and geometric structures: International research conference in honor of Philip Feinsilver, Salah-Eldin A. Mohammed, and Arunava Mukherjea, June 5-7, 2014, Southern Illinois University, Carbondale, Illinois. Edited by Mohammed Salah-Eldin 1946- and Mukherjea Arunava 1941-. Providence, Rhode Island: American Mathematical Society, 2016.

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9

Brown, A. A., and V. V. Petrov. Sums of Independent Random Variables. de Gruyter GmbH, Walter, 2022.

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10

Brown, A. A., and V. V. Petrov. Sums of Independent Random Variables. Springer, 2011.

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11

Petrov, Valentin, and A. A. Brown. Sums of Independent Random Variables. Springer, 2011.

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12

Braverman, Michael Sh. Independent Random Variables and Rearrangement Invariant Spaces. Cambridge University Press, 2010.

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13

Braverman, Michael Sh. Independent Random Variables and Rearrangement Invariant Spaces. Cambridge University Press, 2011.

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14

Gnedenko, B. V., K. L. Chung, and A. N. Kolmogorov. Limit Distributions for Sums of Independent Random Variables. Martino Fine Books, 2021.

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15

A. N. (Andreĭ Nikolaevich) Kolmogorov and B. V. (Boris Vladimirovich) Gnedenko. Limit Distributions for Sums of Independent Random Variables. Creative Media Partners, LLC, 2021.

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16

Korolev, V. Y., and V. M. Zolotarev. Limit Distributions for Sums of Independent Random Variables. Brill Academic Pub, 2007.

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17

Gnedenko, B. V. Limit distributions for sums of independent random variables. 2nd ed. Wiley, 1994.

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18

Independent Component Analysis: Algorithms, Applications and Ambiguities. New York, USA: Nova Science Pub Inc., 2018.

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19

Hájek, Alan, and Christopher Hitchcock. Probability for Everyone—Even Philosophers. Edited by Alan Hájek and Christopher Hitchcock. Oxford University Press, 2017. http://dx.doi.org/10.1093/oxfordhb/9780199607617.013.2.

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In this chapter the basics of probability theory are introduced, with particular attention to those topics that are most important for applications in philosophy. The formalism is described in two passes. The first presents finite probability, which suffices for most philosophical discussions of probability. The second presents measure theory, which is needed for applications involving infinities or limits. Key concepts such as conditional probability, probabilistic independence, random variables, and expectation are defined. In addition, several important theorems, including Bayes’ theorem, the weak and strong laws of large numbers, and the central limit theorem are defined. Along the way, several familiar puzzles or paradoxes involving probability are discussed.

20

Butyrskiy, Evgeniy. Methods for modeling and estimating random variables and processes. Strategy of the Future, 2020. http://dx.doi.org/10.37468/mon_1850.

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The monograph introduces the basics of theory and practice of mathematical research methods of stochastic systems and processes. It examines the models, methods of describing and forming random events, values and processes, as well as methods of their optimal and suboptimal assessment. The monograph can be useful for a wide range of specialists in various fields of expertise in mathematical and statistical modeling in their research, and can also be used in the learning process to conduct both classroom, and independent theoretical and practical classes with students and masters of St. Petersburg State University engaged in the program «Mathematical modeling» and «Optimal and suboptimal assessment of random processes and systems».

21

Meerschaert, Mark M., and Hans-Peter Scheffler. Limit Distributions for Sums of Independent Random Vectors: Heavy Tails in Theory and Practice (Wiley Series in Probability and Statistics). Wiley-Interscience, 2001.

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22

Bellhouse, David. Probability and Its Application in Britain during the 17th and 18th Centuries. Edited by Alan Hájek and Christopher Hitchcock. Oxford University Press, 2017. http://dx.doi.org/10.1093/oxfordhb/9780199607617.013.5.

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In the 18th and 19th centuries, probability was a part of moral and natural sciences, rather than of mathematics. Still, since Laplace’s 1812 Théorie analytique des probabilités, specific analytic methods of probability aroused the interest of mathematicians, and probability began to develop a purely mathematical quality. In the 20th century the mathematical essence reached full autonomy and constituted “modern” probability. Significant in this development was the gradual introduction of a measure theoretic framework. In this way, the main subfields of modern probability, as axiomatics, weak and strong limit theorems, sequences of non-independent random variables, and stochastic processes, could be integrated into a well-connected complex until World War II.

23

Scarani, Valerio. Bell Nonlocality. Oxford University Press, 2019. http://dx.doi.org/10.1093/oso/9780198788416.001.0001.

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Nonlocality was discovered by John Bell in 1964, in the context of the debates about quantum theory, but is a phenomenon that can be studied in its own right. Its observation proves that measurements are not revealing pre-determined values, falsifying the idea of “local hidden variables” suggested by Einstein and others. One is then forced to make some radical choice: either nature is intrinsically statistical and individual events are unspeakable, or our familiar space-time cannot be the setting for the whole of physics. As phenomena, nonlocality and its consequences will have to be predicted by any future theory, and may possibly play the role of foundational principles in these developments. But nonlocality has found a role in applied physics too: it can be used for “device-independent” certification of the correct functioning of random number generators and other devices. After a self-contained introduction to the topic, this monograph on nonlocality presents the main tools and results following a logical, rather than a chronological, order.

24

Adams, Karen Ruth. The Causes of War. Oxford University Press, 2017. http://dx.doi.org/10.1093/acrefore/9780190846626.013.323.

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The scientific study of war is a pressing concern for international politics. Given the destructive nature of war, ordinary citizens and policy makers alike are eager to anticipate if not outright avoid outbreaks of violence. Understanding the causes of war can be a complex process. Scholars of international relations must first define war, and then establish a universe of actors or conflicts in which both war and peace are possible. Next, they must collect data on the incidence of war in the entire universe of cases over a particular period of time, a random sample of relevant cases, a number of representative cases, or a set of cases relevant to independent variables in the theories they are testing. Finally, scholars must use this data to construct quantitative and qualitative tests of hypotheses about why actors fight instead of resolving their differences in other ways and, in particular, why actors initiate wars by launching the first attack. Instead of taking the inductive approach of inventorying the causes of particular wars and then attempting to find general rules, it is necessary for scholars to approach the problem deductively, developing theories about the environment in which states operate, deriving hypotheses about the incidence of war and attack, and using quantitative and qualitative methods to test these hypotheses.

25

RANGANATHAN, VINAY, and E. ESWARA REDDY. A STUDY ON LEADERSHIP STYLES OF PRINCIPALS AND ORGANIZATIONAL COMMITMENT OF TEACHERS IN SECONDARY SCHOOLS OF BENGALURU CITY. Jupiter Publications Consortium, 2023. http://dx.doi.org/10.47715/jpc.b.978-93-91303-72-3.

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The problem statement of the study was to compare the educational leadership behaviours of government and private school principals in Bengaluru city and to understand the organizational commitment of teachers in relation to demographic variables. The objectives were i) to study perceptions of secondary school teachers on the leadership styles of their Principals ii) to compare the differences in leadership attributes between government and private school principals in select schools of Bengaluru city iii) to study the influence of demographic variables on the organizational commitment of the teachers iv) to provide valuable suggestions to policy makers on building a successful institution to get better results The sample of the study was drawn using random sampling technique from 56 schools and consisted of 384 teachers: 107 teachers from government and 277 teachers from private high schools in Bengaluru city (urban district). The theoretical backdrop of the research was based on transactional and transformational leadership theories. Modified versions of the multifactor leadership and the organizational commitment questionnaire was used for the study. Statistical analysis using mean, standard deviation, independent samples ‘t’ tests, one-way ANOVA and confirmatory factor analysis was used for analysis of data. The major findings of the study were that i) differences on certain attributes were observed in both transactional and transformational leadership styles between government and private school principals. ii) ‘Critical thinking’ and ‘participative’ were the styles of leadership practiced in government schools. iii) ‘Micromanagement’ and ‘charismatic’ were the styles of leadership practiced in private schools iv) personal variables like gender and age were found to have significant impact on organizational commitment of teachers iv) academic variables like experience and educational qualifications were found to have significant impact on organizational commitment of teachers. Separate leadership models for both government and private schools were developed by the researcher highlighting important attributes that lead to the growth and the success of an organization. The study has also provided principals with an overview on what factors affected the teacher’s commitment in their schools and how they could effectively modify their leadership style to improve efficiency in teaching and learning. Suggestions are provided separately for policy makers in the government and for private managements on approaches to improve effective leadership in government and private schools In conclusion, experience of these principals, journey into their administration and the way in which they have articulated their role over the years has given valuable insights for the future generation. There is no doubt that transformational leadership is the right way forward in Indian educational administration and implications of this research must reach beyond Bengaluru to enable teachers and Principals across the country to work together to build a strong society for the citizens of tomorrow.