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Maria Cristina Mariani - Data Science in Theory and Practice

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Название:
Data Science in Theory and Practice
Автор:
Maria Cristina Mariani
Жанр:
unrecognised / на английском языке
Год:
неизвестен
ISBN:
нет данных
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Data Science in Theory and Practice: краткое содержание, описание и аннотация

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DATA SCIENCE IN THEORY AND PRACTICE delivers a comprehensive treatment of the mathematical and statistical models useful for analyzing data sets arising in various disciplines, like banking, finance, health care, bioinformatics, security, education, and social services. Written in five parts, the book examines some of the most commonly used and fundamental mathematical and statistical concepts that form the basis of data science. The authors go on to analyze various data transformation techniques useful for extracting information from raw data, long memory behavior, and predictive modeling. The book offers readers a multitude of topics all relevant to the analysis of complex data sets. Along with a robust exploration of the theory underpinning data science, it contains numerous applications to specific and practical problems. The book also provides examples of code algorithms in R and Python and provides pseudo-algorithms to port the code to any other language. Ideal for students and practitioners without a strong background in data science, readers will also learn from topics like: Analyses of foundational theoretical subjects, including the history of data science, matrix algebra and random vectors, and multivariate analysis A comprehensive examination of time series forecasting, including the different components of time series and transformations to achieve stationarity Introductions to both the R and Python programming languages, including basic data types and sample manipulations for both languages An exploration of algorithms, including how to write one and how to perform an asymptotic analysis A comprehensive discussion of several techniques for analyzing and predicting complex data sets Perfect for advanced undergraduate and graduate students in Data Science, Business Analytics, and Statistics programs,
will also earn a place in the libraries of practicing data scientists, data and business analysts, and statisticians in the private sector, government, and academia.

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where denotes the population covariance matrix which is defined in 35 - фото 465

where картинка 466 denotes the population covariance matrix which is defined in ( 3.5).

Finally, the population correlation of and is defined as where - фото 467 and is defined as where denotes the population covariance matrix which is - фото 468 is defined as

where denotes the population covariance matrix which is defined in 35 - фото 469

where картинка 470 denotes the population covariance matrix which is defined in ( 3.5).

Remarks 3.1If картинка 471 is a scalar matrix and картинка 472 are random vectors, then represents several linear combinations. The population mean vector and covariance matrix are given by

where denotes the population mean vector and - фото 474

where denotes the population mean vector and denotes the population covari - фото 475

where картинка 476 denotes the population mean vector and картинка 477 denotes the population covariance matrix which is defined in ( 3.5).

The proof of Remark 3.1 is left as an exercise. Please see Problem 2.

Please refer to Johnson and Wichern (2014), Rencher (2002), and Axler (2002) and references therein for more details of multivariate analysis.

3.7 Problems

1 The following are four measurements on the variables and :91251600143587Use the above information to answer the following questions:Find the sample mean vector, .Find the sample covariance matrix, .Find the sample correlation matrix, .

2 For random vectors and , scalar matrices and , and scalar vectors and , prove the following:..., where denotes the population covariance matrix which is defined in ( 3.5)...

3 Consider the five pairs of measurements :3426855.54410CalculateThe sample means and .The sample variances and .The sample covariances

4 Consider the data matrix:Calculate the matrix of deviations (residuals), . Is this matrix of full rank?Note: A matrix is of full rank if all rows and columns are linearly independent. A square matrix is full rank if and only if its determinant is nonzero.

5 Calculate the sample covariance matrix using the data matrix in Problem 4.

6 Consider the data matrix:Obtain the mean corrected data matrix, sample covariance matrix and verify that the columns are linearly dependent.

7 If for , show that , where is a constant.

8 If for , show that , where is a constant.

9 The data in Table 3.1(Elston and Grizzle 1962) consist of measurements , and of the ramus bone at four different ages on each of 20 boys.Find .Find .Find . Table 3.1 Ramus Bone Length at Four Ages for 20 Boys.AgeIndividual147.848.849.049.7246.447.347.748.4346.346.847.848.5445.145.346.147.2547.648.548.949.3652.553.253.353.7751.253.054.354.5849.850.050.352.7948.150.852.354.41045.047.047.348.31151.251.451.651.91248.549.253.055.51352.152.853.755.01448.248.949.349.81549.650.451.251.81650.751.752.753.31747.247.748.449.51853.354.655.155.31946.247.548.148.42046.347.651.351.8

10 For the data in Table 3.1, define and .Find , , , and using ( 3.12) and ( 3.13).Find and using ( 3.14) and ( 3.15).

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