Statistics Academic Discipline
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A Statistics Academic Discipline is a mathematical discipline that studies the properties of a statistics subject area.
- Context:
- It can add Statistical Concepts.
- It can involve:
- Statistics Research into Statistics Theory, produces Statistics Algorithms and new Statistics Tasks.
- Statistics Application/Statistics Applied Practice/Applied Statistics of Statistics Theory to some Applied Domains.
- Statistics Education, that produces Statistics Practitioners.
- It can involve Statistics Systems.
- It has a Statistics Terminology that can be partially represented in a Statistics Glossary.
- …
- Counter-Example(s):
- See: Statistics Subject Area, Probability Theory, Bayesian Theory, Frequentist Theory.
References
2017
- (Wikipedia, 2017) ⇒ https://en.wikipedia.org/wiki/Statistics Retrieved:2017-8-17.
- Statistics is a branch of mathematics dealing with the collection, analysis, interpretation, presentation, and organization of data.[1] In applying statistics to, e.g., a scientific, industrial, or social problem, it is conventional to begin with a statistical population or a statistical model process to be studied. Populations can be diverse topics such as "all people living in a country" or "every atom composing a crystal." Statistics deals with all aspects of data including the planning of data collection in terms of the design of surveys and experiments. When census data cannot be collected, statisticians collect data by developing specific experiment designs and survey samples. Representative sampling assures that inferences and conclusions can reasonably extend from the sample to the population as a whole. An experimental study involves taking measurements of the system under study, manipulating the system, and then taking additional measurements using the same procedure to determine if the manipulation has modified the values of the measurements. In contrast, an observational study does not involve experimental manipulation. Two main statistical methods are used in data analysis: descriptive statistics, which summarize data from a sample using indexes such as the mean or standard deviation, and inferential statistics, which draw conclusions from data that are subject to random variation (e.g., observational errors, sampling variation). Descriptive statistics are most often concerned with two sets of properties of a distribution (sample or population): central tendency (or location) seeks to characterize the distribution's central or typical value, while dispersion (or variability) characterizes the extent to which members of the distribution depart from its center and each other. Inferences on mathematical statistics are made under the framework of probability theory, which deals with the analysis of random phenomena. A standard statistical procedure involves the test of the relationship between two statistical data sets, or a data set and synthetic data drawn from idealized model. A hypothesis is proposed for the statistical relationship between the two data sets, and this is compared as an alternative to an idealized null hypothesis of no relationship between two data sets. Rejecting or disproving the null hypothesis is done using statistical tests that quantify the sense in which the null can be proven false, given the data that are used in the test. Working from a null hypothesis, two basic forms of error are recognized: Type I errors (null hypothesis is falsely rejected giving a "false positive") and Type II errors (null hypothesis fails to be rejected and an actual difference between populations is missed giving a "false negative"). Multiple problems have come to be associated with this framework: ranging from obtaining a sufficient sample size to specifying an adequate null hypothesis. Measurement processes that generate statistical data are also subject to error. Many of these errors are classified as random (noise) or systematic (bias), but other types of errors (e.g., blunder, such as when an analyst reports incorrect units) can also be important. The presence of missing data or censoring may result in biased estimates and specific techniques have been developed to address these problems.
Statistics can be said to have begun in ancient civilization, going back at least to the 5th century BC, but it was not until the 18th century that it started to draw more heavily from calculus and probability theory.
- Statistics is a branch of mathematics dealing with the collection, analysis, interpretation, presentation, and organization of data.[1] In applying statistics to, e.g., a scientific, industrial, or social problem, it is conventional to begin with a statistical population or a statistical model process to be studied. Populations can be diverse topics such as "all people living in a country" or "every atom composing a crystal." Statistics deals with all aspects of data including the planning of data collection in terms of the design of surveys and experiments. When census data cannot be collected, statisticians collect data by developing specific experiment designs and survey samples. Representative sampling assures that inferences and conclusions can reasonably extend from the sample to the population as a whole. An experimental study involves taking measurements of the system under study, manipulating the system, and then taking additional measurements using the same procedure to determine if the manipulation has modified the values of the measurements. In contrast, an observational study does not involve experimental manipulation. Two main statistical methods are used in data analysis: descriptive statistics, which summarize data from a sample using indexes such as the mean or standard deviation, and inferential statistics, which draw conclusions from data that are subject to random variation (e.g., observational errors, sampling variation). Descriptive statistics are most often concerned with two sets of properties of a distribution (sample or population): central tendency (or location) seeks to characterize the distribution's central or typical value, while dispersion (or variability) characterizes the extent to which members of the distribution depart from its center and each other. Inferences on mathematical statistics are made under the framework of probability theory, which deals with the analysis of random phenomena. A standard statistical procedure involves the test of the relationship between two statistical data sets, or a data set and synthetic data drawn from idealized model. A hypothesis is proposed for the statistical relationship between the two data sets, and this is compared as an alternative to an idealized null hypothesis of no relationship between two data sets. Rejecting or disproving the null hypothesis is done using statistical tests that quantify the sense in which the null can be proven false, given the data that are used in the test. Working from a null hypothesis, two basic forms of error are recognized: Type I errors (null hypothesis is falsely rejected giving a "false positive") and Type II errors (null hypothesis fails to be rejected and an actual difference between populations is missed giving a "false negative"). Multiple problems have come to be associated with this framework: ranging from obtaining a sufficient sample size to specifying an adequate null hypothesis. Measurement processes that generate statistical data are also subject to error. Many of these errors are classified as random (noise) or systematic (bias), but other types of errors (e.g., blunder, such as when an analyst reports incorrect units) can also be important. The presence of missing data or censoring may result in biased estimates and specific techniques have been developed to address these problems.
2009
- Master's Degree in Statistics at the University of Chicago. http://www.stat.uchicago.edu/admissions/ms-degree.html
- Data Analysis: This is the core of the subject, teaching you the principles and methods for analyzing data and designing experiments. Provides a broad background for working as a statistician in industry or government.
- Mathematical Statistics: Focuses on theoretical statistics, probability and stochastic processes. Provides an excellent background for pursuing doctoral studies in statistics, finance and other disciplines in which probability and statistics are heavily used.
- Biostatistics: Biology, medicine and psychology are major areas where quantitative analysis are essential. The program relies on an intimate collaboration with practitioners in the University of Chicago Pritzker School of Medicine. Several courses that are suitable for this track are offered by the Health Studies Department.
- Statistical Genetics: Statistics plays an important role in modern genetics and bioinformatics. Faculty in the Department of Statistics have broad interests in this area including gene mapping, analysis of gene expression data, and other mathematical and statistical problems arising in genetics. Additional coursework beyond the usual program may be required, and even well-prepared students may need at least part of a second year to specialize in statistical genetics.
- Statistics and Finance: The use of statistics and probability both for derivative securities and in other areas of finance is a rapidly increasing phenomenon. The program is, in particular, designed to provide you with a deep understanding of the hedging principles that underlie options theory. Sophisticated mathematical techniques for analyzing both standard and exotic options are taught. Due to the advanced nature of some of the topics covered in the relevant courses, even well-prepared students may need at least part of a second year to specialize in finance.
- Computer Vision: Object recognition and detection, in medical imaging, regular photos, digitized documents and a variety of other sources - is a recurrent and critical issue in science, industry and modern communications. The faculty includes specialists in the analysis of visual signals.
- Survey Statistics: Statistical surveys are important and pervasive in the modern world. Governments use survey statistics to establish policy and trigger actions; businesses use survey data to make important decisions about products and services, prices, and promotions; academic and other researchers conduct analysis of survey data to make new scientific discoveries in fields such as education, labor economics, environmetrics, health care, agriculture, forestry, sociology, and criminal justice, among many others. This program provides students instruction in the design, operations, and analysis of modern surveys. It offers students an opportunity to collaborate with survey experts among the faculty of the university and with survey practitioners at the NORC, a renowned survey organization that is affiliated with the university.
2006
- (Dubnicka, 2006c) ⇒ Suzanne R. Dubnicka. (2006). “Introduction to Probability and Statistics I, STAT 510. Kansas State University, Fall 2006.
2003
- (Davison, 2003) ⇒ Anthony C. Davison. (2003). “Statistical Models." Cambridge University Press. ISBN:0521773393
- Statistics concerns what can be learned from data. Applied statistics comprises a body of methods for data collection and analysis across the whole range of science, and in areas such as engineering, medicine, business, and law — wherever variable data must be summarized, or used to test or confirm theories, or to inform decisions. Theoretical statistics underpins this by providing a framework for understanding the properties and scope of methods used in applications.
1987
- (Hogg & Ledolter, 1987) ⇒ Robert V. Hogg and Johannes Ledolter. (1987). “Engineering Statistics. Macmillan Publishing Company.
1986
- (Larsen & Marx, 1986) ⇒ Richard J. Larsen, and Morris L. Marx. (1986). “An Introduction to Mathematical Statistics and Its Applications, 2nd edition." Prentice Hall
- ↑ Dodge, Y. (2006) The Oxford Dictionary of Statistical Terms, OUP.