Start Date: 09/15/2019
Course Type: Common Course |
Course Link: https://www.coursera.org/learn/bayesian-statistics
Explore 1600+ online courses from top universities. Join Coursera today to learn data science, programming, business strategy, and more.In this module, we review the basics of probability and Bayes’ theorem. In Lesson 1, we introduce the different paradigms or definitions of probability and discuss why probability provides a coherent framework for dealing with uncertainty. In Lesson 2, we review the rules of conditional probability and introduce Bayes’ theorem. Lesson 3 reviews common probability distributions for discrete and continuous random variables.
This course introduces the Bayesian approach to statistics, starting with the concept of probability
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Robust Bayesian analysis | In statistics, robust Bayesian analysis, also called Bayesian sensitivity analysis, is a type of sensitivity analysis applied to the outcome from Bayesian inference or Bayesian optimal decisions. |
Bayesian statistics | Bayesian statistics, named for Thomas Bayes (1701–1761), is a theory in the field of statistics in which the evidence about the true state of the world is expressed in terms of "degrees of belief" known as Bayesian probabilities. Such an interpretation is only one of a number of interpretations of probability and there are other statistical techniques that are not based on 'degrees of belief'. One of the key ideas of Bayesian statistics is that "probability is orderly opinion, and that inference from data is nothing other than the revision of such opinion in the light of relevant new information." |
Foundations of statistics | Statistics later developed in different directions including decision theory (and possibly game theory), Bayesian statistics, exploratory data analysis, robust statistics and nonparametric statistics. Neyman–Pearson hypothesis testing contributed strongly to decision theory which is very heavily used (in statistical quality control for example). Hypothesis testing readily generalized to accept prior probabilities which gave it a Bayesian flavor. |
Data science | Data science is a "concept to unify statistics, data analysis and their related methods" in order to "understand and analyze actual phenomena" with data. |
Bayesian inference | Bayesian inference is a method of statistical inference in which Bayes' theorem is used to update the probability for a hypothesis as more evidence or information becomes available. Bayesian inference is an important technique in statistics, and especially in mathematical statistics. Bayesian updating is particularly important in the dynamic analysis of a sequence of data. Bayesian inference has found application in a wide range of activities, including science, engineering, philosophy, medicine, sport, and law. In the philosophy of decision theory, Bayesian inference is closely related to subjective probability, often called "Bayesian probability". |
Geometric data analysis | Geometric data analysis can refer to geometric aspects of image analysis, pattern analysis and shape analysis or the approach of multivariate statistics that treats arbitrary data sets as "clouds of points" in "n"-dimensional space. This includes topological data analysis, cluster analysis, inductive data analysis, correspondence analysis, multiple correspondence analysis, principal components analysis and . |
Bayesian statistics | Bayesian inference is an approach to statistical inference that is distinct from frequentist inference. It is specifically based on the use of Bayesian probabilities to summarize evidence. |
Computational Statistics & Data Analysis | Computational Statistics & Data Analysis is a monthly peer-reviewed scientific journal covering research on and applications of computational statistics and data analysis. The journal was established in 1983 and is the official journal of the International Association for Statistical Computing, a section of the International Statistical Institute. |
Bayesian Operational Modal Analysis | Bayesian Operational Modal Analysis (BAYOMA) adopts a Bayesian system identification approach for Operational Modal Analysis (OMA). Operational Modal Analysis (OMA) aims at identifying the modal properties (natural frequencies, damping ratios, mode shapes, etc.) of a constructed structure using only its (output) vibration response (e.g., velocity, acceleration) measured under operating conditions. The (input) excitations to the structure are not measured but are assumed to be 'ambient' ('broadband random'). In a Bayesian context, the set of modal parameters are viewed as uncertain parameters or random variables whose probability distribution is updated from the prior distribution (before data) to the posterior distribution (after data). The peak(s) of the posterior distribution represents the most probable value(s) (MPV) suggested by the data, while the spread of the distribution around the MPV reflects the remaining uncertainty of the parameters. |
Data analysis | Statistician John Tukey defined data analysis in 1961 as: "Procedures for analyzing data, techniques for interpreting the results of such procedures, ways of planning the gathering of data to make its analysis easier, more precise or more accurate, and all the machinery and results of (mathematical) statistics which apply to analyzing data." |
Bayesian statistics | The formulation of statistical models using Bayesian statistics has the unique feature of requiring the specification of prior distributions for any unknown parameters. These prior distributions are as integral to a Bayesian approach to statistical modelling as the expression of probability distributions. Prior distributions can be either hyperparameters or hyperprior distributions. |
Bayesian Analysis (journal) | Bayesian Analysis is an open-access peer-reviewed scientific journal covering theoretical and applied aspects of Bayesian methods. It is published by the International Society for Bayesian Analysis and is hosted at the Project Euclid web site. |
Data analysis | Barriers to effective analysis may exist among the analysts performing the data analysis or among the audience. Distinguishing fact from opinion, cognitive biases, and innumeracy are all challenges to sound data analysis. |
Statistics | There are two applications for machine learning and data mining: data management and data analysis. Statistics tools are necessary for the data analysis. |
Data analysis | Data mining is a particular data analysis technique that focuses on modeling and knowledge discovery for predictive rather than purely descriptive purposes, while business intelligence covers data analysis that relies heavily on aggregation, focusing on business information. In statistical applications data analysis can be divided into descriptive statistics, exploratory data analysis (EDA), and confirmatory data analysis (CDA). EDA focuses on discovering new features in the data and CDA on confirming or falsifying existing hypotheses. Predictive analytics focuses on application of statistical models for predictive forecasting or classification, while text analytics applies statistical, linguistic, and structural techniques to extract and classify information from textual sources, a species of unstructured data. All are varieties of data analysis. |
Bayesian statistics | The Bayesian design of experiments includes a concept called 'influence of prior beliefs'. This approach uses sequential analysis techniques to include the outcome of earlier experiments in the design of the next experiment. This is achieved by updating 'beliefs' through the use of prior and posterior distribution. This allows the design of experiments to make good use of resources of all types. An example of this is the multi-armed bandit problem. |
Data analysis | Data integration is a precursor to data analysis, and data analysis is closely linked to data visualization and data dissemination. The term "data analysis" is sometimes used as a synonym for data modeling. |
Structured data analysis (statistics) | Structured data analysis is the statistical data analysis of structured data. This can arise either in the form of an "a priori" structure such as multiple-choice questionnaires or in situations with the need to search for structure that fits the given data, either exactly or approximately. This structure can then be used for making comparisons, predictions, manipulations etc. |
Bayesian network | Given data formula_27 and parameter formula_28, a simple Bayesian analysis starts with a prior probability ("prior") formula_29 and likelihood formula_30 to compute a posterior probability formula_31. |
Bayesian classifier | In computer science and statistics, Bayesian classifier may refer to: |