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Bayesian Inference In Marketing
In marketing, Bayesian inference allows for decision making and market research evaluation under uncertainty and with limited data. Introduction Bayes’ theorem is fundamental to Bayesian inference. It is a subset of statistics, providing a mathematical framework for forming inferences through the concept of probability, in which evidence about the true state of the world is expressed in terms of degrees of belief through subjectively assessed numerical probabilities. Such a probability is known as a Bayesian probability. The fundamental ideas and concepts behind Bayes' theorem, and its use within Bayesian inference, have been developed and added to over the past centuries by Thomas Bayes, Richard Price and Pierre Simon Laplace as well as numerous other mathematicians, statisticians and scientists. Bayesian inference has experienced spikes in popularity as it has been seen as vague and controversial by rival frequentist statisticians. In the past few decades Bayesian infere ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bayes' Theorem
In probability theory and statistics, Bayes' theorem (alternatively Bayes' law or Bayes' rule), named after Thomas Bayes, describes the probability of an event, based on prior knowledge of conditions that might be related to the event. For example, if the risk of developing health problems is known to increase with age, Bayes' theorem allows the risk to an individual of a known age to be assessed more accurately (by conditioning it on their age) than simply assuming that the individual is typical of the population as a whole. One of the many applications of Bayes' theorem is Bayesian inference, a particular approach to statistical inference. When applied, the probabilities involved in the theorem may have different probability interpretations. With Bayesian probability interpretation, the theorem expresses how a degree of belief, expressed as a probability, should rationally change to account for the availability of related evidence. Bayesian inference is fundamental to Baye ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Conditional Probabilities
In probability theory, conditional probability is a measure of the probability of an event occurring, given that another event (by assumption, presumption, assertion or evidence) has already occurred. This particular method relies on event B occurring with some sort of relationship with another event A. In this event, the event B can be analyzed by a conditional probability with respect to A. If the event of interest is and the event is known or assumed to have occurred, "the conditional probability of given ", or "the probability of under the condition ", is usually written as or occasionally . This can also be understood as the fraction of probability B that intersects with A: P(A \mid B) = \frac. For example, the probability that any given person has a cough on any given day may be only 5%. But if we know or assume that the person is sick, then they are much more likely to be coughing. For example, the conditional probability that someone unwell (sick) is coughing might b ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Probability Distributions
In probability theory and statistics, a probability distribution is the mathematical Function (mathematics), function that gives the probabilities of occurrence of different possible outcomes for an Experiment (probability theory), experiment. It is a mathematical description of a Randomness, random phenomenon in terms of its sample space and the Probability, probabilities of Event (probability theory), events (subsets of the sample space). For instance, if is used to denote the outcome of a coin toss ("the experiment"), then the probability distribution of would take the value 0.5 (1 in 2 or 1/2) for , and 0.5 for (assuming that fair coin, the coin is fair). Examples of random phenomena include the weather conditions at some future date, the height of a randomly selected person, the fraction of male students in a school, the results of a Survey methodology, survey to be conducted, etc. Introduction A probability distribution is a mathematical description of the probabilit ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Normal Distribution
In statistics, a normal distribution or Gaussian distribution is a type of continuous probability distribution for a real-valued random variable. The general form of its probability density function is : f(x) = \frac e^ The parameter \mu is the mean or expectation of the distribution (and also its median and mode), while the parameter \sigma is its standard deviation. The variance of the distribution is \sigma^2. A random variable with a Gaussian distribution is said to be normally distributed, and is called a normal deviate. Normal distributions are important in statistics and are often used in the natural and social sciences to represent real-valued random variables whose distributions are not known. Their importance is partly due to the central limit theorem. It states that, under some conditions, the average of many samples (observations) of a random variable with finite mean and variance is itself a random variable—whose distribution converges to a normal dist ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bayesian Decision Theory
In estimation theory and decision theory, a Bayes estimator or a Bayes action is an estimator or decision rule that minimizes the posterior expected value of a loss function (i.e., the posterior expected loss). Equivalently, it maximizes the posterior expectation of a utility function. An alternative way of formulating an estimator within Bayesian statistics is maximum a posteriori estimation. Definition Suppose an unknown parameter \theta is known to have a prior distribution \pi. Let \widehat = \widehat(x) be an estimator of \theta (based on some measurements ''x''), and let L(\theta,\widehat) be a loss function, such as squared error. The Bayes risk of \widehat is defined as E_\pi(L(\theta, \widehat)), where the expectation is taken over the probability distribution of \theta: this defines the risk function as a function of \widehat. An estimator \widehat is said to be a ''Bayes estimator'' if it minimizes the Bayes risk among all estimators. Equivalently, the estimator whic ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Decision Trees
A decision tree is a decision support tool that uses a tree-like model of decisions and their possible consequences, including chance event outcomes, resource costs, and utility. It is one way to display an algorithm that only contains conditional control statements. Decision trees are commonly used in operations research, specifically in decision analysis, to help identify a strategy most likely to reach a goal, but are also a popular tool in machine learning. Overview A decision tree is a flowchart-like structure in which each internal node represents a "test" on an attribute (e.g. whether a coin flip comes up heads or tails), each branch represents the outcome of the test, and each leaf node represents a class label (decision taken after computing all attributes). The paths from root to leaf represent classification rules. In decision analysis, a decision tree and the closely related influence diagram are used as a visual and analytical decision support tool, where ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Decision Theory
Decision theory (or the theory of choice; not to be confused with choice theory) is a branch of applied probability theory concerned with the theory of making decisions based on assigning probabilities to various factors and assigning numerical consequences to the outcome. There are three branches of decision theory: # Normative decision theory: Concerned with the identification of optimal decisions, where optimality is often determined by considering an ideal decision-maker who is able to calculate with perfect accuracy and is in some sense fully rational. # Prescriptive decision theory: Concerned with describing observed behaviors through the use of conceptual models, under the assumption that those making the decisions are behaving under some consistent rules. # Descriptive decision theory: Analyzes how individuals actually make the decisions that they do. Decision theory is closely related to the field of game theory and is an interdisciplinary topic, studied by ec ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Numerical Data
Level of measurement or scale of measure is a classification that describes the nature of information within the values assigned to variables. Psychologist Stanley Smith Stevens developed the best-known classification with four levels, or scales, of measurement: nominal, ordinal, interval, and ratio. This framework of distinguishing levels of measurement originated in psychology and is widely criticized by scholars in other disciplines. Other classifications include those by Mosteller and Tukey, and by Chrisman. Stevens's typology Overview Stevens proposed his typology in a 1946 ''Science'' article titled "On the theory of scales of measurement". In that article, Stevens claimed that all measurement in science was conducted using four different types of scales that he called "nominal", "ordinal", "interval", and "ratio", unifying both "qualitative" (which are described by his "nominal" type) and "quantitative" (to a different degree, all the rest of his scales). The co ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Weighted Mean
The weighted arithmetic mean is similar to an ordinary arithmetic mean (the most common type of average), except that instead of each of the data points contributing equally to the final average, some data points contribute more than others. The notion of weighted mean plays a role in descriptive statistics and also occurs in a more general form in several other areas of mathematics. If all the weights are equal, then the weighted mean is the same as the arithmetic mean. While weighted means generally behave in a similar fashion to arithmetic means, they do have a few counterintuitive properties, as captured for instance in Simpson's paradox. Examples Basic example Given two school with 20 students, one with 30 test grades in each class as follows: :Morning class = :Afternoon class = The mean for the morning class is 80 and the mean of the afternoon class is 90. The unweighted mean of the two means is 85. However, this does not account for the difference in number o ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Marketing Mix
The term "marketing mix" is a foundation model for businesses, historically centered around product, price, place, and promotion (also known as the "4 Ps"). The marketing mix has been defined as the "set of marketing tools that the firm uses to pursue its marketing objectives in the target market".Kotler, P., Marketing Management, (Millennium Edition), Custom Edition for University of Phoenix, Prentice Hall, 2001, p. 9. Marketing theory emerged in the early twenty-first century. The contemporary marketing mix which has become the dominant framework for marketing management decisions was first published in 1984. In services marketing, an extended marketing mix is used, typically comprising 7 Ps ( product, price, promotion, place, packaging, positioning and people), made up of the original 4 Ps extended by process, people and physical evidence. Occasionally service marketers will refer to 8 Ps (product, price, place, promotion, people, positioning, packaging, and performance), comp ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Internet
The Internet (or internet) is the global system of interconnected computer networks that uses the Internet protocol suite (TCP/IP) to communicate between networks and devices. It is a ''internetworking, network of networks'' that consists of private, public, academic, business, and government networks of local to global scope, linked by a broad array of electronic, wireless, and optical networking technologies. The Internet carries a vast range of information resources and services, such as the inter-linked hypertext documents and Web application, applications of the World Wide Web (WWW), email, electronic mail, internet telephony, telephony, and file sharing. The origins of the Internet date back to the development of packet switching and research commissioned by the United States Department of Defense in the 1960s to enable time-sharing of computers. The primary precursor network, the ARPANET, initially served as a backbone for interconnection of regional academic and mi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
World Wide Web
The World Wide Web (WWW), commonly known as the Web, is an information system enabling documents and other web resources to be accessed over the Internet. Documents and downloadable media are made available to the network through web servers and can be accessed by programs such as web browsers. Servers and resources on the World Wide Web are identified and located through character strings called uniform resource locators (URLs). The original and still very common document type is a web page formatted in Hypertext Markup Language (HTML). This markup language supports plain text, digital image, images, embedded video and audio signal, audio contents, and scripting language, scripts (short programs) that implement complex user interaction. The HTML language also supports hyperlinks (embedded URLs) which provide immediate access to other web resources. Web navigation, or web surfing, is the common practice of following such hyperlinks across multiple websites. Web applicatio ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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