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Information about Statistical Modeling

A statistical model is used in applied statistics. Three basic notions are sufficient to describe all statistical models.
  1. We choose a statistical unit which we will observe directly. Multiple observations of the same unit over time is called longitudinal research. Observations of a variety of statistical attributes is a common way of studying relationships among the attributes of a single unit.
  2. We may really be interested in a statistical population (or set) of similar units rather than in any statistical unit per se. Survey sampling offers an example of this type of application.
  3. Our interest may be focused on a statistical assembly where we examine functional subunits of the statistical unit. Physiology is an example in which we probe the organs which compose the unit. A common model for this type of research is the stimulus-response model.


In mathematical terms, a statistical model is frequently thought of as a parametrized set of probability distributions of the form



It is assumed that there is a distinct element in the above set from which the observed data are generated. Statistical inference is the art of making statements about which elements of this set are likely to be the true one.

So, for example, Bayes theorem in its raw form may be intractable, but assuming a general model H allows it to become
which may be easier. Models can also be compared, using methods such as Bayes factors.

See also

Statistics is a mathematical science pertaining to the collection, analysis, interpretation or explanation, and presentation of data. It is applicable to a wide variety of academic disciplines, from the physical and social sciences to the humanities.
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In different statistical disciplines, the statistical unit is the source of a random variable. There are different ways to study a unit and different names applied:
  1. We may be interested in a unit

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A longitudinal study is a correlational research study that involves repeated observations of the same items over long periods of time, often many decades. Longitudinal studies are often used in psychology to study developmental trends across the life span.
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In statistics, a statistical population is a set of entities concerning which statistical inferences are to be drawn, often based on a random sample taken from the population.
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SET may stand for:
  • Sanlih Entertainment Television, a television channel in Taiwan
  • Secure electronic transaction, a protocol used for credit card processing,

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In statistics, survey sampling is random selection of a sample from a finite population. It is an important part of planning statistical research and design of experiments. Sophisticated sampling techniques that are both economical and scientifically reliable have been developed.
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A statistical assembly is a study of the relationships among the components in a statistical unit that is made of discrete components like organs or machine parts. Much of the observation for statistical assembly requires special preparation of the unit, which demands that the
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In different statistical disciplines, the statistical unit is the source of a random variable. There are different ways to study a unit and different names applied:
  1. We may be interested in a unit

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Physiology (from Greek: φυσις, physis, “nature, origin”; and λόγος, logos, "knowledge") is the study of the mechanical, physical, and biochemical functions of living organisms.
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The stimulus-response model describes a statistical unit as making a quantitative response to a quantitative stimulus administered by the researcher. The object of this kind of research is to establish a mathematical function that describes the relation f
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probability distribution that assigns a probability to every subset (more precisely every measurable subset) of its state space in such a way that the probability axioms are satisfied.
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Inferential statistics or statistical induction comprises the use of statistics to make inferences concerning some unknown aspect of a population. It is distinguished from descriptive statistics.
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Bayes' theorem (also known as Bayes' rule or Bayes' law) is a result in probability theory, which relates the conditional and marginal probability distributions of random variables.
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In statistics, the use of Bayes factors is a Bayesian alternative to classical hypothesis testing[1][2].

Given a model selection problem in which we have to choose between two models M1 and M2
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A/B testing is a method of advertising testing by which a baseline control sample is compared to a variety of single-variable test samples. A classic direct mail tactic, this method has been recently adopted within the interactive space to test tactics such as banner ads, emails
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