Posterior probabilityThe posterior probability is a type of conditional probability that results from updating the prior probability with information summarized by the likelihood via an application of Bayes' rule.Prior probabilityDistribution of an uncertain quantityA prior probability distribution (often simply called the prior probability, prior distribution, or prior) of an uncertain quantity is its assumed probability distribution before evidence is taken into account. For example, the prior could be the probability distribution representing the relative proportions of voters who will vote for a particular politician in a future election.Bayes' theoremIn probability theory, Bayes' theorem (alternatively Bayes' law or Bayes' rule), named after Thomas Bayes (), gives a mathematical rule for inverting conditional probabilities, allowing the probability of a cause to be found given its effect. For example, with Bayes' theorem, the probability that a patient has a disease given that they tested positive for that disease can be found using the probability that the test yields a positive result when the disease is present.
Statistical inferenceStatistical inference is the process of using data analysis to infer properties of an underlying probability distribution. Inferential statistical analysis infers properties of a population, for example by testing hypotheses and deriving estimates. It is assumed that the observed data set is sampled from a larger population. Inferential statistics can be contrasted with descriptive statistics.
Sequential analysisIn statistics, sequential analysis or sequential hypothesis testing is statistical analysis where the sample size is not fixed in advance. Instead data is evaluated as it is collected, and further sampling is stopped in accordance with a pre-defined stopping rule as soon as significant results are observed.
EvidenceEvidence for a proposition is what supports the proposition. It is usually understood as an indication that the proposition is true. The exact definition and role of evidence vary across different fields. In epistemology, evidence is what justifiesbeliefs or what makes it rational to hold a certain attitude. For example, a perceptual experience of a tree may serve as evidence to justify the belief that there is a tree.
StatisticsStudy of collection and analysis of dataThe normal distribution, a very common probability density, is used extensively in inferential statistics.Scatter plots and line charts are used in descriptive statistics to show the observed relationships between different variables, here using the Iris flower data set.Statistics (from German: Statistik, orig.
Mathematical statisticsMathematical statistics is the application of probability theory and other mathematical concepts to statistics, as opposed to techniques for collecting statistical data. Specific mathematical techniques that are commonly used in statistics include mathematical analysis, linear algebra, stochastic analysis, differential equations, and measure theory.
InformationInformation is an abstract concept that refers to something which has the power to inform. At the most fundamental level, it pertains to the interpretation (perhaps formally) of that which may be sensed, or their abstractions. Any natural process that is not completely random and any observable pattern in any medium can be said to convey some amount of information.
ScienceSystematic endeavour to gain knowledgeScience is a systematic discipline that builds and organises knowledge in the form of testable explanations about nature and society. It is driven by the scientific method: an empirical cycle that typically involves making observations, producing hypotheses, testing them with evidence, and drawing conclusions.
EngineeringEngineering is the practice of systematically applying natural science and mathematics to design and improve systems, devices, or processes that solve problems under constraints. It is typically motivated by satisfying human needs, resulting in creations such as bridges, engines, smartphones, pacemakers, the internet, spacecraft, and washing machines.
PhilosophyStudy of general and fundamental questionsThe statue The Thinker by Auguste Rodin is a symbol of philosophical thought.*As an Amazon Associate I earn from qualifying purchases.