Bayes' theoremIn probability theory and statistics, Bayes' theorem (beɪz or beɪzɪz ; alternatively Bayes' law or Bayes' rule), and occasionally Bayes's theorem, 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 relative to their age, rather than simply assuming that the individual is typical of the population as a whole.
Decision theoryDecision theory (or the theory of choice; not to be confused with choice theory) is a branch of applied probability theory and analytic philosophy 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.
OverweightBeing overweight or fat is having more body fat than is optimally healthy. Being overweight is especially common where food supplies are plentiful and lifestyles are sedentary. excess weight reached epidemic proportions globally, with more than 1 billion adults being either overweight or obese. In 2013, this increased to more than 2 billion. Increases have been observed across all age groups.
Variational Bayesian methodsVariational Bayesian methods are a family of techniques for approximating intractable integrals arising in Bayesian inference and machine learning. They are typically used in complex statistical models consisting of observed variables (usually termed "data") as well as unknown parameters and latent variables, with various sorts of relationships among the three types of random variables, as might be described by a graphical model. As typical in Bayesian inference, the parameters and latent variables are grouped together as "unobserved variables".
2007–2008 financial crisisThe 2007–2008 financial crisis, or Global Financial Crisis (GFC), was a severe worldwide economic crisis that occurred in the early 21st century. It was the most serious financial crisis since the Great Depression (1929). Predatory lending targeting low-income homebuyers, excessive risk-taking by global financial institutions, and the bursting of the United States housing bubble culminated in a "perfect storm". Mortgage-backed securities (MBS) tied to American real estate, as well as a vast web of derivatives linked to those MBS, collapsed in value.
High-yield debtIn finance, a high-yield bond (non-investment-grade bond, speculative-grade bond, or junk bond) is a bond that is rated below investment grade by credit rating agencies. These bonds have a higher risk of default or other adverse credit events, but offer higher yields than investment-grade bonds in order to compensate for the increased risk. As indicated by their lower credit ratings, high-yield debt entails more risk to the investor compared to investment grade bonds.
European debt crisisThe European debt crisis, often also referred to as the eurozone crisis or the European sovereign debt crisis, was a multi-year debt crisis that took place in the European Union (EU) from 2009 until the mid to late 2010s. Several eurozone member states (Greece, Portugal, Ireland, Spain, and Cyprus) were unable to repay or refinance their government debt or to bail out over-indebted banks under their national supervision without the assistance of third parties like other eurozone countries, the European Central Bank (ECB), or the International Monetary Fund (IMF).
Debt crisisDebt crisis is a situation in which a government (nation, state/province, county, or city etc.) loses the ability of paying back its governmental debt. When the expenditures of a government are more than its tax revenues for a prolonged period, the government may enter into a debt crisis. Various forms of governments finance their expenditures primarily by raising money through taxation. When tax revenues are insufficient, the government can make up the difference by issuing debt.
Mixture modelIn statistics, a mixture model is a probabilistic model for representing the presence of subpopulations within an overall population, without requiring that an observed data set should identify the sub-population to which an individual observation belongs. Formally a mixture model corresponds to the mixture distribution that represents the probability distribution of observations in the overall population.
Short-rate modelA short-rate model, in the context of interest rate derivatives, is a mathematical model that describes the future evolution of interest rates by describing the future evolution of the short rate, usually written . Under a short rate model, the stochastic state variable is taken to be the instantaneous spot rate. The short rate, , then, is the (continuously compounded, annualized) interest rate at which an entity can borrow money for an infinitesimally short period of time from time .
Conditional random fieldConditional random fields (CRFs) are a class of statistical modeling methods often applied in pattern recognition and machine learning and used for structured prediction. Whereas a classifier predicts a label for a single sample without considering "neighbouring" samples, a CRF can take context into account. To do so, the predictions are modelled as a graphical model, which represents the presence of dependencies between the predictions. What kind of graph is used depends on the application.
Hidden Markov modelA hidden Markov model (HMM) is a statistical Markov model in which the system being modeled is assumed to be a Markov process — call it — with unobservable ("hidden") states. As part of the definition, HMM requires that there be an observable process whose outcomes are "influenced" by the outcomes of in a known way.
