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The Bayes factor is a ratio of two competing statistical models represented by their evidence, and is used to quantify the support for one model over the other. [1] The models in question can have a common set of parameters, such as a null hypothesis and an alternative, but this is not necessary; for instance, it could also be a non-linear model compared to its linear approximation.
Whereas the frequentist approach (i.e., risk) averages over possible samples , the Bayesian would fix the observed sample and average over hypotheses . Thus, the Bayesian approach is to consider for our observed x {\displaystyle x\,\!} the expected loss
The Bayes risk of ^ is defined as ((, ^)), where the expectation is taken over the probability distribution of : this defines the risk function as a function of ^. An estimator θ ^ {\displaystyle {\widehat {\theta }}} is said to be a Bayes estimator if it minimizes the Bayes risk among all estimators.
Decision analysis (DA) is the discipline comprising the philosophy, methodology, and professional practice necessary to address important decisions in a formal manner. . Decision analysis includes many procedures, methods, and tools for identifying, clearly representing, and formally assessing important aspects of a decision; for prescribing a recommended course of action by applying the ...
A Bayesian network (also known as a Bayes network, Bayes net, belief network, or decision network) is a probabilistic graphical model that represents a set of variables and their conditional dependencies via a directed acyclic graph (DAG). [1] While it is one of several forms of causal notation, causal networks are special cases of Bayesian ...
The Journal of Risk Research is a monthly peer-reviewed academic journal covering all aspects of risk analysis, communication, judgment, and decision-making. It was established in 1998 and is published by Routledge. The editor-in-chief is Ragnar Löfstedt (King's College London).
An influence diagram (ID) (also called a relevance diagram, decision diagram or a decision network) is a compact graphical and mathematical representation of a decision situation. It is a generalization of a Bayesian network , in which not only probabilistic inference problems but also decision making problems (following the maximum expected ...
Risk assessment involves two parts: risk analysis and risk evaluation, although the term “risk assessment” can be seen used indistinguishable with “risk analysis”. In general, risk assessment can be divided into these steps: [8] Plan and prepare the risk analysis. Define and delimit the system and the scope of the analysis.