Existence of a stochastic function consistent with the conditional likelihood relation. (English. Russian original) Zbl 0545.93060
Cybernetics 18, 494-498 (1983); translation from Kibernetika 1982, No. 4, 80-83 (1982).
The concept of relative likelihood (RL), as a binary relation between events indicating which one is more probable, is used to prove the existence of a stochastic function.
The term conditional likelihood relation is defined in terms of intervals \(A_ 1\), \(A_ 2\) which belong to the 1-system. A number of axioms and theorems are proved which give the properties of a 1-system vis-a-vis a relative likelihood. Properties, definitions and theorems involve a lot of notations. It is proved that relative likelihood can be associated with stochastic functions. The case of multi-dimensional distributions is also discussed. The paper ends with a long list of references.
The term conditional likelihood relation is defined in terms of intervals \(A_ 1\), \(A_ 2\) which belong to the 1-system. A number of axioms and theorems are proved which give the properties of a 1-system vis-a-vis a relative likelihood. Properties, definitions and theorems involve a lot of notations. It is proved that relative likelihood can be associated with stochastic functions. The case of multi-dimensional distributions is also discussed. The paper ends with a long list of references.
Reviewer: B.L.Agarwal
MSC:
| 93E03 | Stochastic systems in control theory (general) |
| 62A01 | Foundations and philosophical topics in statistics |
| 62B10 | Statistical aspects of information-theoretic topics |
| 93E20 | Optimal stochastic control |
| 62E99 | Statistical distribution theory |
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