# Posterior Probability on Finite Set

Open access

## Summary

In [14] we formalized probability and probability distribution on a finite sample space. In this article first we propose a formalization of the class of finite sample spaces whose element’s probability distributions are equivalent with each other. Next, we formalize the probability measure of the class of sample spaces we have formalized above. Finally, we formalize the sampling and posterior probability.

Keywords:
References
• [1] Grzegorz Bancerek. Cardinal numbers. Formalized Mathematics, 1(2):377-382, 1990.

• [2] Grzegorz Bancerek. The ordinal numbers. Formalized Mathematics, 1(1):91-96, 1990.

• [3] Grzegorz Bancerek and Krzysztof Hryniewiecki. Segments of natural numbers and finite sequences. Formalized Mathematics, 1(1):107-114, 1990.

• [4] Czesław Bylinski. Basic functions and operations on functions. Formalized Mathematics, 1(1):245-254, 1990.

• [5] Czesław Bylinski. Finite sequences and tuples of elements of a non-empty sets. Formalized Mathematics, 1(3):529-536, 1990.

• [6] Czesław Bylinski. Functions and their basic properties. Formalized Mathematics, 1(1):55-65, 1990.

• [7] Czesław Bylinski. Functions from a set to a set. Formalized Mathematics, 1(1):153-164, 1990.

• [8] Czesław Bylinski. Partial functions. Formalized Mathematics, 1(2):357-367, 1990.

• [9] Czesław Bylinski. Some basic properties of sets. Formalized Mathematics, 1(1):47-53, 1990.

• [10] Agata Darmochwał. Finite sets. Formalized Mathematics, 1(1):165-167, 1990.

• [11] Shunichi Kobayashi and Kui Jia. A theory of Boolean valued functions and partitions. Formalized Mathematics, 7(2):249-254, 1998.

• [12] Andrzej Kondracki. Basic properties of rational numbers. Formalized Mathematics, 1(5):841-845, 1990.

• [13] Andrzej Nedzusiak. σ-fields and probability. Formalized Mathematics, 1(2):401-407, 1990.

• [14] Hiroyuki Okazaki. Probability on finite and discrete set and uniform distribution. Formalized Mathematics, 17(2):173-178, 2009, doi: 10.2478/v10037-009-0020-z.

• [15] Hiroyuki Okazaki and Yasunari Shidama. Probability on finite set and real-valued random variables. Formalized Mathematics, 17(2):129-136, 2009, doi: 10.2478/v10037-009-0014-x.

• [16] Beata Padlewska. Families of sets. Formalized Mathematics, 1(1):147-152, 1990.

• [17] Andrzej Trybulec. Domains and their Cartesian products. Formalized Mathematics, 1(1):115-122, 1990.

• [18] Andrzej Trybulec. On the sets inhabited by numbers. Formalized Mathematics, 11(4):341-347, 2003.

• [19] Michał J. Trybulec. Integers. Formalized Mathematics, 1(3):501-505, 1990.

• [20] Wojciech A. Trybulec. Pigeon hole principle. Formalized Mathematics, 1(3):575-579, 1990.

• [21] Zinaida Trybulec. Properties of subsets. Formalized Mathematics, 1(1):67-71, 1990.

• [22] Edmund Woronowicz. Many argument relations. Formalized Mathematics, 1(4):733-737, 1990.

• [23] Edmund Woronowicz. Relations and their basic properties. Formalized Mathematics, 1(1):73-83, 1990.

• [24] Edmund Woronowicz. Relations defined on sets. Formalized Mathematics, 1(1):181-186, 1990.

• [25] Bo Zhang and Yatsuka Nakamura. The definition of finite sequences and matrices of probability, and addition of matrices of real elements. Formalized Mathematics, 14(3):101-108, 2006, doi:10.2478/v10037-006-0012-1.

# Formalized Mathematics

## (a computer assisted approach)

### Journal Information

SCImago Journal Rank (SJR) 2016: 0.207
Source Normalized Impact per Paper (SNIP) 2016: 0.315

Target Group

researchers in the fields of formal methods and computer-checked mathematics

### Metrics

All Time Past Year Past 30 Days
Abstract Views 0 0 0
Full Text Views 27 27 24