# Global Geometry of Bayesian Statistics

## Abstract

**:**

## 1. Introduction

## 2. Results

#### 2.1. Symplectic/Contact Geometry

#### 2.2. Bayesian Statistics

#### 2.3. The Information Geometry

#### 2.4. The Geometry of Normal Distributions

#### 2.5. The Generalization

**Proposition**

**1.**

**Proof.**

**Proposition**

**2.**

**Proof.**

**Proposition**

**3.**

**Proof.**

**Proposition**

**4.**

**Proof.**

**Proposition**

**5.**

**Proof.**

**Proposition**

**6.**

**Proposition**

**7.**

**Proof.**

**Proposition**

**8.**

**Proof.**

**Definition**

**1.**

**Proposition**

**9.**

**Proof.**

**Theorem**

**1.**

**Corollary**

**1.**

**Proof.**

#### 2.6. The Symmetry

## 3. Discussion

## Funding

## Conflicts of Interest

## References

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**Figure 1.**On any leaf of the primary foliation of ${U}_{1}\times {U}_{2}$, there is a bi-contact hypersurface N carrying the bi-contact Hamiltonian vector field Y. Because of the dimension, the surface F in the figure presents simultaneously a leaf of the secondary foliation and a leaf of the tertiary foliation of that leaf. The flow on the tertiary leaf $F={F}_{0,\delta}$ traces the common lift of the iteration of ∗ on ${L}_{1}$ and the iteration of · on ${L}_{2}$.

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**MDPI and ACS Style**

Mori, A.
Global Geometry of Bayesian Statistics. *Entropy* **2020**, *22*, 240.
https://doi.org/10.3390/e22020240

**AMA Style**

Mori A.
Global Geometry of Bayesian Statistics. *Entropy*. 2020; 22(2):240.
https://doi.org/10.3390/e22020240

**Chicago/Turabian Style**

Mori, Atsuhide.
2020. "Global Geometry of Bayesian Statistics" *Entropy* 22, no. 2: 240.
https://doi.org/10.3390/e22020240