Sadeghi, Kayvan, Rinaldo, Alessandro

We define and study the statistical models in exponential family form whose sufficient statistics are the degree distributions and the bi-degree distributions of undirected labelled simple graphs. Graphs that are constrained by the joint degree distributions are called $dK$-graphs in the computer science literature and this paper attempts to provide the first statistically grounded analysis of this type of models. In addition to formalizing these models, we provide some preliminary results for the parameter estimation and the asymptotic behaviour of the model for degree distribution, and discuss the parameter estimation for the model for bi-degree distribution.

Bayesian Statistics continues to remain incomprehensible in the ignited minds of many analysts. Being amazed by the incredible power of machine learning, a lot of us have become unfaithful to statistics. Our focus has narrowed down to exploring machine learning. We fail to understand that machine learning is only one way to solve real world problems. In several situations, it does not help us solve business problems, even though there is data involved in these problems. To say the least, knowledge of statistics will allow you to work on complex analytical problems, irrespective of the size of data. In 1770s, Thomas Bayes introduced'Bayes Theorem'.

If you have little experience in applying machine learning algorithm, you would have discovered that it does not require any knowledge of Statistics as a prerequisite. However, knowing some statistics can be beneficial to understand machine learning technically as well intuitively. Knowing some statistics will eventually be required when you want to start validating your results and interpreting them. After all, when there is data, there are statistics. Like Mathematics is the language of Science. Statistics is one of a kind language for Data Science and Machine Learning. Statistics is a field of mathematics with lots of theories and findings. However, there are various concepts, tools, techniques, and notations are taken from this field to make machine learning what it is today. You can use descriptive statistical methods to help transform observations into useful information that you will be able to understand and share with others.

Since their early days, humans have had an important, often antagonistic relationship with uncertainty; we try to kill it everywhere we find it. Without an explanation for many natural phenomena, humans invented gods to explain them, and without certainty of the future, they consulted oracles. It was precisely the oracle's role to reduce uncertainty for their fellow humans, predicting their future and giving counsel according to their gods' will, and even though their accuracy left much to be desired, they were believed, for any measure of certainty is better than none. As society grew sophisticated, oracles were (not completely) displaced by empiric thought, which proved much more successful at prediction and counsel. Empiricism itself evolved into the collection of techniques we call the scientific method, which has proven to be much more effective at reducing uncertainty, and is modern society's most trustworthy way of producing predictions.