Bayes

conditional probability: P(A|B) means probability of A assuming B

P(A|B) = P(A and B)/P(B)

here P(A and B) = P(A) * P(B|A)

Probability of aggressive drivers in the population= 40% or 0.4

Probability of nonaggressive drivers in the population = 60% or 0.6

Probability of aggressive drivers getting into three accidents a year = 15% or 0.15

Probability of nonaggressive drivers getting into three accidents a year= 5% or 0.05

John is known to have 3 accidents in the past year.

What is the probability that he is an aggressive driver?

P(A|B) =P(B|A)*P(A)/P(B)

Probability of accident

P(B)=P(agressive)*P(accidentA) + P(Ni-agressive)*P(accidentN) = 10.4*0.15+0.6*0.05

P(B|A)*P(A)=0.15*0.4

P(A|B) = 0.15*0.4 / (10.4*0.15+0.6*0.05)

Bayes showed how to convert the probability of the observations given a hypothesis (the deductive problem) to what we actually want, the probability that the hypothesis is true given some observations (the inductive problem).

Bayesian conversion involves assigning a value to the probability that your hypothesis is right before any observations have been made (the ‘prior probability’). Bayes’s theorem allows that prior probability to be converted to what we want, the probability that the hypothesis is true given some relevant observations, which is known as the ‘posterior probability’.

https://en.wikipedia.org/wiki/P-value

The p-value is defined as the probability of obtaining a result equal to or "more extreme" than what was actually observed, when the null hypothesis is true

The postulate that there is no real effect is called the null hypothesis, and the probability is called the p-value.

the p-value gives the right answer to the wrong question. What we really want to know is not the probability of the observations given a hypothesis about the existence of a real effect, but rather the probability that there is a real effect – that the hypothesis is true – given the observations. And that is a problem of induction.

https://github.com/liviu-/notebooks/blob/master/bayesian_linear_regression.ipynb

https://aeon.co/essays/it-s-time-for-science-to-abandon-the-term-statistically-significant

https://habrahabr.ru/company/yandex/blog/321434/

https://www.datascience.com/blog/introduction-to-bayesian-inference-learn-data-science-tutorials

https://habrahabr.ru/company/surfingbird/blog/150207/

https://camdavidsonpilon.github.io/Probabilistic-Programming-and-Bayesian-Methods-for-Hackers/

http://efavdb.com/metropolis/

https://www.analyticsvidhya.com/blog/2016/06/bayesian-statistics-beginners-simple-english/

https://metacademy.org/roadmaps/rgrosse/bayesian_machine_learning

https://news.ycombinator.com/item?id=10843680

http://homepages.inf.ed.ac.uk/vlavrenk/iaml.html Bayes

http://habrahabr.ru/post/232639/ Bayes