HallsofIvy said:
[sp]Albert said:
Good question! I hadn't thought of that possibility. The method will be similar to the previous one, but this time the angle ABC ($\angle A'B'C$ in the diagram below) will be $40^\circ - 10^\circ = 30^\circ$ instead of $40^\circ + 10^\circ = 50^\circ$. Then $\angle A'CB' = 120^\circ$ and $\overset{\frown} {BN} = 20^\circ.$Albert said:
$\overset{\frown}{BN}$, also known as the Bayes net or Bayesian network, is a probabilistic graphical model used for representing and reasoning about uncertainty in a system. It is based on the principles of conditional independence and Bayes' rule.
$\overset{\frown}{BN}$ is used in a variety of research fields, including artificial intelligence, machine learning, statistics, and bioinformatics. It is used to model and analyze complex systems with uncertainty, such as medical diagnoses, financial predictions, and ecological systems.
The parameters needed to find $\overset{\frown}{BN}$ include a set of variables, the relationships between these variables, and the associated probabilities. These parameters are usually obtained through data collection, expert knowledge, or a combination of both.
To find $\overset{\frown}{BN}$ with given parameters, one can use a variety of methods such as the maximum likelihood estimation, the expectation-maximization algorithm, or the Bayesian structure learning. These methods aim to find the most probable structure and parameters of the Bayesian network given the data and prior knowledge.
The benefits of using $\overset{\frown}{BN}$ in research include its ability to handle uncertainty and incomplete data, its graphical representation that allows for easy interpretation, and its ability to perform probabilistic inference. It also allows for the incorporation of expert knowledge and can be used to make predictions and decisions based on the available evidence.
