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How to go from Bayes theorem to Bayesian inference?
Intuitively, while probability set the parameter fix, and estimate the probability of data, which is variable. In likelihood we set the data fix, and vary the parameter until we find the best parameter which provides the best model to generate such dataset.
How is Bayes theorem used in machine learning?
In the machine learning context, it can be used to estimate the model parameters (e.g. the weights in a neural network) in a statistically robust way. It can also be used in model selection e.g. choosing which machine learning model is the best to address a given problem.
How are Bayesian statistics used in real life?
In real life, unlike the textbook cancer example, instead of having a certain value for our likelihood probability, in Bayesian statistics we will say “I, as a data analyst, collect many data from the stock market, and conclude that the stock return follows a normal distribution.
How are we able to ignore the calculation of Bayes formula?
How we are able to ignore the calculation of both the denominator and nominator of Bayes formula in practice most of the time with a simple real life example in a posterior model to estimate stock market return. Again, I want to reiterate that I will focus on the intuition rather than the math here.
2. Bayesian statistics is about multiplication of probability function, not real number We established that prior is always modeled as a probability distribution. And a probability distribution will always have a probability mass function (for discrete variable) or probability density function (for continuous variable).
How to formulate a Bayesian linear regression model?
In the Bayesian viewpoint, we formulate linear regression using probability distributions rather than point estimates. The response, y, is not estimated as a single value, but is assumed to be drawn from a probability distribution. The model for Bayesian Linear Regression with the response sampled from a normal distribution is: