I want to use Bayesian model to predict the values of signal in the future.
The process is like:
a. 1000 observations are given. First 800 consecutive observations are training data, and 200 observations are test data. {data: (x,y),x-time, y- amplitude} I just want to use y to predict the following values.
b. Training data approximately follow a Gaussian distribution. Here, for simplicity, we assume the mean is unknown, and the variance is known. We put a prior distribution on the mean(prior is also a Gaussian distribution). By using Bayes' rule, we can have the posterior distribution of the mean. Then the predictive distribution can be derived.
And predictive distribution is also a Gaussian distribution. I can use training data to solve the parameters of the predictive distribution. My model should be outputed 200 predictive values, then I can compare them with the actual values to evaluate the model.
Here is the question.How can I get the predictive values from the predictive distribution? I just achieve the distributions of the new values. Shoud I use some sampling methods to get the values?
Thank you!!
