This is a problem I am currently facing in my research...

I have a dataset collected over time for time=0 to T

I need to estimate some parameters (regarding this data) using Bayesian Inference. I use data for each time instance for Bayesian inference with prior as the posterior obtained in the previous time instance. The posterior obtained in this time instant is used as prior for the next time instance and so on...

However I do not have any priors available to start with. I wanted to know if the following methodology is correct...

(1) Divide the dataset into two parts say from time=0 to t and from time =t to T

(2) Use the dataset from t=0 to t to determine prior probabilities for my parameters.

(3) Use dataset from time= t to T for Bayesian inference with priors obtained in previous step.