Hello, in an article I've read bayesian approach update posterior and then prior according to previous data. so someone can predict the true value of the parameter in parameter estimation. my question is that how do bayesian iterative updates avoid previous wrong samples? is there a mechanism that can tolerate the faulty samples after some iteration such that it is like that in a feedback mechanism. or do faulty samples lead to bad results once it included in the calculation?.
Thank you,
or is there a method for the Bayesian prediction that scientist can label the quality of data that will affect the calculation?
There's an approach to evaluate the quality of predictions, and if the quality of predictions based on a particular set of variables is not acceptable, then these variables may be excluded.
For the evaluation the quality of predictions, let me recommend these works:
Article Assessing Point Forecast Bias Across Multiple Time Series: M...
Chapter Forecast Error Measures: Critical Review and Practical Recommendations
In particular, the article above describes some simple visual tools that can be used. I recommend the FEW-L1 workflow to see how good your predictions are depending on a data sample used.
Bayesian probability theory does not predict "the true value of the parameter in parameter estimation". It computes the most probable estimate and the estimate's uncertainty given the data and everything we know about the meaurement. The true value exists, but it is unobtainable because all measurements are imperfect. The error(s) can be extremely small, but they are never zero.
The contribution from a "faulty sample" would be minimized by using objective prior information for all the parameters in the model for the data in the form of probability density functions. The model should include parameters for all noise and error sources
Objective prior information is the minimum amount of fact-based information about the measurement method and circumstances, the system undergoing measurement and the data (noise).
Parameter estimates for a "previous sample" will have uncertainty estimates if they too were made using objective Bayesian probability theory. If the parameter estimate uncertainties are high, their contributions will be low because their prior probability density functions will be uninformative (wide distributions). But when the previous parameter estimate uncertainties are low, they will improve the current parameter estimate certainties.
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