An important job of a scientist is to explain results of experiments. Once you have an explanation, you can design further experiments. Without good explanations, you will design bad experiments and fail.

Using Bayes rule, the formula for an explanation given results of experiments is:

P(explanation | experiment_results) = P(experiment_results | explanation) * P(explanation) / P(experiment_results)

= P (experiment_results | explanation) * P(explanation) / \sum_{explanation_i}^{all_explanations} P(experiment_result | explanation_i) P(explanation_i)

Ok so what does it mean? The algorithm for interpreting results of experiments is:

  1. Have a complete set of explanations
  2. Estimate their relative likelihood if you can (otherwise uniform distribution on most likely ones is fine)
  3. Make complete observations of experiment results
  4. Use those results to update your likelihood of explanations using formula above.