Thank you for your response. I think the condition is the latter one, 20 categories are the observed data. However, I think normal needs less parameter than multinomial distribution and therefore I speculate when the dataset is not very large, the normal distribution has less possibility to over fit? I am a psychology student and I read some papers that require participants to do some trial-by-trial questionnaires. However, different papers choose different distributions. For example, in this paper, participants indicated their happiness after each decision, and the author modeled this happiness data by putting a utility function into a normal regression model, so they choose normal distribution as likelihood. On the contrary, this paper choose a multinomial distribution. I am a little confused about which distribution is more suitable in this condition, cause both papers are published in relatively good journals. Thank you very much. BTW, thank you for responding to me. I am always a big fan of you, cause you have done plenty of jobs in Pymc3 community.