facebook / facebook/prophet

Impact of mcmc sampling in the predictions

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Description

Hello, I am running the prophet model to predict the demand of Mar'23 using the data from Nov'2020 to Feb'2022. I am using price as the additional regressor in the model.
Following is the fit of the prophet (without mcmc sampling) in the data and correspondingly the predictions for the month of Mar'23:
![image](https://user-images.githubusercontent.com/118460864/224754800-340346e9-e67b-4e87-8cf2-ede8fff707bc.png)
and below is the regression coefficient of price:
![image](https://user-images.githubusercontent.com/118460864/224755192-9fe331e5-9dc2-48e3-9d16-7565b52a57d6.png)

Now, when I run the prophet with mcmc sampling (mcmc sample=500) on the same dataset, suddenly the predictions for the month of Mar'23 reduces drastically:
![image](https://user-images.githubusercontent.com/118460864/224755704-aef34aee-e7b5-4435-93cc-e22d2d06b629.png)
, below is the updated regression coefficient of price
![image](https://user-images.githubusercontent.com/118460864/224755988-88154b83-629f-409c-88cb-8e064fce0ee6.png)

**Can someone please explain the reason why mcmc sampling leads to sudden drop in the prediction values?**

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