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I am currently calculating a bayesian average using Q1 data using the following equation:

enter image description here

I would like to incorporate data from other quarters for several years back, i.e. Q4 2021, Q3 2021, Q2 2021, etc. I plan to use exponential decay to add weights to each quarter so that more recent quarters are weighted heavier. How would I go about creating the following variables: productRatingsAvg x productRatingsCount, and productRatingsCount in the denominator?

Would productRatingsAvg x productRatingsCount look like something as follows? If so, what do I use for the denominator? Total products from all the quarters or averaged?

[(Q1productRatingsCount x Q1productRatingsAvg)*weight1 + (Q2productRatingsCount x Q2productRatingsAvg)*weight2 + (Q3productRatingsCount x Q3productRatingsAvg)*weight3 + (Q4productRatingsCount x Q4productRatingsAvg)*weight4] / 4

Would C and m then be calculated over the total dataset? Or just the current quarter since it's the one I want weighted heaviest anyway?

Apologies for the formatting with my equation.

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