METHODS, SYSTEMS AND APPARATUS TO IMPROVE BAYESIAN POSTERIOR GENERATION EFFICIENCY
Methods, apparatus, systems and articles of manufacture are disclosed to improve Bayesian posterior generation efficiency. An example apparatus to improve posterior calculation efficiency includes a logit model engine to generate a logit model associated with prior data, the logit model engine to assign initial logit coefficient values to products of interest for respective segments of interest, a penalty engine to improve posterior calculation efficiency by generating penalty modifiers, the penalty modifiers to balance modification of the initial logit coefficient values without merging the prior data with store conditions, and an analysis engine to calculate posterior output values of the prior data by evaluating the initial logit coefficient values with the penalty modifiers via a maximum likelihood estimation, the posterior output values indicative of modifications to the initial logit coefficient values caused by empirical store data sales activity.
1 . An apparatus to improve posterior calculation efficiency, comprising:
a logit model engine to generate a logit model associated with prior data, the logit model engine to assign initial logit coefficient values to products of interest for respective segments of interest;
a penalty engine to improve posterior calculation efficiency by generating penalty modifiers, the penalty modifiers to balance modification of the initial logit coefficient values without merging the prior data with store conditions; and
an analysis engine to calculate posterior output values of the prior data by evaluating the initial logit coefficient values with the penalty modifiers via a maximum likelihood estimation, the posterior output values indicative of modifications to the initial logit coefficient values caused by empirical store data sales activity.
2 . The apparatus as defined in claim 1 , further including:
a market share penalty engine to calculate a first one of the penalty modifiers as a market share penalty;
a segment size penalty engine to calculate a second one of the penalty modifiers as a segment size penalty; and
a within-segment penalty engine to calculate a third one of the penalty modifiers as a within-segment penalty.
3 . The apparatus as defined in claim 2 , wherein the analysis engine is to apply the penalty modifiers as a maximized sum of the first one of the penalty modifiers, the second one of the penalty modifiers, and the third one of the penalty modifiers.
4 . The apparatus as defined in claim 1 , further including a raw data summary engine to calculate an observed item share value based on a sum of respective ones of the products of interest from the empirical store data sales activity.
5 . The apparatus as defined in claim 4 , further including a market share penalty engine to calculate a market share penalty based on the observed item share, an item ratio of respective first ones of the initial logit coefficients, and a segment ratio of respective second ones of the initial logit coefficients.
6 . The apparatus as defined in claim 5 , wherein the market share penalty engine is to calculate the item ratio as a ratio of (a) respective ones of coefficients of the products of interest and (b) a sum of all coefficients of the products of interest.
7 . The apparatus as defined in claim 5 , wherein the market share penalty engine is to calculate the segment ratio as a ratio of (a) respective ones of coefficients of the segments of interest and (b) a sum of all coefficients of the segments of interest.
8 . A computer-implemented method to improve posterior calculation efficiency, the method comprising:
generating, by executing an instruction with a processor, a logit model associated with prior data, the logit model engine to assign initial logit coefficient values to products of interest for respective segments of interest;
improving, by executing an instruction with the processor, posterior calculation efficiency by generating penalty modifiers, the penalty modifiers to balance modification of the initial logit coefficient values without merging the prior data with store conditions; and
calculating, by executing an instruction with the processor, posterior output values of the prior data by evaluating the initial logit coefficient values with the penalty modifiers via a maximum likelihood estimation, the posterior output values indicative of modifications to the initial logit coefficient values caused by empirical store data sales activity.
9 . The computer-implemented method as defined in claim 8 , further including:
calculating a first one of the penalty modifiers as a market share penalty;
calculating a second one of the penalty modifiers as a segment size penalty; and
calculating a third one of the penalty modifiers as a within-segment penalty.
10 . The computer-implemented method as defined in claim 9 , further including applying the penalty modifiers as a maximized sum of the first one of the penalty modifiers, the second one of the penalty modifiers, and the third one of the penalty modifiers.
11 . The computer-implemented method as defined in claim 8 , further including calculating an observed item share value based on a sum of respective ones of the products of interest from the empirical store data sales activity.
12 . The computer-implemented method as defined in claim 11 , further including calculating a market share penalty based on the observed item share, an item ratio of respective first ones of the initial logit coefficients, and a segment ratio of respective second ones of the initial logit coefficients.
13 . The computer-implemented method as defined in claim 12 , further including calculating the item ratio as a ratio of (a) respective ones of coefficients of the products of interest and (b) a sum of all coefficients of the products of interest.
14 . The computer-implemented method as defined in claim 12 , further including calculating the segment ratio as a ratio of (a) respective ones of coefficients of the segments of interest and (b) a sum of all coefficients of the segments of interest.
15 . A tangible computer readable storage medium comprising instructions that, when executed, cause a processor to, at least:
generate a logit model associated with prior data, the logit model engine to assign initial logit coefficient values to products of interest for respective segments of interest;
improve posterior calculation efficiency by generating penalty modifiers, the penalty modifiers to balance modification of the initial logit coefficient values without merging the prior data with store conditions; and
calculate posterior output values of the prior data by evaluating the initial logit coefficient values with the penalty modifiers via a maximum likelihood estimation, the posterior output values indicative of modifications to the initial logit coefficient values caused by empirical store data sales activity.
16 . The tangible computer readable storage medium as defined in claim 15 , wherein the instructions, when executed, cause the processor to:
calculate a first one of the penalty modifiers as a market share penalty;
calculate a second one of the penalty modifiers as a segment size penalty; and
calculate a third one of the penalty modifiers as a within-segment penalty.
17 . The tangible computer readable storage medium as defined in claim 16 , wherein the instructions, when executed, cause the processor to apply the penalty modifiers as a maximized sum of the first one of the penalty modifiers, the second one of the penalty modifiers, and the third one of the penalty modifiers.
18 . The tangible computer readable storage medium as defined in claim 15 , wherein the instructions, when executed, cause the processor to calculate an observed item share value based on a sum of respective ones of the products of interest from the empirical store data sales activity.
19 . The tangible computer readable storage medium as defined in claim 18 , wherein the instructions, when executed, cause the processor to calculate a market share penalty based on the observed item share, an item ratio of respective first ones of the initial logit coefficients, and a segment ratio of respective second ones of the initial logit coefficients.
20 . The tangible computer readable storage medium as defined in claim 19 , wherein the instructions, when executed, cause the processor to calculate the item ratio as a ratio of (a) respective ones of coefficients of the products of interest and (b) a sum of all coefficients of the products of interest.