Bayesian Estimation with Aggregate Data

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Bayesian Estimation with Aggregate Data

• Eric T. Bradlow U. of Pennsylvania (Wharton)
• Andrés Musalem Duke U. (Fuqua)
• Marcelo Olivares Columbia U. (CBS)
• Christian Terwiesch U. of Pennsylvania (Wharton)
• Daniel Corsten IE Business School

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Motivation iPhone
How would the analyst with Apple store-level
data know whether when YOU went to buy the
product the store was Out Of Stock on the shelf?
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Motivation Coupon Distribution
How would the analyst with data on aggregate
purchase information and information on
aggregate coupon distribution know that YOU had
received a coupon?
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Motivation Store Path Tracking
How would the store manager with aggregate store
information on store traffic know where YOU went
and which products you therefore considered?
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Big Picture

• Many situations in which we dont observe
  individual behavior (or arent allowed to because
  of privacy/legal reasons), but we may have some
  aggregate or limited information.
• Many marketing problems involve making statements
  (targeting or pricing) individual consumers
• Key use aggregate data to formulate mathematical
  constraints on the unobserved individual behavior.

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Estimation
Initial Values Sequence of Choices, Availability
and Demand Parameters
Gibbs Sampler
Individual Choices Availability
Prior Parameters
Population Parameters
MCMC Simulation
Individual Parameters
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Example Out of Stocks

• Observed data act as constraints

choice indicator
sales
Choices
initial inventory
inventory faced by customer i
Constraints
Inventory
product availability indicator
Product Availability
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Example

• Available information
• N total number of customers20.
• SA number of customers buying A 10.
• SB number of customers buying B 3.
• IA inventory at the beginning and the end of the
  period for brand A 10?0.
• IB inventory at the beginning and the end of the
  period for brand B 5?2.

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Out-of-Stocks (OOS)

• Available information
• N total number of customers20.
• NA number of customers buying A 10.
• NB number of customers buying B 3.
• IA inventory at the beginning and the end of the
  period for brand A 10?0.
• IB inventory at the beginning and the end of the
  period for brand B 5?2.

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Given the fake pseudo-datafit a demand model

• Multinomial Logit Model with heterogeneous
  customers.

marketing variables
demand shock
availability indicator
product
choice
market
consumer
period
Infer individual-level data, and hence product
availability from the fake pseudo data sets
and fit the model using standard software
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Conclusions

• There are many situations in which
• Information on individual consumers is
  unavailable
• Information on individual consumers is available,
  but there is also aggregate information (data
  fusion problem)
• Methods to analyze such data will increase the
  ability of firms to target consumers with limited
  information.
• Reality is that many firms are unable to deal
  with large quantities of information, hence these
  methods are here to stay.

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Thank You