An independent study reference written by Dr Phuc V. Nguyen. It is not official subject material — for assessment requirements always follow your subject outline and vUWS.

What Business Analytics Isintermediate

Descriptive, predictive and prescriptive analytics

Q: A supermarket demand model gives a median forecast of 200 units for a chilled line tomorrow, with a continuous spread of possible demand on either side. Wasting a unit costs A0.90 and running out forgoes A3.10 of margin. What does prescriptive analytics recommend?

Order more than 200, because running out costs over three times as much as waste. A forecast is the centre of a distribution, not an instruction. Expected cost is lowest at the demand quantile set by the underage cost over the two costs combined, here 3.10 divided by 4.00, or the 77.5th percentile. That sits above the median of 200, so the recommended quantity is above 200. Ordering exactly the median treats the two errors as equally painful, which they clearly are not here, and ordering below it makes the costlier error more likely.

Q: An analyst reports that customers who received a discount code renewed at a higher rate, and recommends sending codes to everyone. Which layer is missing?

Prescription, because no objective, cost or constraint is stated and the comparison may not be causal. The observation is descriptive. Turning it into an action needs the margin given away by the discount, the budget available to fund it, and evidence that the code caused renewal rather than being redeemed by customers who would have renewed regardless. Without those, a recommendation has been made with the prescriptive step skipped.

Analytics is usually sorted into three questions. Descriptive analytics establishes what happened, including the diagnostic work of slicing data until the pattern is explained. Predictive analytics estimates what is likely next, producing a probability or a range rather than a certainty. Prescriptive analytics adds an objective, the available actions and the cost of each kind of error, so the prediction becomes a recommendation. The layers stack. A prescription resting on a shaky forecast, or a forecast resting on a description nobody trusts, inherits every weakness underneath it.

Why it matters

A cafe owner looks at last month and sees that Tuesday is quiet. That is description. She expects about four hundred and thirty customers tomorrow because the weather is warm and a market runs in the square. That is prediction. She then works out how many pastries to bake, knowing that throwing one out costs less than turning a customer away. The last step, where cost enters, is prescription.

Before you read on — recall

A supermarket demand model gives a median forecast of 200 units for a chilled line tomorrow, with a continuous spread of possible demand on either side. Wasting a unit costs A$0.90 and running out forgoes A$3.10 of margin. What does prescriptive analytics recommend?

Formulas

Prescription is prediction plus an objective

a^{\star} = \arg\max_{a \in A} \sum_{s} P(s \mid x)\, u(a, s)

The prediction supplies

P(s \mid x)

, the chance of each future state

s

given what is known now. The business supplies

u(a, s)

, the value of taking action

a

if state

s

occurs, and

A

, the actions actually available. Prescriptive analytics is the step that joins them. Predictive analytics stops at the first term and leaves the rest to a person.

Asymmetric costs move the recommended action

E[\text{cost}](q) = c_o \, E\big[(q - D)^{+}\big] + c_u \, E\big[(D - q)^{+}\big]

Prepare

q

units against uncertain demand

D

. The notation

(q - D)^{+}

means the leftover when it is positive and zero otherwise, so the first term is waste priced at the overage cost

c_o

and the second is missed sales priced at the underage cost

c_u

. Expected cost is minimised at the demand quantile

F^{-1}(c_u/(c_o + c_u))

, known as the critical fractile. When missing a sale hurts more than wasting a unit that fraction exceeds one half, so the order sits above the median of demand. Whether it also sits above a quoted point forecast depends on what that forecast reports and on the shape of the distribution, which is why a prescription is never simply the forecast read off a chart.

Worked examples

Scenario

A cafe chain has a dashboard of daily sales by store, a demand model, and an afternoon decision about how much to prepare for tomorrow. Show what each layer contributes.

Solution

Description says the eastern store sold 9 per cent less last month, and that the drop sits between seven and nine in the morning, which points at the road closure rather than at price. Prediction says tomorrow brings about 430 customers, with a plausible range of 380 to 480, given warm weather and a Saturday market. Prescription asks what to bake. A discarded pastry costs A$1.20 and a missed sale forgoes A$2.60 of margin, so a missed sale carries 2.60 of every 3.80 of error cost. The chain should prepare at approximately the 68th percentile of demand, which lies above the median. The exact quantity requires the demand distribution, which a range of 380 to 480 does not supply.

Scenario

A hospital emergency department wants shorter waiting times and has been told it needs predictive analytics.

Solution

A forecast of arrivals by hour is useful, but by itself it changes nothing, because the department cannot alter how many people fall ill. The decision that exists is the roster. Turning the forecast into a roster needs the objective, which is waiting time inside a target, the constraints, which are staff available and minimum skill mix, and the cost of being wrong in each direction. Without those, the department has bought a prediction and left the prescriptive step to a manager with a whiteboard.

Common mistakes

✗The three types form a maturity ladder with prescriptive at the top. They are three different questions. Many valuable projects are purely descriptive, and a prescription is only ever as good as the description and prediction beneath it.
✗Diagnostic analytics has to be a separate fourth type. Some published taxonomies do list it separately, and that split is defensible. This atlas folds diagnosis into descriptive work, because the question is still what happened, cut finer until the pattern becomes explainable. Either convention works as long as you say which one you are using.
✗A prediction tells you what to do. A prediction gives probabilities. It becomes a recommendation only once someone states the objective, the feasible actions and the cost of each kind of error.
✗Prescriptive analytics removes the need for judgement. It moves judgement earlier. Someone still decides what is being maximised, which actions are permitted and which mistakes are worse, and those choices drive the answer that comes out.

Revision bullets

•Descriptive = what happened, diagnosis included
•Predictive = what is likely, stated as a probability or a range
•Prescriptive = prediction plus objective, feasible actions and error costs
•Each layer inherits the weaknesses of the layer below it
•Asymmetric error costs push the action away from the central forecast

Quick check

An analyst reports that customers who received a discount code renewed at a higher rate, and recommends sending codes to everyone. Which layer is missing?

Connected topics

What Analytics Is BI vs Analytics Analytics Workflow Correlation vs Cause Models & Abstraction Decision Support Supervised vs Unsup.KPI Design

More in What Business Analytics Is

Analytics in Practice Why Analytics Stalls

Sources

Shmueli (2010)
Shmueli, G. "To Explain or to Predict?" Statistical Science, 25(3), 289-310, 2010.
Shows that explaining what happened and predicting what will happen are different goals that can call for different models.
Provost & Fawcett (2013)
Provost, F., & Fawcett, T. Data Science for Business. O'Reilly Media, 2013.
Works through how a predictive model becomes a business action once costs and benefits of each outcome are attached.

How to cite this page

Dr. Phil's Quant Lab. (2026). Descriptive, predictive and prescriptive analytics. Derivatives Atlas. https://phucnguyenvan.com/concept/ba-descriptive-predictive-prescriptive