Bayesian Forecast Studio

Prices · Revenue · Profitability

Full posterior distributions over the profit-maximising price p* = c·η/(η−1), expected revenue, and horizon profit — combining conjugate priors (Normal–Normal for elasticity, Normal– Inverse-Gamma for log-revenue drift, Beta–Binomial for conversion, Gamma for AOV and fixed costs) with Monte-Carlo pushforward. Every KPI is a credible interval, not a point estimate.

Priors & data

Unit cost c

Elasticity prior N(μ, σ²)

Prior mean |η|

Prior sd

Data likelihood

Sample |η̂|

Sample sd

N observations

Demand at ref price

Reference price

Fixed cost F ~ Gamma(k,θ)

Shape k

Scale θ

Posterior draws: 4000

Seed

Posterior on |η|

Posterior mean 2.493 · sd 0.088. Prior weight vs data set by relative precisions 1/σ_prior² vs N/σ_data².

2.185% 2.35 · med 2.49 · 95% 2.642.80

Optimal price p*

$20.03

90% CI $19.32 — $20.90

$18.675% $19.32 · med $20.03 · 95% $20.90$22.17

Gross margin

40.1%

90% CI 37.9% — 42.6%

35.7%5% 37.9% · med 40.1% · 95% 42.6%45.9%

Expected revenue at p*

$52,155.62

90% CI $47,713.78 — $57,128.70

$43,182.195% $47,713.78 · med $52,155.62 · 95% $57,128.70$63,345.20

Expected profit (net of F)

$20,343.56

90% CI $19,504.84 — $21,174.62

$18,330.405% $19,504.84 · med $20,343.56 · 95% $21,174.62$22,105.46