How fast will a technology nobody has bought yet be adopted?
Deep-tech products have no sales history. The standard move — fit a Bass curve to the first few data points — produces point forecasts with intervals that barely cover anything that actually happens.
The question behind diffusim is what can be known before the data exists: which priors genuinely carry information about adoption speed and market size, and which only look like they do.
How it works
Deterministic core. The Bass (1969) and Generalized Bass (1994) models with closed-form solutions; the generalized model adds price and advertising through an exact time change.
Stochastic extension. dF = (p + qF)(1 − F) dt + σF(1 − F) dW, simulated on the logit scale so paths stay inside [0, 1]. Monte Carlo output gives fan charts and distributions of peak time and penetration.
Informative priors. A prior over diffusion speed that depends on the launch era, and a unit-free prior over market potential. A Laplace posterior updates both as adoption data arrives.
Validation before claims. The simulator agrees with an independent Euler–Maruyama scheme within Monte Carlo error; dropping or flipping the Itô correction is detected at z > 45.
What came out of it
Both studies use 17 CHAT technologies (391 complete S-curves) and hold out one technology at a time; priors are estimated on the others only.
CRPS against NLS baselines — paired difference −0.035, 95% CI [−0.050, −0.022]
actual coverage of the NLS baseline’s nominal 80% intervals
MAE of a launch-era regression for diffusion speed, versus 0.625 for the training mean
CRPS increase when the market plateau is unknown — the dominant source of error
| NLS Bass | 0.141 |
|---|---|
| NLS logistic | 0.135 |
| Bayes · literature prior | 0.139 |
| Bayes · mean prior | 0.133 |
| Bayes · launch-era prior | 0.106 |
Source: diffusim M2 rolling-origin benchmark. Origins at 10%, 25% and 50% of plateau; horizon up to 15 years.
| NLS Bass | 0.20 |
|---|---|
| NLS logistic | 0.22 |
| Bayes · literature prior | 0.67 |
| Bayes · mean prior | 0.73 |
| Bayes · launch-era prior | 0.78 |
| + stochastic model | 0.85 |
The stochastic model leaves CRPS unchanged but evens out coverage across curve stages.
| Meta-analysis prior | 0.687 |
|---|---|
| Training mean | 0.625 |
| Ridge on MiniLM embeddings | 0.570 |
| Launch-era regression | 0.164 |
Adding text embeddings to launch era leaves MAE at 0.164 — product descriptions add nothing measurable at this sample size.
Stated plainly
- 17 technologies, with approximate launch years; only complete S-curves are included, so failed diffusions are absent.
- Tempering power and the scale of the stochastic term were chosen on 6 technologies; the posterior is a Laplace approximation (full NumPyro inference is the next milestone).
- Results so far are on historical technologies, not yet on a deep-tech holdout.
Under the hood
References
- Bass, F. M. (1969). A new product growth model for consumer durables. Management Science, 15(5).
- Bass, F. M., Krishnan, T. V., Jain, D. C. (1994). Why the Bass model fits without decision variables. Marketing Science, 13(3).
- Gneiting, T., Raftery, A. E. (2007). Strictly proper scoring rules, prediction, and estimation. JASA, 102(477).
- Comin, D., Hobijn, B. (2009). The CHAT dataset. NBER Working Paper 15319.