Quant Library · Evidence and gear · Any

Random-Effects Meta-Analysis with Shrinkage

Pool disagreeing studies honestly, then borrow strength across a class of products.

DerSimonian and Laird within a product, empirical-Bayes shrinkage across products, and a flag on every maker-funded study rather than a quiet exclusion.

Read the specification (PDF) Run it on the API The evidence and gear family · £599

Inputs

What it takes

Name	Type	Units	Where it comes from
studies	list of (product, effect, standard error, n, funded)	mixed	the literature
prior optional	string	-	method of moments, or your own

Outputs

What it gives back

Name	Type	Units	Notes
pooled effect and interval	floats	the effect's units
tau, I2	floats	-	how much the studies disagree beyond their errors
shrunk estimate	float	-	and how much of its own number the product kept

Method

How it works

Estimate the between-study variance τ² from Cochran's Q, floored at zero.
2 further steps in the licensed specification

Assumptions

Effects are exchangeable within a class, which is what licences the borrowing. A shoe with a plate and one without are arguably not.

Limits

Publication bias is not modelled. Funded and independent studies are both carried and labelled, which lets a reader see the split rather than trusting a correction.
1 further limits in the licensed specification

Validation

What it was measured at

Computed now, over the shoe literature in the catalogue.

Products pooled	9	from 14 studies, 1 of them maker-funded
The most-studied shoe	+3.5 ± 0.7%	over 4 studies, I² 61%
After shrinkage	+3.5%	it keeps 93% of its own number
Class mean	2.9%	what a one-study product is pulled towards

In the package

The full specification: inputs, method, assumptions and limits
The validation panel as measured on the day of purchase
A reference implementation extracted from the running source
Perpetual commercial use for one entity

Reference modules:

1 module(s), named in the licensed specification and shipped in the package

Read this before you buy. The platform's own walk-forward tests say the closing line forecasts football better than these models do. What they give you is a coherent price for every market and match, before the market opens, with the band and the working attached. Any model here that has been beaten by something simpler says so in its limits, and the validation panel above is generated from the platform's result files rather than typed in.