Infer.NET Counting (net8.0)

This sample demonstrates Bayesian inference with Microsoft Infer.NET: given repeated draws from an urn with two colours, infer a posterior distribution over the number of balls in the urn.

The model assumes the proportion of colours is known a priori (here 50/50). Each draw selects a ball uniformly at random with replacement. Optionally, observations can be noisy via a colour flip variable.

Problem

Given a sequence of observed colours from repeated draws, estimate the discrete distribution over the total number of balls. For example, if 10 draws are all blue, how likely is each possible count from 0 to a maximum?

Solution (model)

• The prior over numBalls is uniform over [0, maxBalls].
• For each hypothetical ball, its colour is Bernoulli(0.5).
• Each draw indexes a ball uniformly from 0..numBalls-1 and observes its (possibly flipped) colour.
• Inference is performed with InferenceEngine to obtain a Discrete posterior for numBalls.

See Counting.cs for the full model.

Requirements

• .NET 8 SDK

Build and run

dotnet build
dotnet run --project Counting.csproj

You can tweak the observations in Counting.cs to explore different scenarios (e.g., add noise, change number of draws, or increase maxBalls).

Scenarios and interpretation

The program runs several predefined scenarios:

• 10 blue (noiseless): strong evidence for larger feasible counts up to the prior support.
• 5 blue / 5 green (noiseless): evidence spreads more evenly since both colours appear.
• 10 blue (20% noise): the posterior broadens; some unlikely outcomes can be explained by noise.
• Mixed sequence (20% noise): reflects ambiguity due to both colour variety and noise.

The printed posterior is a Discrete distribution over counts 0..maxBalls. Read it as the probability mass for each possible number of balls.

Model and assumptions

This is a simple generative Bayesian model:

• A discrete latent variable numBalls ∈ {0..maxBalls} with a uniform prior encodes the unknown count.
• Each hypothetical ball has a latent colour sampled i.i.d. from Bernoulli(0.5) (known 50/50 colour mix).
• Each draw selects a ball uniformly at random with replacement.
• An optional noise variable flips the observed colour with probability noise to capture measurement/error.

Key assumptions to be aware of:

• The colour proportions are known and fixed at 50/50. If proportions are unknown, they should be modelled with a prior (e.g., Beta-Bernoulli) and inferred jointly.
• Draws are independent and identically distributed (with replacement, no depletion).
• Noise is symmetric and i.i.d. across draws; domain-specific asymmetries should be modelled explicitly when needed.
• The support maxBalls truncates the posterior; choose it large enough to avoid truncation bias.

Where this model is useful

This pattern—inferring a discrete count from noisy binary (or categorical) observations—appears in many domains:

• Quality control and reliability: estimate the number of defective items given pass/fail tests with known false positive/negative rates.
• Sensor fusion and telemetry: infer the number of active sources/signals from binary detections with misclassification/noise.
• Epidemiology and ecology: estimate population sizes from repeated detection/non-detection surveys with imperfect detection.
• A/B testing style telemetry: infer the size of an engaged subgroup from noisy user events.
• Inventory and operations: estimate stock counts from spot-check samples when observations can be erroneous.

The model can be extended by:

• Learning the colour proportion with a Beta prior; extending to multi-colour with a Dirichlet-Categorical prior.
• Using hierarchical priors to share strength across multiple urns/segments.
• Replacing the symmetric flip-noise with asymmetric error models learned from data.

Notes

• This project targets net8.0 and uses SDK-style csproj with PackageReference.
• Packages: Microsoft.ML.Probabilistic and Microsoft.ML.Probabilistic.Compiler.

License

Licensed under the Apache License, Version 2.0. See LICENSE for details.