Enter Model Inputs
This calculator applies the expectation maximization procedure to a one-dimensional Gaussian mixture model with configurable starting values.
Example Data Table
This sample illustrates a two-cluster dataset suitable for testing mixture estimation and checking whether the algorithm separates low and high value groups.
| Observation # | Value | Suggested Interpretation |
|---|---|---|
| 1 | 1.1 | Lower cluster candidate |
| 2 | 1.4 | Lower cluster candidate |
| 3 | 1.7 | Lower cluster candidate |
| 4 | 2.0 | Lower cluster candidate |
| 5 | 2.2 | Lower cluster candidate |
| 6 | 2.4 | Lower cluster candidate |
| 7 | 7.8 | Upper cluster candidate |
| 8 | 8.1 | Upper cluster candidate |
| 9 | 8.4 | Upper cluster candidate |
| 10 | 8.8 | Upper cluster candidate |
| 11 | 9.0 | Upper cluster candidate |
| 12 | 9.3 | Upper cluster candidate |
Formula Used
p(xi) = Σ [ πk × N(xi | μk, σk2) ]
γik = ( πk × N(xi | μk, σk2) ) / Σ [ πj × N(xi | μj, σj2) ]
Nk = Σ γik
μk = (Σ γikxi) / Nk
σk2 = (Σ γik(xi - μk)2) / Nk
πk = Nk / n
L = Σ log [ Σ πk × N(xi | μk, σk2) ]
The routine stops when the absolute change in log-likelihood falls below the selected tolerance or when the maximum iteration count is reached.
How to Use This Calculator
- Enter your one-dimensional observations using commas, spaces, or separate lines.
- Choose the number of Gaussian components you want to estimate.
- Optionally provide initial means, variances, and weights for manual starting values.
- Set the iteration cap, convergence tolerance, and variance floor.
- Click Run EM Algorithm to estimate latent component parameters.
- Review final weights, means, variances, responsibilities, and convergence history.
- Use the CSV or PDF buttons to save the generated output.
- Compare AIC and BIC values when testing different numbers of components.
Frequently Asked Questions
1. What does this calculator estimate?
It estimates the parameters of a one-dimensional Gaussian mixture model. The output includes component weights, means, variances, responsibilities, convergence history, and model fit statistics.
2. What kind of data should I enter?
Enter numeric observations from a single variable. Values may be separated by commas, spaces, or line breaks. Non-numeric text will trigger an input validation error.
3. Why would I set manual starting values?
Manual starts help when you already know reasonable cluster centers or want to compare solutions. Different starts can lead EM toward different local optima.
4. What does convergence mean here?
Convergence means the log-likelihood changed by less than your tolerance between iterations. When that happens, the parameter updates are considered stable enough to stop.
5. What is the responsibility value?
A responsibility is the estimated probability that one component generated a specific observation. Higher responsibility means stronger membership in that latent component.
6. Why is a minimum variance floor included?
The variance floor prevents a component variance from collapsing toward zero. That improves numerical stability and reduces degenerate solutions during estimation.
7. How should I use AIC and BIC?
Use them to compare models fit to the same dataset. Lower values generally suggest a better balance between fit quality and model complexity.
8. Can I use this for multivariate mixtures?
No. This version is designed for one-dimensional Gaussian mixtures only. Multivariate EM requires covariance matrices and a different likelihood calculation.