36 lines
906 B
Markdown
36 lines
906 B
Markdown
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# MCMC Sampling
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Metropolis-Hastings sampler for Bayesian inference with Rust acceleration.
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## Usage
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```python
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import numpy as np
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from optimizr import mcmc_sample
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# Log-likelihood of a Gaussian model
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def log_likelihood(params, data):
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mu, sigma = params
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residuals = (data - mu) / sigma
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return -0.5 * np.sum(residuals**2) - len(data) * np.log(sigma)
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observations = np.random.randn(1000) + 1.2
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samples = mcmc_sample(
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log_likelihood_fn=log_likelihood,
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data=observations,
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initial_params=np.array([0.0, 1.0]),
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param_bounds=[(-5, 5), (0.1, 5.0)],
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n_samples=8000,
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burn_in=500,
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proposal_std=0.2,
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)
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print("Posterior mean:", samples.mean(axis=0))
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```
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## Tips
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- Keep `proposal_std` modest to maintain acceptance rate (20–40%).
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- `burn_in` should be at least 5–10% of total samples for stable chains.
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- Provide tight `param_bounds` to avoid exploring invalid regions.
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