Metropolis-Hastings Normal Sampler
Use a Gaussian random-walk Metropolis-Hastings chain targeting the standard normal density. Report acceptance rate; samples are correlated.
Description
Use a Gaussian random-walk Metropolis-Hastings chain targeting the standard normal density. Report acceptance rate; samples are correlated.
Metropolis-Hastings Normal Sampler: Use a Gaussian random-walk Metropolis-Hastings chain targeting the standard normal density. Report acceptance rate; samples are correlated.
When to use Metropolis-Hastings Normal Sampler
Use this probability or sampling tool to compute a stated quantity or generate reproducible draws from a precisely parameterized distribution or stochastic model.
- start
- Required number input.
- proposal Scale
- Required number input.
- count
- Required integer input.
- seed
- Required string input.
How Metropolis-Hastings Normal Sampler works
Use a Gaussian random-walk Metropolis-Hastings chain targeting the standard normal density. Report acceptance rate; samples are correlated. The tool evaluates the supplied inputs together and returns the named outputs below; it does not infer omitted operating conditions or change the units shown.1
- samples
- The resulting samples returned as a list.
- acceptance Rate
- The resulting acceptance rate returned as a number.
Limitations and assumptions
- Results depend on parameterization, support, random source, seed, convergence, burn-in, autocorrelation, proposal quality, normalization, numerical tails, and whether model assumptions match the process. Samples are not exact evidence of convergence.
- Use finite inputs in the displayed units and preserve more precision than the final presentation requires. Independently verify safety-critical, financial, compliance, or production decisions.
Alternative or Complementary approaches
Check analytic moments or known test cases, use independent chains and diagnostics for Monte Carlo methods, report seed and effective sample size, and inspect tail behavior.
References
-
Monte Carlo method — Wikipedia contributors
Similar or alternative tools
- Hamiltonian Monte Carlo Standard Normal Sampler
Run one-dimensional HMC with leapfrog integration and Metropolis correction for the standard normal target; report acceptance rate.
- Bivariate Normal Gibbs Sampler
Alternate conditional Gaussian draws for a zero-mean, unit-variance bivariate normal with caller-supplied correlation. Samples are autocorrelated.
- Sequential Monte Carlo Gaussian Filter
Run a bootstrap particle filter for a one-dimensional Gaussian random walk observed with Gaussian noise; report weighted posterior means and resampled final particles.