Calculator Form
Enter pooled counts directly, or paste per-chain rows. If valid chain rows are provided, they override manual totals.
Example Data Table
| Chain | Accepted | Rejected | Total Proposals | Acceptance Rate (%) |
|---|---|---|---|---|
| Chain 1 | 420 | 180 | 600 | 70.00 |
| Chain 2 | 390 | 210 | 600 | 65.00 |
| Chain 3 | 360 | 240 | 600 | 60.00 |
| Chain 4 | 450 | 150 | 600 | 75.00 |
In this example, pooled accepted proposals equal 1,620 and rejected proposals equal 780. The overall acceptance rate is 67.50%.
Formula Used
Acceptance Rate = (Accepted Proposals ÷ Total Proposals) × 100
Rejection Rate = (Rejected Proposals ÷ Total Proposals) × 100
Total Proposals = Accepted Proposals + Rejected Proposals
Target Gap = Observed Acceptance Rate − Target Acceptance Rate
Accept / Reject Ratio = Accepted Proposals ÷ Rejected Proposals
Retained Iterations = floor((Total Proposals − Burn-in Iterations) ÷ Thinning Interval)
ESS Efficiency = (Effective Sample Size ÷ Retained Iterations) × 100
Acceptance rate is a tuning summary, not a proof of convergence. It should be interpreted together with trace plots, autocorrelation, effective sample size, and domain-specific diagnostics.
How to Use This Calculator
- Enter accepted and rejected proposal counts, or paste per-chain rows.
- Select the algorithm family so the calculator can compare your rate with a practical tuning band.
- Provide burn-in, thinning, ESS, and proposal scale if you want deeper diagnostics.
- Click Calculate to show the results above the form.
- Review the graph, summary cards, interpretation text, and per-chain table.
- Download the result summary as CSV or PDF for reporting.
Frequently Asked Questions
1) What does MCMC acceptance rate measure?
It measures how often proposed moves are accepted by the sampler. A higher value means proposals are accepted more often, while a lower value means proposals are rejected more often.
2) Is a higher acceptance rate always better?
No. Extremely high acceptance can signal tiny proposal moves, which may slow exploration. Good tuning balances acceptance with meaningful movement across the target distribution.
3) Why can a low acceptance rate be a problem?
Low acceptance often means proposals are too large or poorly matched to the target shape. The chain may stay stuck, mix slowly, and produce less efficient samples.
4) What target rate should I use?
That depends on the sampler. Random-walk methods often prefer moderate rates, while HMC-style samplers usually work with higher rates. This calculator compares your result against a practical band.
5) Should burn-in change the acceptance rate?
Burn-in does not change the raw acceptance formula itself. It changes how many retained iterations remain for later analysis after early transient samples are removed.
6) Can I combine several chains here?
Yes. Paste per-chain accepted and rejected counts into the chain table box. The calculator pools totals and also reports acceptance rate for each chain separately.
7) Does acceptance rate prove convergence?
No. A reasonable acceptance rate can still hide poor convergence. Always inspect trace behavior, effective sample size, autocorrelation, and other diagnostics before trusting the chain.
8) Why include ESS efficiency in this page?
Acceptance alone is incomplete. ESS efficiency links retained iterations to usable information, helping you judge whether the sampler is both accepting enough moves and producing effective samples.