# Why Credibility Interval (CI) is slightly changing while estimating Posterior Coverage by using SQUEAC coverage estimate calculator (Version 3.01)

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### Anonymous 1310

Nutrition Manager

Normal user

30 Oct 2013, 12:52

I used: Alpha: 26.9, Beta: 13 and precision %: 10,

From wide area survey, we found 48 SAM children out of which 27 SAM children were in OTP program and 21 SAM children were not in OTP program. SQUEAC Coverage estimate calculator gives the posterior coverage:

61.6% ( CI 50.9%-71.0),

61.6% ( CI 51.0%-70.9%),

61.6% (CI 51.1%.-71.1%) ....

My question is: Why different CI though all other parameters are same?

### Lio

CMAM advisor

Technical expert

31 Oct 2013, 10:16

Dear Sanjay,

Mark, as the inventor of the SQUEAC Bayes, will give you more details but you should not worry about the slightly different figures. This is just a question of "computer internal calculations" and, as you can see, the difference doesn't really impact on the result. By the way, sometime you may also see that the posterior figure will be slightly different (which is not the case in your example), again............... this is just a computer matter.

### Mark Myatt

Consultant Epideomiologist

Frequent user

31 Oct 2013, 11:16

The difference is due to BayesSQUEAC using a bootstrap estimator (a modified bagging approach is used).

This "resampling" approach is better than the approximate methods presented in the SQUEAC / SLEAC technical reference in the sense that the coverage of the credible interval is very close to 95% regardless of the value of the posterior mode even when small effective sample sizes are used. The approximate method does this only when the posterior mode is 50% and the effective sample size is above about n = 30. Coverage of the approximate credible interval can be different from the (stated) 95% when the posterior mode is below about 20% or above about 80% or when effective sampled sizes are small.

The effect of using a bootstrap approach is that it is a little "wobbly" WRT the exact position of the credible limits. In your example the "wobble" is plus or minus 0.1%. This can be reduced but doing so would make BayesSQUEAC run slowly on older computers.

I hope this helps.

### Mark Myatt

Consultant Epideomiologist

Frequent user

1 Nov 2013, 10:10

A computer / tech post ... I forgot to say that BayesSQUEAC is open source software. You can get the TCL source code here. The bagging code is on lines 1251 thru 1262. This code is free for you (and anyone else) to use and modify.

You can reduce the "wobble" by increasing the value '100' in line 1255. The current code uses 100 bags of size 100 (i.e. 10,000 bootstrap replicates). These procedures behaves in a similar way to survey sample sizes in that the degree of "wobble" decreases with the square root of the increase in the number of replicates used. Having (e.g.) 1000 bags of size 100 (i.e. 100,000 bootstrap replicates) will reduce the "wobble" by about 3.16 times (from 0.1% to 0.03% in your example) but take 10 times longer to run. The number of replicates used in BayesSQUEAC was set as a compromise between "wobble" and keeping the software fast enough to be interactive.