UPDATE:

I would say the most efficient AND readable way of working out confidence intervals from bootstraps is

Where

Confidence intervals can be computed by bootstrapping the calculation of a descriptive statistic and then finding the appropriate percentiles of the data. I saw that scipy.stats has a built in percentile function and assumed that it would work really fast because (presumably) the code is in C. I was using a simple minded Python/Numpy implementation by first sorting and then picking the appropriate percentile data. I thought this was going to be inefficient timewise and decided that using scipy.stats.scoreatpercentile was going to be blazing fast because

I would say the most efficient AND readable way of working out confidence intervals from bootstraps is

`:`

`numpy.percentile(r,[2.5,50,97.5],axis=1)`

Where

`r`

is a `n x b`

array where `n`

are different runs (e.g different data sets) and `b`

are the individual bootstraps within a run. This code returns the 95% CIs as three numpy arrays.Confidence intervals can be computed by bootstrapping the calculation of a descriptive statistic and then finding the appropriate percentiles of the data. I saw that scipy.stats has a built in percentile function and assumed that it would work really fast because (presumably) the code is in C. I was using a simple minded Python/Numpy implementation by first sorting and then picking the appropriate percentile data. I thought this was going to be inefficient timewise and decided that using scipy.stats.scoreatpercentile was going to be blazing fast because

- It was native C
- It was vectorized - I could compute the CIs for multiple bootstrap runs at the same time
- It could pick out multiple percentiles (low and high ends) at the same time.

python test.py | grep 'function calls' 38 function calls (36 primitive calls) in 0.001 seconds 12 function calls in 0.001 seconds 38 function calls (36 primitive calls) in 0.001 seconds 12 function calls in 0.001 seconds 38 function calls (36 primitive calls) in 0.876 seconds 17 function calls in 0.705 seconds 38 function calls (36 primitive calls) in 0.814 seconds 17 function calls in 0.704 seconds

```
import pylab, cProfile, scipy.stats as ss
def conf_int_scipy(x, ci=0.95):
low_per = 100*(1-ci)/2.
high_per = 100*ci + low_per
mn = x.mean()
cis = ss.scoreatpercentile(x, [low_per, high_per])
return mn, cis
def conf_int_native(x, ci=0.95):
ci2 = (1-ci)*.5
low_idx = int(ci2*x.size)
high_idx = int((1-ci2)*x.size)
x.sort()
return x.mean(), x[low_idx], x[high_idx]
def conf_int_scipy_multi(x, ci=0.95):
low_per = 100*(1-ci)/2.
high_per = 100*ci + low_per
mn = x.mean(axis=0)
cis = ss.scoreatpercentile(x, [low_per, high_per],axis=0)
return mn, cis
def conf_int_native_multi(x, ci=0.95):
ci2 = (1-ci)*.5
low_idx = int(ci2*x.shape[1])
high_idx = int((1-ci2)*x.shape[1])
mn = x.mean(axis=1)
xs = pylab.sort(x)
cis = pylab.empty((mn.size,2),dtype=float)
cis[:,0] = xs[:,low_idx]
cis[:,1] = xs[:,high_idx]
return mn, cis
r = pylab.randn(10000)
cProfile.run('conf_int_scipy(r)')
cProfile.run('conf_int_native(r)')
r = pylab.randn(10000)
cProfile.run('conf_int_scipy(r)')
cProfile.run('conf_int_native(r)')
r = pylab.randn(1000,10000)
cProfile.run('conf_int_scipy_multi(r)')
cProfile.run('conf_int_native_multi(r)')
r = pylab.randn(1000,10000)
cProfile.run('conf_int_scipy_multi(r)')
cProfile.run('conf_int_native_multi(r)')
```

## Comments

## Post a Comment