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ex-1: change ε to 0.88 and write the correct results

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Giù Marcer 2020-06-08 17:59:14 +02:00 committed by rnhmjoj
parent 7f5ffa5949
commit 1833ab0613
2 changed files with 9 additions and 9 deletions
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2
ex-1/bootstrap.c
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@ -150,7 +150,7 @@ double gauss_kde(double x, void * params) {
* by the sample variance times a factor which * by the sample variance times a factor which
* depends on the number of points and dimension. * depends on the number of points and dimension.
*/ */
double bw = 0.4 * p.var * pow((double)p.n*3.0/4, -2.0/5); double bw = 0.777 * p.var * pow((double)p.n*3.0/4, -2.0/5);
double sum = 0; double sum = 0;
for (size_t i = 0; i < p.n; i++) for (size_t i = 0; i < p.n; i++)

16
notes/sections/1.md
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@ -289,10 +289,10 @@ where $\mathcal{N}$ is the kernel and the parameter $\varepsilon$, called
determined in several ways. For simplicity, it was chosen to use Silverman's determined in several ways. For simplicity, it was chosen to use Silverman's
rule of thumb [@silverman86], which gives: rule of thumb [@silverman86], which gives:
$$ $$
\varepsilon = 0.63 \, S_N \varepsilon = 0.88 \, S_N
\left(\frac{d + 2}{4}N\right)^{-1/(d + 4)} \left(\frac{d + 2}{4}N\right)^{-1/(d + 4)}
$$ $$
where the $0.63$ factor was chosen to compensate for the distortion that where the $0.88$ factor was chosen to compensate for the distortion that
systematically reduces the peaks height, which affects the estimation of the systematically reduces the peaks height, which affects the estimation of the
mode, and: mode, and:
@ -303,13 +303,13 @@ With the empirical density estimation at hand, the FWHM can be computed by the
same numerical method described for the true PDF. Again this was bootstrapped same numerical method described for the true PDF. Again this was bootstrapped
to estimate the standard error giving: to estimate the standard error giving:
$$ $$
\text{observed FWHM: } w_o = \num{4.06 \pm 0.08} \text{observed FWHM: } w_o = \num{4.11 \pm 0.07}
$$ $$
Applying the $t$-test to these two values gives Applying the $t$-test to these two values gives
- $t=0.495$ - $t=1.338$
- $p=0.620$ - $p=0.181$
which shows a very good agreement and proves the estimator is robust. which shows a good agreement and proves the estimator is robust. For reference,
For reference, the initial estimation based on an histogram gave a rather the initial estimation based on an histogram gave a rather inadequate \si{4 \pm
inadequate \si{4 \pm 2}. 2}.