I numerically integrate a differential equation of the form $y’ = f(y, a, b)$ where the parameters $a$ and $b$ are real numbers.
Also, I have many real numbers $v$ from $v_1$ to $v_m$ ($m$ is around 5000 to 6000) and a few $b$'s from $b_1$ to $b_n$ ($n$ is usually 9 or 10).
To obtain the nominal result of my procedure:
$A$ = average of $v$'s
$r_1$ = result of the integration of $y’ = f(y, A, b_1)$
...
$r_n$ = result of the integration of $y’ = f(y, A, b_n)$
the nominal value of my output is the average of $r$'s.
To obtain the upper bound of the "nominal value of my output" @80% confidence level:
$L$ = lower bound of the confidence interval of $A$ @80% confidence level
$r_1$ = result of the integration of $y’ = f(y, L, b_1)$
...
$r_n$ = result of the integration of $y’ = f(y, L, b_n)$
the upper bound of my output is the average of $r$'s.
To obtain the lower bound of the "nominal value of my output" @80% confidence level:
$U$ = upper bound of the confidence interval of $A$ @80% confidence level
$r_1$ = result of the integration of $y’ = f(y, U, b_1)$
...
$r_n$ = result of the integration of $y’ = f(y, U, b_n)$
the lower bound of my output is the average of $r$'s.
I’m not sure that the correct results are the average of the $r$'s.
Should I calculate the confidence interval of those $r$'s?