Filtering Artifacts with IBIGF set to 3

memexp-6.0.exe simple dir4/data.004 1 none 1. 1. 2 40 0 5.0D-4 0

memexp-6.0.exe simple dir4b/data.004 1 none 1. 1. 2 40 0 5.0D-4 3 0.813 -1.1

The fourth test case analyzes a noisy data set with a uniform prior model (IBIGF = 0), and based on the peaks seen at short liftimes, the fifth test case repeats the analysis with IBIGF = 3, applying a filter at LTCUT = -0.9. Setting IBIGF to 3 allows the prior model to be derived from the data by omitting the shortest-lifetime peak(s) resolved using a uniform prior, here those peaks at lifetimes shorter than log $\tau$ = -0.9. This example involves tri-exponential kinetics simulated with amplitudes that sum to zero and time-independent standard errors. Here, the noise-free signal is $D(t) = e^{-t} - 2e^{-3.333t} + e^{-10t}$, and $\sigma = 0.25$. See [2] for more details of a similar analysis with $\sigma = 0.2$. Notice that the lifetime distribution obtained using a uniform prior model is improved by incorporarting only the slowest processes resolved into the revised (bootstrapped) prior model. Again, it is wise to assess the variability in the lifetime distribution that is afforded by the signal-to-noise, in particular, whether peaks obtained at the shortest lifetimes are needed to fit the data.

Again, these simple calculations performs three different calculations in succession: a preliminary MEM inversion, an estimation of the data's standard errors based on the appropriate MEM fit, and a final series of fits to the data by both continuous and discrete kinetic descriptions.

Note that the simple estimates of D0 automated in MemExp (when D0 is set to zero) are based on the first and last data points (see definition of D0OPT). Clearly, these estimates are insufficient for data that are very noisy and/or have appreciable slope at short times. Therefore, for these data, D0 is set to 1.0 on the command line:

Compare iterations 301 and 422 plotted in dir4b/data.004_e1.out.ps. Note that after the peaks obtained at early times in iteration 391 are excluded from the prior model (black dotted lines plotted with iteration 422), a lower value of $\chi^2$ is reached in iteration 422 with fewer peaks than in iteration 301, and the mean of the slowest process is improved.