As monotonic trends are more biologically plausible than noisy trends, this suggests that the parameter estimates absorbed relatively little noise, i.e. that restriction to a parsimonious model basis set of only 3-parameter models kept noise out of the model average parameter estimates.
The curves in Fig. 8 show a noisy linear trend, which could be smoothed to better demonstrate this linearity by sampling the data from multiple points located along different branches, but at the same fixed distance away from x, in the manner of an expanding sphere of radius y, with origin at x.
Though the raw data are noisy, the general trend (25-year moving average) shows a fairly constant rate of recording through the 17th and 18th centuries, then an increasing rate to present day.
These monthly numbers are particularly noisy, so the trend is key, and it shows the share of the population in the labor force bouncing around 63% (it was 62.8% last month) for over a year.
Even though the activity profile of each replicate is noisy, the overall trend across the eight replicates in the (i) treatment group appears to be reproducible.
Networks and clustering methods have become important tools to comprehend instances of these large-scale structures, but without methods to distinguish between real trends and noisy data, these approaches are not useful for studying how networks change.
Our conclusions still hold in the absence of this filter, even though the average trend is noisier.
In Figure 3, as SNPs with low ReliefF scores were removed sequentially, the histogram of p-values started to shift toward 0. Also in Figure 4, the global test p-values were in decreasing trends when noisy SNPs were removed one by one.
That doesn't mean the short-term trend isn't noisy.
However, for truncated, noisy time series with background trends this unique mapping breaks down and the question reduces to an inference problem of identifying the most probable frequencies.
