Figure 1.
Biomedical example of interval-based parameter estimation - probabilistic representation of the 3D shape of the right hippocampus in the computational Alzheimer's disease brain atlas.
Figure 2.
The SOCR distributions applet provides interactive calculation of critical and probability values for over 70 different probability distributions.
Figure 3.
Output window of the SOCR confidence interval applet.
Figure 4.
Input window of the SOCR confidence interval applet.
Figure 5.
An example: Normal distribution, , 20 confidence intervals.
Figure 6.
Results of a single run of the CI experiment.
Figure 7.
Results of 10 runs of the experiment.
Figure 8.
Input of the experiment when is not known.
Figure 9.
Results of 10 runs of the experiment.
Figure 10.
Confidence intervals for - sampling from normal distribution.
Figure 11.
Confidence intervals for - sampling from non-normal distribution, e.g. exponential,
.
Figure 12.
Confidence intervals for - sampling from non-normal distribution,
.
Figure 13.
Large samples confidence intervals for - sampling from non-normal distribution.
Figure 14.
Confidence interval for proportion : Sampling from
.
Figure 15.
Confidence interval for proportion : Poor coverage using the Wald confidence interval.
Figure 16.
Confidence interval for proportion : Good coverage using the Clopper-Pearson confidence interval.
Figure 17.
Confidence intervals using asymptotic properties of maximum likelihood estimates - Poisson distribution with parameter .
Figure 18.
Confidence intervals using asymptotic properties of maximum likelihood estimates - Exponential distribution with parameter .
Figure 19.
US Unemployment distribution (1959–2009).
Figure 20.
Modeling the unemployment data using generalized Beta distribution.
The coordinate axes represent X = (values) unemployment rate and Y = (frequencies) number of months (1959–2009) when unemployment rate was at the given X value.
Figure 21.
SOCR Confidence interval simulation settings panel for estimating the unemployment rate (proportion of US unemployed workers) using the generalized Beta () distribution model described above.
Figure 22.
Results of 100 simulations (samples include N = 2,000 random observations from Beta distribution) of 0.99 confidence intervals for the population proportion (using the exact method) provide effective coverage of 95%.
Five of the 100 simulations miss the real population proportion p = 0.47, which represents the shaded area below the Beta density function. This proportion indicates a healthy US unemployment rate between .
Figure 23.
Illustration of the relation between local cortical folding patterns and the values of the curvedness measure computed for each vertex on the shape.
Averaging all local curvedness measures over the entire surface provides a global curvedness index measuring the overall complexity of a shape. This figure shows the left lateral view of the cortical surface of one subject color coded by the local curvedness.
Table 1.
Bilateral (left and right) point (median) and interval (0.99 confidence intervals using bootstrapping with 20,000 resampling simulations) estimates for the hippocampal surface complexity (measured using curvedness) for the 3 cohorts.