Welcome to Prof. Edward Voigtman's
simulation software web site!
The LightStone software is entirely FREE, with full, commented source code! Note that LightStone is an add-on to the ExtendSim (or ExtendCP) simulation program and requires a variety of the ExtendSim (or ExtendCP) program, in order to run. To purchase ExtendSim, or obtain a free demo version of ExtendSim, contact Imagine That, Inc. for all details, pricing, varieties of the program, etc. The last released version of ExtendCP was 6.0.8, which works great. In fact, I am still using it! ExtendCP was then superceded by ExtendSim, the latest version of which is 7.0.4. This also works great, based on my evaluation of the demo version.
Scroll down past the hundreds of free "as is" models
for the Limit of Detection papers!
| Libraries | Libraries |
| Runtime libraries | Runtime libraries |
| Models for LOD papers | Models for LOD papers |
| Literature references |
|---|
LightStone Annotated Models
These are updated versions of models released well over a decade ago:
LightStone Model sets ("as is"):
You will also need this: Retired Library (Mac)
or this: Retired Library (PC)
for some of the hundreds of "as is" model sets!
| Macintosh 1 | Windows PC 1 |
| Macintosh 2 | Windows PC 2 |
| Macintosh 3 | Windows PC 3 |
| Macintosh 4 | Windows PC 4 |
| Macintosh 5 | Windows PC 5 |
| Macintosh 6 | Windows PC 6 |
| Macintosh 7 | Windows PC 7 |
| Macintosh 8 | Windows PC 8 |
| Macintosh 9 | Windows PC 9 |
| Macintosh 10 | Windows PC 10 |
| Macintosh 11 | Windows PC 11 |
| Macintosh 12 | Windows PC 12 |
| Macintosh 13 | Windows PC 13 |
| Macintosh 14 | Windows PC 14 |
| Macintosh 15 | Windows PC 15 |
| Macintosh 16 | Windows PC 16 |
| Macintosh 17 | Windows PC 17 |
| Macintosh 18 | Windows PC 18 |
| Macintosh 19 | Windows PC 19 |
| Macintosh 20 | Windows PC 20 |
More will be added in the coming weeks!
Voigtman's PittCon 2008 Talk in New Orleans, LA
(Apple Keynote presentation format, zipped)
Limits of Detection as of 2008
At the very heart of Analytical Chemistry, the part of chemistry I call home, lives the fundamental concept of limit of detection (LOD). In simple terms, this is essentially the lowest chemical content (net response) that is statistically different than a 'blank', i.e., a chemical system lacking the chemical moiety of interest (which substance is called the 'analyte'). In the years since World War II, the concept has been investigated and elaborated by many researchers because it serves the important purpose of allowing comparison of the 'detection power' of competing analytical techniques. The LOD is therefore a figure of merit for how 'good' an analytical technique (or method) is and the analytical literature contains vast numbers of tabulated LODs, with lower LODs always being considered better than comparable higher LODs.
Unfortunately for researchers, there are many possible instantiations of limits of detection and these do not yield the same results. At present, there are two main schools of thought on the matter, with numerous sub-varieties of LOD definitions and protocols. Even when attention is restricted to instrumental LODs, and the measurement noise is Gaussian and white, there are still major differences between the first camp (researchers who employ the simplest classical LOD definitions, that entirely ignore false negative detection errors) and the second camp (researchers who follow a variation of Lloyd Currie's classic Neyman-Pearson hypothesis testing formulation of LODs).
These two camps have been locked in battle since Currie's seminal paper was published in 1968. Forty years on, Currie's schema is very slowly winning, amid on-going attempts by various international organizations (e.g., IUPAC, ISO, the European Commission) and United States government agencies (e.g., the seven MARLAP agencies: DoE, DoD, DHS, NIST, EPA, USGS and NRC) to 'harmonize' detection limit definitions, protocols, etc. (Note: 'MARLAP' stands for 'Multi-Agency Radiological Laboratory Analytical Protocols'.)
Given the parties involved and the many thousands of analysts who would welcome such standardization, it is clear, a priori, that this is a worthy goal that is definitely non-trivial. Metaphorically speaking, the task of standardizing and harmonizing LOD concepts and protocols is akin to salvaging treasure from a sunken ship. In either case, there is almost no prospect of success without a map and a good starting spot, and this is a major factor that has obstructed progress. A second obstruction arises from the on-going battle between the two camps, which has the result that the 'fog of war' has confused the refereed scientific literature. This manifests as demonstrably wrong results, theories, interpretations and conclusions being published, and then vigorously defended. Another problem is that dead-ends also get planted in the scientific literature and then take on the status of 'folk theorems'.
So this is where the limit of detection situation stood at the end of May, 2006, when I was sent a manuscript to review for the journal (which I had never heard of before) MATCH Communications in Mathematical and in Computer Chemistry. The authors, a pair of statisticians named Nadarajah and Kotz, had demonstrated a simple way to improve upon a result, that I had published in 1997, involving signal-to-noise ratios (SNRs). However, it was instantly apparent to me that their seemingly unrelated and merely technical result gave me the exact starting spot needed to attack the limit of detection problem. So, I spent the summer of 2006 working on the problem, reading the literature extensively, performing Monte Carlo calculations, and so on. Basically, this was finding the 'map'. During the Fall, 2006 semester, I tabled everything to focus on teaching, and then, during the Spring and Summer of 2007, I worked relentlessly on limits of detection. The paper by Nadarajah and Kotz (see References below) was published on January 15, 2007, but repeated attempts to get a copy failed (UMass, MIT and Harvard do not get the journal), until I finally got a copy via interlibrary loan from Vanderbilt University on August 15, 2007.
Thanks to having the exact starting spot I needed, and the preceding summer's work, I now have five, single author papers on limits of detection (see References below). Below are nutshell synopses (from the published abstracts) and commentaries:
Paper 1 ("Limits of Detection and Decision. Part 1"): This paper demonstrated that Currie scheme prediction interval-based experimental detection limits were significantly negatively biased, in both the net response domain and the chemical content domain, resulting in substantially higher rates of false negatives than specified via customary critical t values. The diagnostic fix for the bias problem provided clear proof that hypothesis-based detection limits need not be unique, even as distributions of random variates, if the alternate hypothesis is non-unique. It was also demonstrated that hypothesis-based decision and detection limits have finite support that does not include the region near zero analyte content, so that both have finite moments and finite confidence intervals.
Commentary: In this first paper, I discarded Currie's unsupportable notion that limits of detection exist only in theory, showing, instead, that there are four inter-related concepts as a consequence of the theoretical/experimental and the net response/chemical content dichotomies. Then I refuted the classic 1970 Hubaux and Vos prediction interval formulation of Currie's detection limits, which was based on an erroneous understanding of the canonical measurement protocol for an unknown and of what homoscedastic noise must imply in this case. This refutation was done by a combination of theory and extensive Monte Carlo calculations. My rigorously correct re-formulation was then shown to be in perfect agreement with Monte Carlo simulation results.
Demonstration of Negative Bias in Hubaux & Vos's method
(Apple Keynote presentation format, zipped)
Paper 2 ("Limits of Detection and Decision. Part 2"): In this paper, extensive Monte Carlo studies of instrumental limits of detection were performed on a simple univariate chemical measurement system having homoscedastic, Gaussian measurement noise and using ordinary least squares processing of tens of millions of independent calibration curve data sets. It was found that experimental decision and detection limits in the content domain were distributed as scaled reciprocals of noncentral t variates. In the response domain, the decision and detection limits were distributed as scaled chi variates. Rates of false negatives were found to be as expected statistically and no bias was found. However, use of detection limit expressions based on critical values of the noncentrality parameter of the noncentral t distribution were found to be significantly biased, resulting in substantial bias in rates of false negatives.
Commentary: In this second paper, I refuted the 1987 Clayton, Hines and Elkins's results concerning the use of 'critical values of the noncentrality parameter of the noncentral t distribution' for the purpose of computing Currie scheme limits of detection. I showed that, under all possible circumstances, they were irrelevant and inferior to limits of detection computed as in my first paper. This results applies for all degrees of freedom and all possible values of false positive and false negative error rates. Furthermore, I derived, for the first time, the actual probability density function (PDF) for Currie scheme detection and decision limits and showed that they are distributed as scaled reciprocals of noncentral t variates. As in the first paper, this research involved a combination of theory and extensive Monte Carlo calculations.
Taken together, these two papers pull the rug out from under two classic, heavily cited papers that have unintentionally been serving as serious obstructions on the path to the long desired goal of harmonization of detection limit methodology and protocols. As a consequence of these two papers, IUPAC, ISO, the European Commission and the seven MARLAP agencies have some serious re-thinking to do, if they want to get it right finally.
Paper 3 ("Limits of Detection and Decision. Part 3"): In this paper, the true theory underlying Currie's limits of decision, detection and quantification, as they apply in a simple linear chemical measurement system having heteroscedastic, Gaussian measurement noise and using weighted least squares processing, was derived. Extensive Monte Carlo simulations were performed, on 900 million independent calibration curves, for linear, "hockey stick" and quadratic noise precision models (NPMs). With errorless NPM parameters, all the simulation results were found to be in excellent agreement with the derived theoretical expressions. Even with as much as 30% noise on all of the relevant NPM parameters, the worst absolute errors in rates of false positives and false negatives, was only 0.3%.
Commentary: This third paper provides the long sought after solution to the Gaussian heteroscedastic noise precision model system and shows why it was so frequently missed: illegitimate re-modeling of the NPM. This paper took three months of solid, uninterrupted work and the paper even includes the heteroscedastic extension of the correct treatment of limits of quantification.
Paper 4 ("Limits of Detection and Decision. Part 4"): In this paper, probability density functions have been derived for a number of commonly used limit of detection definitions, including several variants of the RSDB-BEC method, for a simple linear chemical measurement system having homoscedastic, Gaussian measurement noise and using ordinary least squares processing. All of these detection limit definitions serve as both decision and detection limits, thereby implicitly resulting in 50% rates of Type 2 errors. It has been demonstrated that these are closely related to Currie decision limits, if the coverage factor, k, is properly defined, and that all of the PDFs are scaled reciprocals of noncentral t variates. All of the detection limits have well-defined upper and lower limits, thereby resulting in finite moments and confidence limits, and the problem of estimating the noncentrality parameter has been addressed. Specific recommendations for harmonization of detection limit methodology have also been made.
Commentary: This paper completes my tetrology and, taken with the first three papers, pretty much guarantees that almost no one escaped having their toes stepped on, though only a few got a shove toward Canossa. In this paper, I deal with all the limits of detection favored by those in Camp 1 (vide supra) and even eliminate the long standing annoyance of a fixed 'coverage factor' ('k'), showing how to properly both control, and specify a priori, the desired rate of false positives. As a bonus, I even added another heteroscedastic noise precision model, applicable to dominant shot noise in the Gaussian approximation regime.
Paper 5 ("Comparison of Signal-to-Noise Ratios, Part 2"): This paper follows up one I published way back in 1997. In it, I show that my previously published probability density functions for several common signal-to-noise ratio definitions are simply minor algebraic variants of the noncentral t distribution-based PDF results recently published (2007) by Nadarajah and Kotz. The previously published, but unevaluated, integral expression for the PDF of quotients of SNRs has been shown to be in excellent quantitative agreement with my recent Monte Carlo results. Furthermore, it has been shown that the same integral expression also yields the PDF for quotients of relative standard deviations (RSDs) and the PDF for quotients of simple detection limits. The latter was validated by comparison with detailed Monte Carlo simulations, with the result that accurate expectation values and detection limit 95% confidence intervals were obtained. As a consequence, a major step has been taken toward the goal of being able to compare simple detection limits on a fair basis and being able to perform a statistical test, precisely analogous to a standard F test, to determine whether a given pair of experimental detection limits are plausibly from the same chemical measurement system with the same measurement system parameters and measurement protocol.
Commentary: This paper delivers up what I consider one of several Holy Grails of my discipline: the theoretical basis, corroborated with extensive Monte Carlo simulations, for fairly comparing limits of detection and thereby being able to assign a probable risk to the decision to assume that numerically discrepant detection limits are actually statistically different. No longer is it necessary to waive our hands and say that factors of 2 or 3 are "probably" not statistically significant: now we can compute a probability (within the restrictions of the model assumptions, of course).
In summary, I believe that my five papers are now the definitive work on limits of detection to date and will benefit many researchers, both in Analytical Chemistry and in allied disciplines.
References:
1. E. Voigtman, "Limits of detection and decision. Part 1", Spectrochim. Acta Part B, 63(2), 2008, 115-128, doi:10.1016/j.sab.2007.11.015
2. E. Voigtman, "Limits of detection and decision. Part 2", Spectrochim. Acta Part B, 63(2), 2008, 129-141, doi:10.1016/j.sab.2007.11.018
3. E. Voigtman, "Limits of detection and decision. Part 3", Spectrochim. Acta Part B, 63(2), 2008, 142-153, doi:10.1016/j.sab.2007.11.012
4. E. Voigtman, "Limits of detection and decision. Part 4", Spectrochim. Acta Part B, 63(2), 2008, 154-165, doi:10.1016/j.sab.2007.11.014
5. E. Voigtman, "Comparison of Signal-to-Noise Ratios, Part 2", MATCH Commun. Math. Comput. Chem., 60 (2008) 333-348.
6. S. Nadarajah and S. Kotz, "Computation of Signal-to-Noise Ratios", MATCH Commun. Math. Comput. Chem., 57 (2007) 105-110.
Sample polychromatic models or results
Array formats in monochromatic optical calculus mode
Array formats in polychromatic optical calculus mode
Updated November 16, 2008