Statistical models for firearm and tool mark image comparisons based on the congruent matching cells (CMC) method.

In the branch of forensic science known as firearm evidence identification, various similarity scores have been proposed to compare firearm marks. Some similarity score comparisons, for example, congruent matching cells (CMC) method, are based on pass-or-fail tests. The CMC method compares the pairwise topography images of breech face impressions, from which the similarity score is derived for quantifying their topography similarity. For an image pair, the CMC method determines a certain number of correlated cell pairs. Next, each correlated pair is determined to be a congruent match cell (CMC) pair, or not based on several identification parameters. The number of CMC pairs as a threshold is required so that the two images of surface topographies can be either identified as matching or determined to be non-matching. To reliably estimate error rates or evaluate likelihood ratio (LR), the key is to find an appropriate probability distribution for the frequency distribution of the observed CMC results. This paper discusses four statistical models for CMC measurements, which are binomial and three binomial-related probability distributions. In previous studies, for a sequence of binomial distributed or other binomial-related distributed random variables (r.v.), the number of Bernoulli trials N for each r.v. is assumed to be the same. However, in practice, N(the number of cell pairs in an image pair) varies from one r.v. (or one image pair) to another. In that case, the term, frequency function, of the CMC results is not appropriate. In this paper, the generalized frequency function is introduced to depict the behavior of the CMC values and its limiting distribution is provided. Based on that, nonlinear regression models are used to estimate the model parameters. The methodology is applied to a set of actual CMC values of fired cartridge cases.

The Use of Correlated Binomial Distribution in Estimating Error Rates for Firearm Evidence Identification.

In the branch of forensic science known as firearm evidence identification, estimating error rates is a fundamental challenge. Recently, a new quantitative approach known as the congruent matching cells (CMC) method was developed to improve the accuracy of ballistic identifications and provide a basis for estimating error rates. To estimate error rates, the key is to find an appropriate probability distribution for the relative frequency distribution of observed CMCs overlaid on a relevant measured firearm surface such as the breech face of a cartridge case. Several probability models based on the assumption of independence between cell pair comparisons have been proposed, but the assumption of independence among the cell pair comparisons from the CMC method may not be valid. This article proposes statistical models based on dependent Bernoulli trials, along with corresponding methodology for parameter estimation. To demonstrate the potential improvement from the use of the dependent Bernoulli trial model, the methodology is applied to an actual data set of fired cartridge cases.

Estimating error rates for firearm evidence identifications in forensic science.

Estimating error rates for firearm evidence identification is a fundamental challenge in forensic science. This paper describes the recently developed congruent matching cells (CMC) method for image comparisons, its application to firearm evidence identification, and its usage and initial tests for error rate estimation. The CMC method divides compared topography images into correlation cells. Four identification parameters are defined for quantifying both the topography similarity of the correlated cell pairs and the pattern congruency of the registered cell locations. A declared match requires a significant number of CMCs, i.e., cell pairs that meet all similarity and congruency requirements. Initial testing on breech face impressions of a set of 40 cartridge cases fired with consecutively manufactured pistol slides showed wide separation between the distributions of CMC numbers observed for known matching and known non-matching image pairs. Another test on 95 cartridge cases from a different set of slides manufactured by the same process also yielded widely separated distributions. The test results were used to develop two statistical models for the probability mass function of CMC correlation scores. The models were applied to develop a framework for estimating cumulative false positive and false negative error rates and individual error rates of declared matches and non-matches for this population of breech face impressions. The prospect for applying the models to large populations and realistic case work is also discussed. The CMC method can provide a statistical foundation for estimating error rates in firearm evidence identifications, thus emulating methods used for forensic identification of DNA evidence.

Evaluation of Measurement Precision from Stationary Baseline Noise in Instrumental Analyses.

This paper provides two approaches to estimate the standard deviation of measurements from baseline noise in instrumental output when (i) in theory, the noise can be approximated by a well-established random process in statistics and mathematics, referred to as a stationary process and (ii) in practice, the baseline noise is the predominant source of measurement error. For the first approach proposed, a general evaluation equation for measurement precision, when the baseline noise can be treated as a stationary process, is derived as a function of the process autocorrelations and process variance of the noise. In particular, for the second approach, when the baseline noise is a mixed random process of white noise and a first order autoregressive (AR(1)) process, the corresponding equation for the precision is also derived. The equations derived in the present paper include some results published elsewhere as special cases. For illustration, an example is presented.

Optimizing Hybrid Metrology: Rigorous Implementation of Bayesian and Combined Regression.

Hybrid metrology, e.g., the combination of several measurement techniques to determine critical dimensions, is an increasingly important approach to meet the needs of the semiconductor industry. A proper use of hybrid metrology may yield not only more reliable estimates for the quantitative characterization of 3-D structures but also a more realistic estimation of the corresponding uncertainties. Recent developments at the National Institute of Standards and Technology (NIST) feature the combination of optical critical dimension (OCD) measurements and scanning electron microscope (SEM) results. The hybrid methodology offers the potential to make measurements of essential 3-D attributes that may not be otherwise feasible. However, combining techniques gives rise to essential challenges in error analysis and comparing results from different instrument models, especially the effect of systematic and highly correlated errors in the measurement on the χ2 function that is minimized. Both hypothetical examples and measurement data are used to illustrate solutions to these challenges.

Development of a Standard Reference Material for metabolomics research.

The National Institute of Standards and Technology (NIST), in collaboration with the National Institutes of Health (NIH), has developed a Standard Reference Material (SRM) to support technology development in metabolomics research. SRM 1950 Metabolites in Human Plasma is intended to have metabolite concentrations that are representative of those found in adult human plasma. The plasma used in the preparation of SRM 1950 was collected from both male and female donors, and donor ethnicity targets were selected based upon the ethnic makeup of the U.S. population. Metabolomics research is diverse in terms of both instrumentation and scientific goals. This SRM was designed to apply broadly to the field, not toward specific applications. Therefore, concentrations of approximately 100 analytes, including amino acids, fatty acids, trace elements, vitamins, hormones, selenoproteins, clinical markers, and perfluorinated compounds (PFCs), were determined. Value assignment measurements were performed by NIST and the Centers for Disease Control and Prevention (CDC). SRM 1950 is the first reference material developed specifically for metabolomics research.

Improving optical measurement uncertainty with combined multitool metrology using a Bayesian approach.

Recently, there has been significant research investigating new optical technologies for dimensional metrology of features 22 nm in critical dimension and smaller. When modeling optical measurements, a library of curves is assembled through the simulation of a multidimensional parameter space. A nonlinear regression routine described in this paper is then used to identify an optimum set of parameters that yields the closest experiment-to-theory agreement. However, parametric correlation, measurement noise, and model inaccuracy all lead to measurement uncertainty in the fitting process for optical critical dimension measurements. To improve the optical measurements, other techniques such as atomic force microscopy and scanning electronic microscopy can also be used to provide supplemental a priori information. In this paper, a Bayesian statistical approach is proposed to allow the combination of different measurement techniques that are based on different physical measurements. The effect of this hybrid metrology approach will be shown to reduce the uncertainties of the parameter estimators.

Certification of drugs of abuse in a human serum standard reference material: SRM 1959.

A new standard reference material (SRM) for drugs of abuse in human serum (SRM 1959) has been developed. This SRM is intended to be used as a control material for laboratories performing analysis of drugs of abuse in blood to evaluate the accuracy of their methods. SRM 1959 is a frozen human serum material fortified with seven compounds for which analyses are performed to determine evidence of illegal drug use: benzoylecgonine (BZE), methadone (METH), methamphetamine (MAMP), morphine (MOR), nordiazepam (NOR), phencyclidine (PCP), and 11-nor-Delta(9)-tetrahydrocannabinol-9-carboxylic acid (THC-9-COOH). Two independent methods involving isotope dilution (ID)-gas chromatography/mass spectrometry (GC/MS) and ID-liquid chromatography/mass spectrometry (LC/MS) were used for the value assignment. For THC-9-COOH, an additional measurement using LC/tandem mass spectrometry (LC/MS/MS) was also included. All methods used isotopically labeled compounds as internal standards and solid-phase extractions to isolate the analytes from the serum. The GC/MS methods used different clean-up procedures from those used for the LC/MS-based methods. Repeatability with within-set coefficients of variation (CVs) ranged from 0.5% to 4.3% for the GC/MS methods and from 0.2% to 1.2% for the LC/MS-based methods. Intermediate precision with between-set CVs for all the methods ranged from 0.1% to 1.1%. Agreement between the GC/MS and LC/MS methods ranged from 0.8% to 8.8%. The results from the methods were combined to obtain the certified concentrations and their expanded uncertainties.

Linking the Results of CIPM and RMO Key Comparisons With Linear Trends.

A statistical approach to link the results of interlaboratory comparisons with linear trends is proposed. This approach can be applied to the case that the comparison artifacts have the same nominal values or the measured quantities have the same magnitudes. The degrees of equivalence between the pairs of National Metrology Institutes that have not participated in the same comparisons, and their corresponding uncertainties are established. The approach is applied to link the CCEM-K2 and SIM.EM-K2 comparisons for resistance at 1 G Ω level.

Development of a new standard reference material: SRM 1955 (homocysteine and folate in human serum).

Total homocysteine (tHCY) and folate are interrelated biomarkers for arteriosclerosis and coronary heart disease. Although many different methods for both tHCY and folate are clinically available, the intermethod and interlaboratory results are often poor, resulting in the need for a matrix reference material and reference methods. The National Institute of Standards and Technology (NIST) has developed isotope dilution liquid chromatography/mass spectrometry (LC/MS) and liquid chromatography/ tandem mass spectrometry (LC/MS/MS) methods for determination of tHCY and several folate forms including 5-methyltetrahydrofolic acid (5MT) and folic acid (FA). Additionally, a method for simultaneous measurement of tHCY, 5MT, and FA has been developed and validated. In collaboration with the Centers for Disease Control and Prevention (CDC), mass spectrometric methods and methods used in clinical laboratories have been applied to characterize a new Standard Reference Material (SRM), SRM 1955, "Homocysteine and Folate in Human Serum," containing low, medium, and high levels of tHCY and 5MT. Additionally, FA, 5-formyltetrahydrofolic acid (5FT), vitamin B12, and total folate values are provided. Use of the new SRM should improve clinical measurements and will permit traceability to internationally recognized certified reference materials, as described by European Directive 98/79/EC on in vitro diagnostic medical devices.