Likelihood Ratio Measure Research Articles

Not all identification conclusions are equal: Quantifying the strength of fingerprint decisions

In the pattern comparison disciplines, forensic practitioners evaluate two impressions with respect to the same-source and different-sources propositions. The results are communicated using a pre-determined conclusion scale, and in the friction ridge discipline Identification is typically the highest category on the scale for reporting evidence supporting the same source proposition. Although error rates have been measured in most disciplines, there are no widespread quantitative approaches and therefore most conclusions rely on subjective human evaluations. The current work uses articulation decisions provided by fingerprint examiners in error rate studies to produce a quantitative likelihood ratio measure that characterizes the strength of the support for the two propositions. We use an ordered probit model to summarize the distribution of responses of examiners who participated in error rate and validation studies. We then aggregate the data for all image pairs in a database to construct a set of likelihood ratios based on the ratio of the two strength-of-support values. We find that these values are modest relative to values typically produced by DNA analysis or implied by current fingerprint articulation language. The technique can be applied to any pattern comparison discipline for which error-rate data is available, and therefore can be used to appropriately weigh the evidence from different disciplines.

A measure of evidence based on the likelihood-ratio statistics

In this paper, we show that the likelihood-ratio measure (a) is invariant with respect to dominating sigma-finite measures, (b) satisfies logical consequences which are not satisfied by standard p values, (c) respects frequentist properties, i.e., the type I error can be properly controlled, and, under mild regularity conditions, (d) can be used as an upper bound for posterior probabilities. We also discuss a generic application to test whether the genotype frequencies of a given population are under the Hardy–Weinberg equilibrium, under inbreeding restrictions or under outbreeding restrictions.

How can courts take into account the uncertainty in a likelihood ratio?

As legal practitioners and courts become more aware of scientific methods and evidence evaluation, they are demanding measures of the reliability of expert opinion. In particular, there are calls for error rates to accompany opinion evidence in comparative forensic sciences. While error rates or confidence intervals can be useful for those disciplines that claim to identify the source of a trace, the call for these statistical tools has extended to sciences that present opinions in the form of a likelihood ratio. In this article we argue against presenting both a likelihood ratio and numerical measures of its uncertainty. We explain how the LR already encapsulates uncertainty. Instead we consider how sensitivity analyses can be used to guide the presentation of LRs that are informative to the court and not unfair to defendants.

The Likelihood Ratio Measure and the Logicality Requirement

What sort of evidence can confer the strongest support to a hypothesis? A natural answer is that the evidence entails the hypothesis. Roush (Tracking Truth: Knowledge, Evidence, and Science, Clarendon Press, Oxford, 2005) claims that the likelihood ratio measure of degree of incremental support can deliver this intuitively natural result, and regards it as unifying “[the] account of induction and deduction in the only way that makes sense” (p. 163). In this paper, we highlight a difficulty in the treatment of this case, and question the great significance that is attached to this measure and its alleged capacity to accommodate the logicality requirement. We contrast the likelihood ratio measure with other measures (such as the Kemeny–Oppenheim measure and the difference measure), and argue that problems still emerge in light of tensions with plausible requirements for confirmation measures more generally.

Confirmation, Increase in Probability, and the Likelihood Ratio Measure: a Reply to Glass and McCartney

Bayesian confirmation theory is rife with confirmation measures. Zalabardo (2009) focuses on the probability difference measure, the probability ratio measure, the likelihood difference measure, and the likelihood ratio measure. He argues that the likelihood ratio measure is adequate, but each of the other three measures is not. He argues for this by setting out three adequacy conditions on confirmation measures and arguing in effect that all of them are met by the likelihood ratio measure but not by any of the other three measures. Glass and McCartney (2015), hereafter “G&M,” accept the conclusion of Zalabardo’s argument along with each of the premises in it. They nonetheless try to improve on Zalabardo’s argument by replacing his third adequacy condition with a weaker condition. They do this because of a worry to the effect that Zalabardo’s third adequacy condition runs counter to the idea behind his first adequacy condition. G&M have in mind confirmation in the sense of increase in probability: the degree to which E confirms H is a matter of the degree to which E increases H’s probability. I call this sense of confirmation “IP.” I set out four ways of precisifying IP. I call them “IP1,” “IP2,” “IP3,” and “IP4.” Each of them is based on the assumption that the degree to which E increases H’s probability is a matter of the distance between p(H | E) and a certain other probability involving H. I then evaluate G&M’s argument (with a minor fix) in light of them.

Evaluation of diagnostic accuracy of two rapid stool antigen tests using an immunochromatographic assay to detect Helicobacter pylori

ObjectivesThe stool antigen assay for H. pylori infection diagnosis with monoclonal antibodies is a simple and recommended technique by the Maastricht V/Florence consensus report. Recently, Pylori K-Set K-1219 (Coris Bioconcept Sprl, Belgium) and HP-F23 (Symbiosys, Brazil) have been made commercially available in Brazil. Thus, the aim of this study was to evaluate the diagnostic accuracies of these two rapid stool antigen tests by immunochromatographic assays (index tests) for the clinical practice. Design and methodsA total of 98 patients who underwent upper gastrointestinal endoscopy and 13C-urea breath test entered the study. H. pylori infection status was defined by the combination of the rapid urease test and the 13C-urea breath test (reference standard). Two observers who were aware of H. pylori status performed the reading of index tests. Diagnostic accuracy (sensitivity, specificity, positive predictive value, negative predictive value with 95% confidence intervals, positive likelihood ratio, negative likelihood ratio and kappa index measure of agreement) were determined. ResultsThe index tests where in perfect agreement with the H. pylori status with kappa values of 0.87 for Pylori K-Set K-1219 and 0.92 for HP-F23. The sensitivity of HP-F23 was 97.9% (IC95%: 87.5–100) and specificity was 93.8% (IC95%; 84–97.2).The positive likelihood ratio was 15.8, and the negative likelihood ratio was 0.02. The Pylori K-Set K-1219 had a sensitivity of 87.7% (IC95%: 74.5–94.9) and a specificity of 100% (IC95%: 91.6–100); the positive likelihood ratio was ∞, and the negative likelihood ratio was 0.1. The test line on the cassette device of HP-F23 was stronger than of the Pylori K-Set K-1219. ConclusionThe HP-F23 test performed better in clinical practice. Nonetheless, the 13C-urea breath test is more reliable technique. Moreover, caution must be paid to the trace or clear pale test line readings that were observed in false positive and false negative results, leading to incorrect management of the patient.

A New Argument for the Likelihood Ratio Measure of Confirmation

This paper presents a new argument for the likelihood ratio measure of confirmation by showing that one of the adequacy criteria used in another argument (Zalabardo Analysis 69: 630–635, 2009) can be replaced by a more plausible and better supported criterion which is a special case of the weak likelihood principle. This new argument is also used to show that the likelihood ratio measure is to be preferred to a measure that has recently received support in the literature.

New Axioms for Probability and Likelihood Ratio Measures

Probability ratio and likelihood ratio measures of inductive support and related notions have appeared as theoretical tools for probabilistic approaches in the philosophy of science, the psychology of reasoning, and artificial intelligence. In an effort of conceptual clarification, several authors have pursued axiomatic foundations for these two families of measures. Such results have been criticized, however, as relying on unduly demanding or poorly motivated mathematical assumptions. We provide two novel theorems showing that probability ratio and likelihood ratio measures can be axiomatized in a way that overcomes these difficulties.

On Ratio Measures of Confirmation

There are different Bayesian measures to calculate the degree of confirmation of a hypothesis H in respect of a particular piece of evidence E. Zalabardo (Analysis 69:630–635, 2009) is a recent attempt to defend the likelihood-ratio measure (LR) against the probability-ratio measure (PR). The main disagreement between LR and PR concerns their sensitivity to prior probabilities. Zalabardo invokes intuitive plausibility as the appropriate criterion for choosing between them. Furthermore, he claims that it favours the ordering of pairs evidence/hypothesis generated by LR. We will argue, however, that the intuitive non-numerical example provided by Zalabardo does not show that prior probabilities do not affect the degree of confirmation. On account of this, we conclude that there is no compelling reason to endorse LRqua measure of degree of confirmation. On the other side, we should not forget some technicalities which still benefit PR.

An argument for the likelihood-ratio measure of confirmation

In the recent literature on confirmation there are two leading approaches to the provision of a probabilistic measure of the degree to which a hypothesis is confirmed by evidence. The first is to construe the degree to which evidence E confirms hypothesis H as a function that is directly proportional to p(H'E) and inversely proportional to p(H). I shall refer to this as the probability approach. The second approach construes the notion as a function that is directly proportional to the true-positive rate the probability of the evidence if the hypothesis is true, p(E'H) and inversely proportional to the falsepositive rate the probability of the evidence if the hypothesis is false, p(E I ~H). These reverse conditional probabilities of the evidence on the truth or falsehood of the hypothesis are sometimes known as likelihoods. I shall refer to the approach to confirmation that uses them as the likelihood approach. For each of these approaches, there are two obvious options as to how to define the confirmation function. The first is to define it as the difference

A Critique on Contemporary Reporting of Likelihood Ratios in Test Power Analysis

A Critique on Contemporary Reporting of Likelihood Ratios in Test Power Analysis

A Perspective on Standardizing the Predictive Power of Noninvasive Cardiovascular Tests by Likelihood Ratio Computation: 2. Clinical Applications

Likelihood ratio measures may be used as a standard for expressing the predictive power of noninvasive cardiovascular tests, calculated from sensitivity and specificity measures or as ratios of the predictive value odds to pretest odds for positive and negative test results. The positive likelihood ratio, (+)LR, expresses the power of a positive test result to augment an estimate of disease probability independent of the pretest prevalence of disease in a given population; the negative likelihood ratio, (-)LR, expresses the power of a negative test result to augment an estimate of the probability of no disease independent of the pretest prevalence of no disease in the same population. The likelihood ratio principle is applicable to the evaluation of the predictive power of single or combined test results reported for either dichotomous or continuous end points. This part of the perspective exemplifies application of the likelihood ratio principle in a wide variety of testing conditions for coronary artery disease followed by a discussion of the limitations of likelihood ratio computation in test power evaluation. Likelihood ratios provide a more concise and unambiguous standard for calibrating the predictive power of single and combined noninvasive cardiovascular test results than are provided by measures of sensitivity, specificity, and predictive value.

Distortion Measures for Speech Coding

In this article, we have reviewed some of the existing subjective and objective measures used in the area of speech coding. The mean opinion score and the diagnostic acceptability measure are two of the widely used subjective measures. The most popular class of the time-domain measures is the signal-to-noise ratio (SNR) with its variants such as the segmental SNR, the granular segmentsal SNR etc. Among the spectral distortion measures, the log likelihood ratio measure, the log area ratio measure, the log spectral distortion measure, the cepstral distance and the Itakura-Saito distortion measure are quite well-known. Some of the more recently proposed objective measures place emphasis on the perceptually significant aspects. Three such classes of the psychoacoustically-motivated measures are the information index, the Bark spectral distortion measure and the neural distance measure (e.g., the cochlear discrimination information, the cochlear hidden Markovian measues). The merit of considering important perceptual events is evident in the success of these measures.

A log-index weighted cepstral distance measure for speech recognition

A log-index weighted cepstral distance measure is proposed and tested in speaker-independent and speaker-dependent isolated word recognition systems using statistic techniques. The weights for the cepstral coefficients of this measure equal the logarithm of the corresponding indices. The experimental results show that this kind of measure works better than any other weighted Euclidean cepstral distance measures on three speech databases. The error rate obtained using this measure is about 1.8 percent for three databases on average, which is a 25% reduction from that obtained using other measures, and a 40% reduction from that obtained using Log Likelihood Ratio (LLR) measure. The experimental results also show that this kind of distance measure works well in both speaker-dependent and speaker-independent speech recognition systems.

On the use of bandpass liftering in speech recognition

In a template-based speech recognition system, distortion measures that compute the distance or dissimilarity between two spectral representations have a strong influence on the performance of the recognizer. Accordingly, extensive comparative studies have been conducted to determine good distortion measures for improved recognition accuracy. Previous studies have shown that the log likelihood ratio measure, the likelihood ratio measure, and the truncated cepstral measures all gave good recognition performance (comparable accuracy) for isolated word recognition tasks. In this paper we extend the interpretation of distortion measures, based upon the observation that measurements of speech spectral envelopes (as normally obtained from standard analysis procedures such as LPC or filter banks) are prone to statistical variations due to window position fluctuations, excitation interference, measurement noise, etc., and may not accurately characterize the true speech spectrum because of analysis model constraints. We have found that these undesirable spectral measurement variations can be partially controlled (i.e., reduced in the level of variation) by appropriate signal processing techniques. In particular, we have found that a bandpass process reduces the variability of the statistical components of LPC-based spectral measurements and hence it is desirable to use such a liftering process in a speech recognizer. We have applied this liftering process to several speech recognition tasks: in particular, single frame vowel recognition and isolated word recognition. Using the liftering process, we have been able to achieve an average digit error rate of 1 percent in a speaker-independent isolated digit test. This error rate is about one-half that obtained without the liftering process.

Text‐independent speaker recognition experiments using codebooks in vector quantization

A text‐independent speaker clustering approach to speaker‐indepencent speaker recognition through vector quantization (VQ) was investigated, where the distortion value was used as a clustering measure. To show the possibility of the text‐independent speaker clustering, speaker recognition experiments were carried out using the Harvard sentence database. Nine male speakers uttered ten different Harvard sentences each. Codebooks were generated from the first five sentences for each speaker using Weighted Likelihood Ratio measure (WLR) through LPC analysis. Using 128 vectors in each codebook, a speaker recognition rate of 98% was attained on the latter five Harvard sentences. Effects of codebook size and input length are also discussed. The above approach based on framewise VQ only utilizes the static distribution of LPC spectra. VQ for multiframe codebooks was used to represent the coarticulation units. The results of speaker recognition experiments based on multi‐frame codebooks will be compared with fixed length VQ approaches.

Variance of the likelihood ratio measure of bias

The variance of the logarithm of the likelihood ratio, a commonly used measure of bias in signal detection theory, is derived for the case of an unbiased observer and two underlying normal distributions of equal variance. This variance increases with d’ (the subject’s sensitivity to the two stimuli involved in the discrimination). Accordingly, increased deviation of the In (LR) sample mean from a true mean of zero can be anticipated as signal level increases even when bias and sensitivity are essentially independent.

Isobias and alloiobias functions in animal psychophysics.

An analogue of the human yes-no detection task was used to train six pigeons to discriminate luminance differences under two different reinforcer-scheduling procedures. When a controlled reinforce-ratio procedure was used, relative stimulus frequency was constant at .5, and relative reinforcer frequency for correct detections was held constant at three different values for each of five luminance differences. When an uncontrolled reinforcer-ratio procedure (the typical detection paradigm) was used, relative reinforcer frequency for correct detections was allowed to covary with changes in relative stimulus frequency for each of five luminance differences. Two measures of bias, response bias (Davison & Tustin, 1978) and the detection-theory likelihood-ratio measure (beta obt), were compared. The controlled reinforcer-ratio procedure generated equal- or iso-response-bias functions, and the uncontrolled reinforcer-ratio procedure gave changing or alloio-response-bias functions. The Davison-Tustin model accounted for 88% and 93% of the data variance in the controlled and uncontrolled reinforcer-ratio procedures, respectively. The best-fitting equal-beta functions accounted for an average of 53% and 69%, respectively, in the two procedures. In addition, neither procedure gave constant measures of beta obt for constant bias manipulations across different discriminability measures.

Bias in Estimating Niche Overlap

Bias refers to the accuracy of a particular estimator. We evaluate bias, using analytic and simulation technics, for six measures of overlap: the likelihood ratio measure, the chi—square measure, the measure based on the Freeman—Tukey statistic, Morisita's adjusted index, Morista's original index, and Horn's information index. We present an exact formula for a seventh, the percentage similarity measure. We consider bias due to resource a sample size, total number of different resources, and evenness of resource distribution. Results indicate that of the seven measures, changes in evenness of resource of distribution produce significant bias only in the percentage similarity measure and Morista's adjusted index. All measures show increasing bias with increasing number of resources. For estimating unbiased overlap, Morisita's original measure of overlap gives the most accurate results, especially when using small sample sizes. The percentage similarity measure, one of the most commonly used measures among ecologists, is also one of the most biased and for this reason is not preferred.

An interpretation of the log likelihood ratio as a measure of waveform coder performance

The log likelihood measure has been widely used in speech research for comparing speech signals. Recently, it has been proposed as a measure for assessing the quality of coded speech. In this paper we present an interpretation of the log likelihood ratio measure within the theoretical framework of a waveform coder distortion model. We then discuss the implications of this interpretation and show how it can be applied to the formulation of better objective measures of waveform coder performance.