Likelihood Ratio Approach Research Articles

Effects of prescreening for likelihood ratio approaches in the forensic identification of source problems

Source prescreening is a methodology where forensic examiners select samples that are similar to given trace evidence to represent the background population. This background evidence helps assign a value of evidence using a likelihood ratio or Bayes factor. A potential benefit of prescreening is a mitigation of effects from subpopulation structures within the alternative source population by isolating the relevant subpopulation. This paper examines the impact of prescreening before assigning evidence value. Extensive simulations with synthetic and real data, including trace element and fingerprint score examples, were conducted. The findings indicate that when the subpopulation structure is known, prescreening can provide an accurate evidence value in cases of subpopulation structures. The study suggests that prescreening can be beneficial, but the prescreening method and level should be transparently reported alongside the evidence value.

A Dirichlet Process Model for Directional-linear Data with Application to Bloodstain Pattern Analysis

Directional data require specialized models because of the non-Euclidean nature of their domain. When a directional variable is observed jointly with linear variables, modeling their dependence adds an additional layer of complexity. A Bayesian nonparametric approach is introduced to analyze directional-linear data. Firstly, the projected normal distribution is extended to model the joint distribution of linear variables and a directional variable with arbitrary dimension projected from a higher-dimensional augmented multivariate normal distribution. The new distribution is called the semi-projected normal distribution (SPN) and can be used as the mixture distribution in a Dirichlet process model to obtain a more flexible class of models for directional-linear data. Then, a conditional inverse-Wishart distribution is proposed as part of the prior distribution to address an identifiability issue inherited from the projected normal and preserve conjugacy with the SPN. The SPN mixture model shows superior performance in clustering on synthetic data compared to the semi-wrapped Gaussian model. The experiments show the ability of the SPN mixture model to characterize bloodstain patterns. A hierarchical Dirichlet process model with the SPN distribution is built to estimate the likelihood of bloodstain patterns under a posited causal mechanism for use in a likelihood ratio approach to the analysis of forensic bloodstain pattern evidence.

A control chart for monitoring image processes based on convolutional neural networks

In this paper, the problem of monitoring image processes with spatially correlated pixels over time is considered. An exponentially weighted moving average (EWMA) control chart for monitoring such processes based on a convolutional neural network (CNN) is proposed. A comparison of its performance with a Hotelling's control chart and with a control chart based on generalized likelihood ratio (GLR) approach is conducted through a simulation study. The new method outperforms other methods in most of the cases considered in the simulation study. A technique for mean intensity shift localization based on CNNs is proposed and evaluated.

Forensic Science and How Statistics Can Help It

ABSTRACTThe persistent issue of wrongful convictions in the United States emphasizes the need for scrutiny and improvement of the criminal justice system. While statistical methods for the evaluation of forensic evidence, including glass, fingerprints, and deoxyribonucleic acid, have significantly contributed to solving intricate crimes, there is a notable lack of national‐level standards to ensure the appropriate application of statistics in forensic investigations. We discuss the obstacles in the application of statistics in court and emphasize the importance of making statistical interpretation accessible to non‐statisticians, especially those who make decisions about potentially innocent individuals. We investigate the use and misuse of statistical methods in crime investigations, in particular the likelihood ratio approach. We further describe the use of graphical models, where hypotheses and evidence can be represented as nodes connected by arrows signifying association or causality. We emphasize the advantages of special graph structures, such as object‐oriented Bayesian networks and chain event graphs, which allow for the concurrent examination of evidence of various nature.

Faktor-Faktor yang Mempengaruhi Kemiskinan di Desa Kondamara Kecamatan Lewa

Poverty is a complex problem caused by many interrelated factors. So, this research will analyse the variables that influence poverty in Kondamara Village, Lewa District by analysing important problems that can influence poverty. This research aims to determine the profile and factors that influence poverty in Kondamara Village, Lewa District. The data collection technique uses primary data obtained through distributing questionnaires and direct interviews with poor and non-poor households in Kondamara Village, Lewa District. Meanwhile, the data analysis technique uses binary logistic regression analysis with a Likelihood Ratio approach. The research results show that the income of the head of the household and the number of family dependents have a significant influence on poverty in Kondamara Village, Lewa District.

A robust interpolation-based method for forensic soil provenancing: A Bayesian likelihood ratio approach

Soil is a complex and spatially variable material that has a demonstrated potential as a useful evidence class in forensic casework and intelligence operations. Here, the capability to spatially constrain police search areas and prioritise resources by triaging areas as low and high interest is advantageous. Conducted between 2017 and 2021, a forensically relevant topsoil survey (0–5 cm depth; 1 sample per 1 km2) was carried out over Canberra, Australia, aiming to document the distribution of chemical elements in an urban/suburban environment, and of acting as a testbed for investigating various aspects of forensic soil provenancing. Geochemical data from X-Ray Fluorescence (XRF; for total major oxides) and Inductively Coupled Plasma-Mass Spectrometry (ICP-MS; for trace elements) following a total digestion (HF + HNO3) of the fused XRF beads were obtained from the survey’s 685 topsoil samples (plus 138 additional quality control samples and six “Blind” simulated evidentiary samples). Using those “Blind” samples, we document a likelihood ratio approach where for each grid cell the analytical similarity between the grid cell and evidentiary sample is attributed from a measure of overlap between the two Cauchy distributions, including appropriate uncertainties. Unlike existing methods that base inclusion/exclusion on an arbitrary threshold (e.g., ± three standard deviations), our approach is free from strict binary or Boolean thresholds, providing an unconstrained gradual transition dictated by the analytical similarity. Using this provenancing model, we present and evaluate a new method for upscaling from a fine (25 m x 25 m) interpolated grid to a more appropriate coarser (500 m x 500 m) grid. In addition, an objective method using Random Match Probabilities for ranking individual variables to be used for provenancing prior to receiving evidentiary material was demonstrated. Our results show this collective procedure generates more consistent and robust provenance maps when applied to two different interpolation algorithms (e.g., inverse distance weighting, and natural neighbour), with different grid placements (e.g., grid shifts to the north or east) and by different theoretical users (e.g., different computer systems, or forensic geoscientists).

Intelligent state estimation for fault tolerant integrated frequent RTO and adaptive nonlinear MPC

Combinations of real-time optimization (RTO) and model predictive control (MPC) have been widely employed in the process industry for tracking the economic optimum in the face of drifting disturbances and parameters. Online update of model parameters is a critical step in the implementation of RTO. In this work, an intelligent state and parameter estimation approach is developed by combining a fault diagnosis approach with a simultaneous state and parameter estimator. Since faults are more likely to develop as slow drifts, a nonlinear generalized likelihood ratio (GLR) approach available in the literature is modified by considering ramp models for the progression of faults with time. When a fault is isolated by the fault diagnosis and identification (FDI) component, the magnitude of the isolated fault is refined using a moving window state and parameter estimator until the fault magnitude continues to change. The estimation of fault magnitudes is carried out only when required and triggered by the fault identification scheme. Thus, the subset of parameters/faults that are being estimated online can change with time. The intelligent state and parameter estimator is further combined with an online optimizing control scheme consisting of integrated frequent RTO and adaptive MPC. The integrated optimizing control scheme has embedded intelligence to auto-correct models used for estimation, control, and optimization and decide whether the detected changes require the invocation of RTO. The proposed approach employs a single model to carry out four different tasks: process monitoring, state and parameter estimation, nonlinear predictive control, and real-time optimization. This eliminates difficulties that can arise due to model mismatch between different components of the online optimizing control scheme. The efficacy of the proposed scheme is investigated using the benchmark Williams Otto reactor and a continuously operated fermenter. The economic optimum operating point of these systems is sensitive to mean shifts in unmeasured disturbances or system parameters. The proposed ramp model based approach successfully isolates the parameter/ unmeasured disturbance/ sensor bias/ actuator bias that has undergone slow drift and tracks the shifting economic optimum without significant delays. Thus, the proposed integrated approach has the ability to handle normal and abnormal operating envelopes of the system.

A likelihood ratio approach for utilizing case-control data in the clinical classification of rare sequence variants: application to BRCA1 and BRCA2.

A large number of variants identified through clinical genetic testing in disease susceptibility genes, are of uncertain significance (VUS). Following the recommendations of the American College of Medical Genetics and Genomics (ACMG) and Association for Molecular Pathology (AMP), the frequency in case-control datasets (PS4 criterion), can inform their interpretation. We present a novel case-control likelihood ratio-based method that incorporates gene-specific age-related penetrance. We demonstrate the utility of this method in the analysis of simulated and real datasets. In the analyses of simulated data, the likelihood ratio method was more powerful compared to other methods. Likelihood ratios were calculated for a case-control dataset of BRCA1 and BRCA2 variants from the Breast Cancer Association Consortium (BCAC), and compared with logistic regression results. A larger number of variants reached evidence in favor of pathogenicity, and a substantial number of variants had evidence against pathogenicity - findings that would not have been reached using other case-control analysis methods. Our novel method provides greater power to classify rare variants compared to classical case-control methods. As an initiative from the ENIGMA Analytical Working Group, we provide user-friendly scripts and pre-formatted excel calculators for implementation of the method for rare variants in BRCA1, BRCA2 and other high-risk genes with known penetrance.

Data-driven slicing for dimension reduction in regressions: A likelihood-ratio approach

Data-driven slicing for dimension reduction in regressions: A likelihood-ratio approach

Latent Class Analysis with Measurement Invariance Testing: Simulation Study to Compare Overall Likelihood Ratio vs Residual Fit Statistics Based Model Selection

A standard assumption of latent class (LC) analysis is conditional independence, that is the items of the LC are independent of the covariates given the LCs. Several approaches have been proposed for identifying violations of this assumption. The recently proposed likelihood ratio approach is compared to residual statistics (bivariate residuals [BVR] and expected parameter change [EPC] statistics) for identifying nonuniform direct effect of covariates on the items of the LC model. The simulation study results show that the likelihood ratio (LR) test correctly identifies direct effects more often than the BVR statistics, showing comparable results to the EPC statistic in many situations- this at the price of having also a higher false positive rate than BVR. A real data example illustrates the use of the three procedures. Overall the combined use of residual statistics and LR testing is recommended for applied research.

Generalized fiducial factor: An alternative to the Bayes factor for forensic identification of source problems

One formulation of forensic identification of source problems is to determine the source of trace evidence, for instance, glass fragments found on a suspect for a crime. The current state of the science is to compute a Bayes factor comparing the marginal distribution of measurements of trace evidence under two competing propositions for whether or not the unknown source evidence originated from a specific source. The obvious problem with such an approach is the ability to tailor the prior distributions (placed on the features/parameters of the statistical model for the measurements of trace evidence) in favor of the defense or prosecution which is further complicated by the fact that the typical number of measurements of trace evidence is typically sufficiently small that prior choice/specification has a strong influence on the value of the Bayes factor. To remedy this problem of prior specification and choice, we develop an alternative to the Bayes factor, within the framework of generalized fiducial inference, that we term a generalized fiducial factor. Furthermore, we demonstrate empirically, on synthetic and real Netherlands Forensic Institute casework data, deficiencies in Bayes factor and classical/frequentist likelihood ratio approaches.

Optimized serum ferritin prediction of iron overload in transfusion-dependent thalassemia: likelihood ratio and age-adjustment approach.

Early detection of iron overload in transfusion-dependent thalassemia (TDT) patients is critical to prevent complications and improve survival. Evaluate the utility of serum ferritin (SF) in the prediction of hepatic and myocardial iron overload (HIO and MIO) compared to T2*-MRI. Retrospective SETTINGS: Governmental hospitals. Patients with TDT who had T2*-MRI examinations between January 2016 to October 2019 were included. The predictive value of SF for detection of HIO and MIO was assessed by measuring area under the curve (AUC). A sample size of 123 cases was calculated to detect a correlation of 0.25 with 90% power and a two-sided type I error of 0.05. The correlation between SF and estimated hepatic iron concentration. 137 TDT patients who required regular blood transfusions. The predictive value of SF was excellent for detection of HIO (AUC=0.83-0.87) but fair for detection of MIO (AUC=0.67). The two independent predictors of MIO were age and SF. The log of (age × SF) enhanced the SF predictive value for MIO (AUC=0.78). SF values of 700 and 1250 mg/L effectively excluded mild and moderate HIO with a sensitivity of 97.8% and 94.2%, respectively (LR-=0.1). While SF values of 1640 and 2150 mg/L accurately diagnosed mild and moderate HIO with a specificity of 95.55% and 96.4%, respectively (LR+>10). A log of (age × SF) cut-off value of 4.15 effectively excluded MIO (LR-=0.1), while a value of 4.65 moderately confirmed MIO (LR+=3.2). SF is an excellent predictor of hepatic IO in TDT. Age adjustment enhanced its myocardial IO predictive accuracy. Likelihood ratio-based SF cut-off values may help clinicians in risk stratification and treatment decision-making. The laboratory data were gathered retrospectively and although the risk of selection bias for T2*-MRI examination is thought to be low, it cannot be ignored. None.

A likelihood ratio approach for the evaluation of single point device locations

There is growing awareness that localisation traces recovered from a mobile device should not be presented as fact. Services providing locations to smartphones are influenced by a multitude of potential error sources which may cause differing observations from where the device was at. This work provides an approach to evaluate a single localisation recovered from mobile devices and present a differentiated result to decision makers. An open source implementation is provided, allowing practitioners to evaluate based on reference data they created for their own case. The effectiveness and forensic value of this method are demonstrated using a simulated scenario illustrating the use of the approach. This study demonstrates the method using locations associated to images, and is generalised to any technology providing location to any type of mobile device.

Pedigree reconstruction and population structure using SNP markers in Gir cattle.

Our objective was to establish a SNPs panel for pedigree reconstruction using microarrays of different densities and evaluate the genomic relationship coefficient of the inferred pedigree, in addition to analyzing the population structure based on genomic analyses in Gir cattle. For parentage analysis and genomic relationship, 16,205 genotyped Gir animals (14,458 females and 1747 males) and 1810 common markers to the four SNP microarrays were used. For population structure analyses, including linkage disequilibrium, effective population size, and runs of homozygosity (ROH), genotypes from 21,656 animals were imputed. Likelihood ratio (LR) approach was used to reconstruct the pedigree, deepening the pedigree and showing it is well established in terms of recent information. Coefficients for each relationship category of the inferred pedigree were adequate. Linkage disequilibrium showed rapid decay. We detected a decrease in the effective population size over the last 50 generations, with the average generation interval around 9.08years. Higher ROH-based inbreeding coefficient in a class of short ROH segments, with moderate to high values, was also detected, suggesting bottlenecks in the Gir genome. Breeding strategies to minimize inbreeding and avoid massive use of few proven sires with high genetic value are suggested to maintain genetic variability in future generations. In addition, we recommend reducing the generation interval to maximize genetic progress and increase effective population size.

Relative likelihood ratios for neutral comparisons of statistical tests in simulation studies.

When comparing the performance of two or more competing tests, simulation studies commonly focus on statistical power. However, if the size of the tests being compared are either different from one another or from the nominal size, comparing tests based on power alone may be misleading. By analogy with diagnostic accuracy studies, we introduce relative positive and negative likelihood ratios to factor in both power and size in the comparison of multiple tests. We derive sample size formulas for a comparative simulation study. As an example, we compared the performance of six statistical tests for small-study effects in meta-analyses of randomized controlled trials: Begg's rank correlation, Egger's regression, Schwarzer's method for sparse data, the trim-and-fill method, the arcsine-Thompson test, and Lin and Chu's combined test. We illustrate that comparing power alone, or power adjusted or penalized for size, can be misleading, and how the proposed likelihood ratio approach enables accurate comparison of the trade-off between power and size between competingtests.

Martingale product estimators for sensitivity analysis in computational statistical physics

Abstract We introduce a new class of estimators for the linear response of steady states of stochastic dynamics. We generalize the likelihood ratio approach and formulate the linear response as a product of two martingales, hence the name ‘martingale product estimators’. We present a systematic derivation of the martingale product estimator, and show how to construct such estimator so that its bias is consistent with the weak order of the numerical scheme that approximates the underlying stochastic differential equation. Motivated by the estimation of transport properties in molecular systems, we present a rigorous numerical analysis of the bias and variance for these new estimators in the case of Langevin dynamics. We prove that the variance is uniformly bounded in time and derive a specific form of the estimator for second-order splitting schemes for Langevin dynamics. For comparison, we also study the bias and variance of a Green–Kubo (GK) estimator, motivated, in part, by its variance growing linearly in time. We compare on illustrative numerical tests the new estimators with results obtained by the GK method.

Towards a likelihood ratio approach for bloodstain pattern analysis

In this work, we explore the application of likelihood ratio as a forensic evidence assessment tool to evaluate the causal mechanism of a bloodstain pattern. It is assumed that there are two competing hypotheses regarding the cause of a bloodstain pattern. The bloodstain patterns are represented as a collection of ellipses with each ellipse characterized by its location, size and orientation. Quantitative measures and features are derived to summarize key aspects of the patterns. A bivariate Gaussian model is chosen to estimate the distribution of features under a given hypothesis and thus approximate the likelihood of a pattern. Published data with 59 impact patterns and 55 gunshot patterns is used to train and evaluate the model. Results demonstrate the feasibility of the likelihood ratio approach for bloodstain pattern analysis. The results also hint at some of the challenges that need to be addressed for future use of the likelihood ratio approach for bloodstain pattern analysis.

Two-stage nested simulation of tail risk measurement: A likelihood ratio approach

Estimating tail risk measures is an important task in many financial and actuarial applications and often requires nested simulations, with the outer simulations representing real world scenarios, and the inner simulations typically used for risk neutral pricing or conditional risk measurement. The standard nested simulation method is highly flexible, able to incorporate complex asset models and exotic payoff structures, but it is also computationally highly burdensome, particularly in a multi-period setting, when inner simulation paths are required at each time step of each outer level scenario. In this study, we propose and analyze a two-stage simulation procedure that efficiently estimates the conditional tail expectation of cost of a dynamic hedging program for a Variable Annuity Guaranteed Minimum Withdrawal Benefit (GMWB), under a multi-period nested simulation. In each of the two stages, the method re-uses the same set of inner level simulation paths for each outer scenario at each time point, using a likelihood ratio method to re-weight the probabilities of each individual path for the different outer scenarios. Our numerical study shows that our two-stage, likelihood ratio weighted procedure can offer a very significant improvement in efficiency, of the order of 95% as measured by the RMSE, compared with a standard nested simulation with the same computational cost.

Empirical Likelihood-Based Inference for Functional Means with Application to Wearable Device Data

AbstractThis paper develops a nonparametric inference framework that is applicable to occupation time curves derived from wearable device data. These curves consider all activity levels within the range of device readings, which is preferable to the practice of classifying activity into discrete categories. Motivated by certain features of these curves, we introduce a powerful likelihood ratio approach to construct confidence bands and compare functional means. Notably, our approach allows discontinuities in the functional covariances while accommodating discretization of the observed trajectories. A simulation study shows that the proposed procedures outperform competing functional data procedures. We illustrate the proposed methods using wearable device data from an NHANES study.

A comparison of likelihood ratios with and without assuming relatedness for DNA mixtures interpreted using a continuous model

When evaluating support for the contribution of a person of interest (POI) to a mixed DNA sample, it is generally assumed that the mixture contributors are unrelated to the POI and to each other. In practice, there may be situations where this assumption is violated, for instance if two mixture contributors are siblings. The effect on the likelihood ratio of (in)correctly assuming relatedness between mixture contributors has previously been investigated using simulation studies based on simplified models ignoring peak heights. We revisit this problem using a simulation study that applies peak height models both in the simulation and mixture interpretation part of the study. Specifically, we sample sets of mixtures comprising both related and unrelated contributors and evaluate support for the contribution of the mixture donors as well as unrelated persons with and without incorporating an assumption of relatedness. The results show, consistent with earlier studies, that including a correct assumption of relatedness increases the capacity of the probabilistic genotyping system to distinguish between mixture donors and unrelated persons. Any effect of the relatedness is found to depend strongly on the mixture ratio. We further show that the results do not change materially when a sub-population correction is applied. Finally, we suggest and discuss a likelihood ratio approach that considers relatedness between mixture contributors using a prior probability.