Parsimonious Mixture Models Research Articles

Goodness-of-fit, identifiability and extrapolation: Can the Two-Component Extreme Value distribution be used in at-site flood frequency analysis?

When fitting three-parameter flood frequency models to annual maximum (AM) flood series, the lack-of-fit can be mitigated by censoring potentially influential low flows (PILFs). An alternative and less-studied approach is to apply mixture probability models with four or more parameters, which trade off greater flexibility to fit AM series against the need to deal with degeneracy which arises when there is insufficient information to identify mixture components. However, the issue of degeneracy and the lack of a robust inference framework present a significant barrier to adoption. This study investigated the potential of the most parsimonious mixture model, the four-parameter Two-Component Extreme Value (TCEV) model. A Bayesian framework using Markov chain Monte Carlo sampling was developed to robustly characterize parameter uncertainty even in the presence of degeneracy. Two new posterior diagnostics based on the strength of the TCEV components were developed to aid identification of degeneracy. Armed with a robust inference framework, the study evaluated the potential of TCEV using a case study based on 31 catchments in eastern Australia with records exceeding 70 years. The evaluation used short to long records to compare TCEV and Log Pearson III fit and extrapolative uncertainty. The Log Pearson approach (LP3-PILF) censors PILFs following the approach described in Australian Rainfall and Runoff. With respect to goodness-of-fit, we found in most cases that TCEV fitted AM flood peaks well without the need to censor or stratify data, and overall, no clear difference emerged between TCEV and LP3-PILF. However, and contrary to expectation, TCEV produced high flow quantile confidence intervals consistently narrower than LP3-PILF even in the presence of degeneracy. While more case studies in different regions are needed to confirm the potential of TCEV, this study is a reminder that goodness-of-fit is a necessary but not sufficient criterion for selecting the probability model that best represents flood frequency.

Introducing Two Parsimonious Standard Power Mixture Models for Bimodal Proportional Data with Application to Loss Given Default

The need to model proportional data is common in a range of disciplines however, due to its bimodal nature, U- or J-shaped data present a particular challenge. In this study, two parsimonious mixture models are proposed to accurately characterise this proportional U- and J-shaped data. The proposed models are applied to loss given default data, an application area where specific importance is attached to the accuracy with which the mean is estimated, due to its linear relationship with a bank’s regulatory capital. In addition to using standard information criteria, the degree to which bias reduction in the estimation of the distributional mean can be achieved is used as a measure of model performance. The proposed models outperform the benchmark model with reference to the information criteria and yield a reduction in the distance between the empirical and distributional means. Given the special characteristics of the dataset, where a high proportion of observations are close to zero, a methodology for choosing a rounding threshold in an objective manner is developed as part of the data preparation stage. It is shown how the application of this rounding threshold can reduce bias in moment estimation regardless of the model choice.

Modeling cell-free DNA fragment size densities for non-invasive detection of cancer.

3058 Background: Circulating cell-free DNA (cfDNA) is largely nucleosomal in origin with typical fragment lengths of 167 base-pairs reflecting the length of DNA wrapped around-the histone and H1 linker. Given the nucleosomal origin of cfDNA, we have previously used low coverage whole genome sequencing to evaluate DNA fragmentation profiles to sensitively and specifically detect tumor-derived DNA with altered fragment lengths or coverage. Methods: Here we evaluate the use of Bayesian finite mixtures to model the fragment length distribution and demonstrate how the parameters from these models can be useful to distinguish between individuals with and without cancer. We examined the number of cfDNA fragments by size ranging from 100-220bp and approximated the mixture component location, scale, and weight using Markov Chain Monte Carlo. The performance of the method was determined using a ten-fold, ten repeat cross-validation of Gradient Boosted Machine model using 1) our previously described genome-wide fragmentation profile approach, 2) the parameters from the mixture model and 3) a combination of approaches 1) and 2) as features. Results: In this study of 215 cancer patients and 208 cancer-free individuals, we observed cross-validated AUCs of 1) 0.94, 2) 0.95, and 3) 0.97 among the three approaches. Conclusions: Our findings indicate that parsimonious mixture models may improve detection of cancer in conjunction with fragmentation profile analyses across the genome.

Capturing patterns via parsimonious mixture models

Abstract Parsimonious mixtures of multivariate t -factor analyzers are used for robust clustering of high-dimensional data. Sixteen parsimonious mixtures of t -factor analyzers are utilized and the AECM algorithm is used for parameter estimation. Application to compact facial representation is illustrated.

A Statistical Method for 2-D Facial Landmarking

Many facial-analysis approaches rely on robust and accurate automatic facial landmarking to correctly function. In this paper, we describe a statistical method for automatic facial-landmark localization. Our landmarking relies on a parsimonious mixture model of Gabor wavelet features, computed in coarse-to-fine fashion and complemented with a shape prior. We assess the accuracy and the robustness of the proposed approach in extensive cross-database conditions conducted on four face data sets (Face Recognition Grand Challenge, Cohn-Kanade, Bosphorus, and BioID). Our method has 99.33% accuracy on the Bosphorus database and 97.62% accuracy on the BioID database on the average, which improves the state of the art. We show that the method is not significantly affected by low-resolution images, small rotations, facial expressions, and natural occlusions such as beard and mustache. We further test the goodness of the landmarks in a facial expression recognition application and report landmarking-induced improvement over baseline on two separate databases for video-based expression recognition (Cohn-Kanade and BU-4DFE).

Transitivity of preferences.

Transitivity of preferences is a fundamental principle shared by most major contemporary rational, prescriptive, and descriptive models of decision making. To have transitive preferences, a person, group, or society that prefers choice option x to y and y to z must prefer x to z. Any claim of empirical violations of transitivity by individual decision makers requires evidence beyond a reasonable doubt. We discuss why unambiguous evidence is currently lacking and how to clarify the issue. In counterpoint to Tversky's (1969) seminal "Intransitivity of Preferences," we reconsider his data as well as those from more than 20 other studies of intransitive human or animal decision makers. We challenge the standard operationalizations of transitive preferences and discuss pervasive methodological problems in the collection, modeling, and analysis of relevant empirical data. For example, violations of weak stochastic transitivity do not imply violations of transitivity of preference. Building on past multidisciplinary work, we use parsimonious mixture models, where the space of permissible preference states is the family of (transitive) strict linear orders. We show that the data from many of the available studies designed to elicit intransitive choice are consistent with transitive preferences.

MODELING AVIAN ABUNDANCE FROM REPLICATED COUNTS USING BINOMIAL MIXTURE MODELS

Abundance estimation in ecology is usually accomplished by capture–recapture, removal, or distance sampling methods. These may be hard to implement at large spatial scales. In contrast, binomial mixture models enable abundance estimation without individual identification, based simply on temporally and spatially replicated counts. Here, we evaluate mixture models using data from the national breeding bird monitoring program in Switzerland, where some 250 1‐km2quadrats are surveyed using the territory mapping method three times during each breeding season. We chose eight species with contrasting distribution (wide–narrow), abundance (high–low), and detectability (easy–difficult). Abundance was modeled as a random effect with a Poisson or negative binomial distribution, with mean affected by forest cover, elevation, and route length. Detectability was a logit‐linear function of survey date, survey date‐by‐elevation, and sampling effort (time per transect unit). Resulting covariate effects and parameter estimates were consistent with expectations. Detectability per territory (for three surveys) ranged from 0.66 to 0.94 (mean 0.84) for easy species, and from 0.16 to 0.83 (mean 0.53) for difficult species, depended on survey effort for two easy and all four difficult species, and changed seasonally for three easy and three difficult species. Abundance was positively related to route length in three high‐abundance and one low‐abundance (one easy and three difficult) species, and increased with forest cover in five forest species, decreased for two nonforest species, and was unaffected for a generalist species. Abundance estimates under the most parsimonious mixture models were between 1.1 and 8.9 (median 1.8) times greater than estimates based on territory mapping; hence, three surveys were insufficient to detect all territories for each species. We conclude that binomial mixture models are an important new approach for estimating abundance corrected for detectability when only repeated‐count data are available. Future developments envisioned include estimation of trend, occupancy, and total regional abundance.

Alternating kernel and mixture density estimates

We describe and investigate a data-driven procedure for obtaining parsimonious mixture model estimates or, conversely, kernel estimates with data-driven local smoothing properties. The main idea is to obtain a semiparametric estimate by alternating between the parametric and nonparametric viewpoints.