Choice Of Summary Statistics Research Articles

Local dimension reduction of summary statistics for likelihood-free inference

Approximate Bayesian computation (ABC) and other likelihood-free inference methods have gained popularity in the last decade, as they allow rigorous statistical inference for complex models without analytically tractable likelihood functions. A key component for accurate inference with ABC is the choice of summary statistics, which summarize the information in the data, but at the same time should be low-dimensional for efficiency. Several dimension reduction techniques have been introduced to automatically construct informative and low-dimensional summaries from a possibly large pool of candidate summaries. Projection-based methods, which are based on learning simple functional relationships from the summaries to parameters, are widely used and usually perform well, but might fail when the assumptions behind the transformation are not satisfied. We introduce a localization strategy for any projection-based dimension reduction method, in which the transformation is estimated in the neighborhood of the observed data instead of the whole space. Localization strategies have been suggested before, but the performance of the transformed summaries outside the local neighborhood has not been guaranteed. In our localization approach the transformation is validated and optimized over validation datasets, ensuring reliable performance. We demonstrate the improvement in the estimation accuracy for localized versions of linear regression and partial least squares, for three different models of varying complexity.

A Bayesian Hierarchical Summary Receiver Operating Characteristic Model for Network Meta-Analysis of Diagnostic Tests

ABSTRACTIn studies evaluating the accuracy of diagnostic tests, three designs are commonly used, crossover, randomized, and noncomparative. Existing methods for meta-analysis of diagnostic tests mainly consider the simple cases in which the reference test in all or none of the studies can be considered a gold standard test, and in which all studies use either a randomized or noncomparative design. The proliferation of diagnostic instruments and the diversity of study designs create a need for more general methods to combine studies that include or do not include a gold standard test and that use various designs. This article extends the Bayesian hierarchical summary receiver operating characteristic model to network meta-analysis of diagnostic tests to simultaneously compare multiple tests within a missing data framework. The method accounts for correlations between multiple tests and for heterogeneity between studies. It also allows different studies to include different subsets of diagnostic tests and provides flexibility in the choice of summary statistics. The model is evaluated using simulations and illustrated using real data on tests for deep vein thrombosis, with sensitivity analyses. Supplementary materials for this article are available online.

Learning Summary Statistic for Approximate Bayesian Computation via Deep Neural Network

Approximate Bayesian Computation (ABC) methods are used to approximate posterior distributions in models with unknown or computationally intractable likelihoods. Both the accuracy and computational efficiency of ABC depend on the choice of summary statistic, but outside of special cases where the optimal summary statistics are known, it is unclear which guiding principles can be used to construct effective summary statistics. In this paper we explore the possibility of automating the process of constructing summary statistics by training deep neural networks to predict the parameters from artificially generated data: the resulting summary statistics are approximately posterior means of the parameters. With minimal model-specific tuning, our method constructs summary statistics for the Ising model and the moving-average model, which match or exceed theoretically-motivated summary statistics in terms of the accuracies of the resulting posteriors.

Efficient parameter sensitivity computation for spatially extended reaction networks.

Reaction-diffusion models are widely used to study spatially extended chemical reaction systems. In order to understand how the dynamics of a reaction-diffusion model are affected by changes in its input parameters, efficient methods for computing parametric sensitivities are required. In this work, we focus on the stochastic models of spatially extended chemical reaction systems that involve partitioning the computational domain into voxels. Parametric sensitivities are often calculated using Monte Carlo techniques that are typically computationally expensive; however, variance reduction techniques can decrease the number of Monte Carlo simulations required. By exploiting the characteristic dynamics of spatially extended reaction networks, we are able to adapt existing finite difference schemes to robustly estimate parametric sensitivities in a spatially extended network. We show that algorithmic performance depends on the dynamics of the given network and the choice of summary statistics. We then describe a hybrid technique that dynamically chooses the most appropriate simulation method for the network of interest. Our method is tested for functionality and accuracy in a range of different scenarios.

A Bootstrap Likelihood Approach to Bayesian Computation

SummaryThere is an increasing amount of literature focused on Bayesian computational methods to address problems with intractable likelihood. One approach is a set of algorithms known as Approximate Bayesian Computational (ABC) methods. One of the problems with these algorithms is that their performance depends on the appropriate choice of summary statistics, distance measure and tolerance level. To circumvent this problem, an alternative method based on the empirical likelihood has been introduced. This method can be easily implemented when a set of constraints, related to the moments of the distribution, is specified. However, the choice of the constraints is sometimes challenging. To overcome this difficulty, we propose an alternative method based on a bootstrap likelihood approach. The method is easy to implement and in some cases is actually faster than the other approaches considered. We illustrate the performance of our algorithm with examples from population genetics, time series and stochastic differential equations. We also test the method on a real dataset.

Approximate Bayesian Computation of diversification rates from molecular phylogenies: introducing a new efficient summary statistic, the nLTT

Summary Molecular phylogenies form a potential source of information on rates of diversification, and the mechanisms that underlie diversification patterns. Diversification models have become increasingly complex over the past decade, and we have reached a point where the computation of the analytical likelihood of the model given a phylogeny is either unavailable or intractable. For such models, a likelihood‐free approach such as Approximate Bayesian Computation (ABC) offers a solution. ABC is a Bayesian framework that uses one or more summary statistics instead of the likelihood function. Crucial to the performance of an ABC algorithm is the choice of summary statistics. Here, we analyse the applicability of three traditional and often‐used summary statistics (Gamma statistic, Phylogenetic Diversity and tree size) within an ABC framework and propose a new summary statistic: the normalized Lineages‐Through‐Time (nLTT) statistic. We find that the traditional summary statistics perform poorly and should not be used as a substitute of the likelihood. By contrast, we find that the nLTT statistic performs on par with the likelihood. We suggest to include the nLTT statistic in future ABC applications within phylogenetics. We argue that the use of ABC in diversification rate analysis is a promising new approach, but that care should be taken which summary statistics are chosen.

The potential of likelihood-free inference of cosmological parameters with weak lensing data

AbstractIn the statistical framework of likelihood-free inference, the posterior distribution of model parameters is explored via simulation rather than direct evaluation of the likelihood function, permitting inference in situations where this function is analytically intractable. We consider the problem of estimating cosmological parameters using measurements of the weak gravitational lensing of galaxies; specifically, we propose the use a likelihood-free approach to investigate the posterior distribution of some parameters in the ΛCDM model upon observing a large number of sheared galaxies. The choice of summary statistic used when comparing observed data and simulated data in the likelihood-free inference framework is critical, so we work toward a principled method of choosing the summary statistic, aiming for dimension reduction while seeking a statistic that is as close as possible to being sufficient for the parameters of interest.

MsBayes: Pipeline for testing comparative phylogeographic histories using hierarchical approximate Bayesian computation

BackgroundAlthough testing for simultaneous divergence (vicariance) across different population-pairs that span the same barrier to gene flow is of central importance to evolutionary biology, researchers often equate the gene tree and population/species tree thereby ignoring stochastic coalescent variance in their conclusions of temporal incongruence. In contrast to other available phylogeographic software packages, msBayes is the only one that analyses data from multiple species/population pairs under a hierarchical model.ResultsmsBayes employs approximate Bayesian computation (ABC) under a hierarchical coalescent model to test for simultaneous divergence (TSD) in multiple co-distributed population-pairs. Simultaneous isolation is tested by estimating three hyper-parameters that characterize the degree of variability in divergence times across co-distributed population pairs while allowing for variation in various within population-pair demographic parameters (sub-parameters) that can affect the coalescent. msBayes is a software package consisting of several C and R programs that are run with a Perl "front-end".ConclusionThe method reasonably distinguishes simultaneous isolation from temporal incongruence in the divergence of co-distributed population pairs, even with sparse sampling of individuals. Because the estimate step is decoupled from the simulation step, one can rapidly evaluate different ABC acceptance/rejection conditions and the choice of summary statistics. Given the complex and idiosyncratic nature of testing multi-species biogeographic hypotheses, we envision msBayes as a powerful and flexible tool for tackling a wide array of difficult research questions that use population genetic data from multiple co-distributed species. The msBayes pipeline is available for download at under an open source license (GNU Public License). The msBayes pipeline is comprised of several C and R programs that are run with a Perl "front-end" and runs on Linux, Mac OS-X, and most POSIX systems. Although the current implementation is for a single locus per species-pair, future implementations will allow analysis of multi-loci data per species pair.

A hierarchical regression approach to meta-analysis of diagnostic test accuracy evaluations.

An important quality of meta-analytic models for research synthesis is their ability to account for both within- and between-study variability. Currently available meta-analytic approaches for studies of diagnostic test accuracy work primarily within a fixed-effects framework. In this paper we describe a hierarchical regression model for meta-analysis of studies reporting estimates of test sensitivity and specificity. The model allows more between- and within-study variability than fixed-effect approaches, by allowing both test stringency and test accuracy to vary across studies. It is also possible to examine the effects of study specific covariates. Estimates are computed using Markov Chain Monte Carlo simulation with publicly available software (BUGS). This estimation method allows flexibility in the choice of summary statistics. We demonstrate the advantages of this modelling approach using a recently published meta-analysis comparing three tests used to detect nodal metastasis of cervical cancer.

Optimal lag length in estimating Dickey–Fuller statistics: an empirical note

The purpose of this note is to empirically demonstrate that the choice of summary statistic used in specifying the Dickey-Fuller test equation can determine the outcome of a test for stationarity. A reasonable empirical practice would be to evaluate stationarity over different lagged specifications of the Dickey-Fuller test equation.

Stochastic Simulation for Characterizing Ecological Spatial Patterns and Appraising Risk.

The theory and a case study are presented for a class of techniques known as stochastic simulation. Stochastic simulations can characterize the certainty of estimates of spatially and/or temporally correlated ecological variables. Rather than merely providing a unique estimate, a conditional probability distribution is built for the unsampled location. This distribution provides the researcher with any summary statistic or confidence limit desired. Moreover, the techniques are flexible enough to incorporate expected economic losses into the analysis. A simple analogy of a jigsaw puzzle is used first to introduce key concepts. Then, the mathematical highlights of two leading stochastic simulation procedures are presented. Finally, one simulation method, known as sequential Gaussian conditional simulation, is used to generate multiple, equally probable images of adult corn rootworm densities over a large (225 x 150 km) area in northwestern Iowa during the summer of 1989. The results show the simulated density of rootworms to be influenced strongly by the choice of summary statistic and density threshold. Economic risk is appraised from the point of view of the farmer by incorporating the expected economic losses due to the use of a soil insecticide. Since the cost to the farmer of not using an insecticide when in fact it is needed is over three times greater than the cost of using one when it is not needed, the area identified as potentially requiring treatment is much larger than when a summary statistic like the mean or median is used. Stochastic simulation allows the environmental researcher, policy-maker, or manager the opportunity to characterize uncertainty and economic or other losses, and to determine areas requiring treatment and additional samples.

The analysis of vaginal bleeding patterns induced by fertility regulating methods

Contraceptive methods often induce disturbances in vaginal bleeding patterns which are the main reason for women to discontinue method use. Knowledge of these changes is essential for effective counselling and product development and necessitates adequate methods of collection and analysis of vaginal bleeding data. These issues were reviewed by clinicians, medical statisticians and computer analysts during several consultations organized by the World Health Organization Special Programme of Research, Development and Research Training in Human Reproduction and their discussions are summarized in this paper. Recommendations are made on the use of menstrual diary cards for data collection. It is suggested that the analysis of menstrual patterns be based on the reference period method developed by Rodriguez et al . in 1976 to which several modifications in terminology and choice of summary statistics are proposed. While these are presented as the minimum required for the comparability of studies, other points of analysis are identified which need further study, in an attempt to stimulate research in this field by other investigators.