Statistical Inference in the Learning of Novel Phonetic Categories

ERIC Educational Resources Information Center

Zhao, Yuan

2010-01-01

Learning a phonetic category (or any linguistic category) requires integrating different sources of information. A crucial unsolved problem for phonetic learning is how this integration occurs: how can we update our previous knowledge about a phonetic category as we hear new exemplars of the category? One model of learning is Bayesian Inference,…

The Role of Probability in Developing Learners' Models of Simulation Approaches to Inference

ERIC Educational Resources Information Center

Lee, Hollylynne S.; Doerr, Helen M.; Tran, Dung; Lovett, Jennifer N.

2016-01-01

Repeated sampling approaches to inference that rely on simulations have recently gained prominence in statistics education, and probabilistic concepts are at the core of this approach. In this approach, learners need to develop a mapping among the problem situation, a physical enactment, computer representations, and the underlying randomization…

Thou Shalt Not Bear False Witness against Null Hypothesis Significance Testing

ERIC Educational Resources Information Center

García-Pérez, Miguel A.

2017-01-01

Null hypothesis significance testing (NHST) has been the subject of debate for decades and alternative approaches to data analysis have been proposed. This article addresses this debate from the perspective of scientific inquiry and inference. Inference is an inverse problem and application of statistical methods cannot reveal whether effects…

"Magnitude-based inference": a statistical review.

PubMed

Welsh, Alan H; Knight, Emma J

2015-04-01

We consider "magnitude-based inference" and its interpretation by examining in detail its use in the problem of comparing two means. We extract from the spreadsheets, which are provided to users of the analysis (http://www.sportsci.org/), a precise description of how "magnitude-based inference" is implemented. We compare the implemented version of the method with general descriptions of it and interpret the method in familiar statistical terms. We show that "magnitude-based inference" is not a progressive improvement on modern statistics. The additional probabilities introduced are not directly related to the confidence interval but, rather, are interpretable either as P values for two different nonstandard tests (for different null hypotheses) or as approximate Bayesian calculations, which also lead to a type of test. We also discuss sample size calculations associated with "magnitude-based inference" and show that the substantial reduction in sample sizes claimed for the method (30% of the sample size obtained from standard frequentist calculations) is not justifiable so the sample size calculations should not be used. Rather than using "magnitude-based inference," a better solution is to be realistic about the limitations of the data and use either confidence intervals or a fully Bayesian analysis.

Boosting Bayesian parameter inference of stochastic differential equation models with methods from statistical physics

NASA Astrophysics Data System (ADS)

Albert, Carlo; Ulzega, Simone; Stoop, Ruedi

2016-04-01

Measured time-series of both precipitation and runoff are known to exhibit highly non-trivial statistical properties. For making reliable probabilistic predictions in hydrology, it is therefore desirable to have stochastic models with output distributions that share these properties. When parameters of such models have to be inferred from data, we also need to quantify the associated parametric uncertainty. For non-trivial stochastic models, however, this latter step is typically very demanding, both conceptually and numerically, and always never done in hydrology. Here, we demonstrate that methods developed in statistical physics make a large class of stochastic differential equation (SDE) models amenable to a full-fledged Bayesian parameter inference. For concreteness we demonstrate these methods by means of a simple yet non-trivial toy SDE model. We consider a natural catchment that can be described by a linear reservoir, at the scale of observation. All the neglected processes are assumed to happen at much shorter time-scales and are therefore modeled with a Gaussian white noise term, the standard deviation of which is assumed to scale linearly with the system state (water volume in the catchment). Even for constant input, the outputs of this simple non-linear SDE model show a wealth of desirable statistical properties, such as fat-tailed distributions and long-range correlations. Standard algorithms for Bayesian inference fail, for models of this kind, because their likelihood functions are extremely high-dimensional intractable integrals over all possible model realizations. The use of Kalman filters is illegitimate due to the non-linearity of the model. Particle filters could be used but become increasingly inefficient with growing number of data points. Hamiltonian Monte Carlo algorithms allow us to translate this inference problem to the problem of simulating the dynamics of a statistical mechanics system and give us access to most sophisticated methods that have been developed in the statistical physics community over the last few decades. We demonstrate that such methods, along with automated differentiation algorithms, allow us to perform a full-fledged Bayesian inference, for a large class of SDE models, in a highly efficient and largely automatized manner. Furthermore, our algorithm is highly parallelizable. For our toy model, discretized with a few hundred points, a full Bayesian inference can be performed in a matter of seconds on a standard PC.

From inverse problems to learning: a Statistical Mechanics approach

NASA Astrophysics Data System (ADS)

Baldassi, Carlo; Gerace, Federica; Saglietti, Luca; Zecchina, Riccardo

2018-01-01

We present a brief introduction to the statistical mechanics approaches for the study of inverse problems in data science. We then provide concrete new results on inferring couplings from sampled configurations in systems characterized by an extensive number of stable attractors in the low temperature regime. We also show how these result are connected to the problem of learning with realistic weak signals in computational neuroscience. Our techniques and algorithms rely on advanced mean-field methods developed in the context of disordered systems.

Econophysical visualization of Adam Smith’s invisible hand

NASA Astrophysics Data System (ADS)

Cohen, Morrel H.; Eliazar, Iddo I.

2013-02-01

Consider a complex system whose macrostate is statistically observable, but yet whose operating mechanism is an unknown black-box. In this paper we address the problem of inferring, from the system’s macrostate statistics, the system’s intrinsic force yielding the observed statistics. The inference is established via two diametrically opposite approaches which result in the very same intrinsic force: a top-down approach based on the notion of entropy, and a bottom-up approach based on the notion of Langevin dynamics. The general results established are applied to the problem of visualizing the intrinsic socioeconomic force-Adam Smith’s invisible hand-shaping the distribution of wealth in human societies. Our analysis yields quantitative econophysical representations of figurative socioeconomic forces, quantitative definitions of “poor” and “rich”, and a quantitative characterization of the “poor-get-poorer” and the “rich-get-richer” phenomena.

Exploring High School Students Beginning Reasoning about Significance Tests with Technology

ERIC Educational Resources Information Center

García, Víctor N.; Sánchez, Ernesto

2017-01-01

In the present study we analyze how students reason about or make inferences given a particular hypothesis testing problem (without having studied formal methods of statistical inference) when using Fathom. They use Fathom to create an empirical sampling distribution through computer simulation. It is found that most student´s reasoning rely on…

Learning planar Ising models

DOE PAGES

Johnson, Jason K.; Oyen, Diane Adele; Chertkov, Michael; ...

2016-12-01

Inference and learning of graphical models are both well-studied problems in statistics and machine learning that have found many applications in science and engineering. However, exact inference is intractable in general graphical models, which suggests the problem of seeking the best approximation to a collection of random variables within some tractable family of graphical models. In this paper, we focus on the class of planar Ising models, for which exact inference is tractable using techniques of statistical physics. Based on these techniques and recent methods for planarity testing and planar embedding, we propose a greedy algorithm for learning the bestmore » planar Ising model to approximate an arbitrary collection of binary random variables (possibly from sample data). Given the set of all pairwise correlations among variables, we select a planar graph and optimal planar Ising model defined on this graph to best approximate that set of correlations. Finally, we demonstrate our method in simulations and for two applications: modeling senate voting records and identifying geo-chemical depth trends from Mars rover data.« less

Learning planar Ising models

DOE Office of Scientific and Technical Information (OSTI.GOV)

Johnson, Jason K.; Oyen, Diane Adele; Chertkov, Michael

Inference and learning of graphical models are both well-studied problems in statistics and machine learning that have found many applications in science and engineering. However, exact inference is intractable in general graphical models, which suggests the problem of seeking the best approximation to a collection of random variables within some tractable family of graphical models. In this paper, we focus on the class of planar Ising models, for which exact inference is tractable using techniques of statistical physics. Based on these techniques and recent methods for planarity testing and planar embedding, we propose a greedy algorithm for learning the bestmore » planar Ising model to approximate an arbitrary collection of binary random variables (possibly from sample data). Given the set of all pairwise correlations among variables, we select a planar graph and optimal planar Ising model defined on this graph to best approximate that set of correlations. Finally, we demonstrate our method in simulations and for two applications: modeling senate voting records and identifying geo-chemical depth trends from Mars rover data.« less

Structural mapping in statistical word problems: A relational reasoning approach to Bayesian inference.

PubMed

Johnson, Eric D; Tubau, Elisabet

2017-06-01

Presenting natural frequencies facilitates Bayesian inferences relative to using percentages. Nevertheless, many people, including highly educated and skilled reasoners, still fail to provide Bayesian responses to these computationally simple problems. We show that the complexity of relational reasoning (e.g., the structural mapping between the presented and requested relations) can help explain the remaining difficulties. With a non-Bayesian inference that required identical arithmetic but afforded a more direct structural mapping, performance was universally high. Furthermore, reducing the relational demands of the task through questions that directed reasoners to use the presented statistics, as compared with questions that prompted the representation of a second, similar sample, also significantly improved reasoning. Distinct error patterns were also observed between these presented- and similar-sample scenarios, which suggested differences in relational-reasoning strategies. On the other hand, while higher numeracy was associated with better Bayesian reasoning, higher-numerate reasoners were not immune to the relational complexity of the task. Together, these findings validate the relational-reasoning view of Bayesian problem solving and highlight the importance of considering not only the presented task structure, but also the complexity of the structural alignment between the presented and requested relations.

Inferring action structure and causal relationships in continuous sequences of human action.

PubMed

Buchsbaum, Daphna; Griffiths, Thomas L; Plunkett, Dillon; Gopnik, Alison; Baldwin, Dare

2015-02-01

In the real world, causal variables do not come pre-identified or occur in isolation, but instead are embedded within a continuous temporal stream of events. A challenge faced by both human learners and machine learning algorithms is identifying subsequences that correspond to the appropriate variables for causal inference. A specific instance of this problem is action segmentation: dividing a sequence of observed behavior into meaningful actions, and determining which of those actions lead to effects in the world. Here we present a Bayesian analysis of how statistical and causal cues to segmentation should optimally be combined, as well as four experiments investigating human action segmentation and causal inference. We find that both people and our model are sensitive to statistical regularities and causal structure in continuous action, and are able to combine these sources of information in order to correctly infer both causal relationships and segmentation boundaries. Copyright © 2014. Published by Elsevier Inc.

Parametric inference for biological sequence analysis.

PubMed

Pachter, Lior; Sturmfels, Bernd

2004-11-16

One of the major successes in computational biology has been the unification, by using the graphical model formalism, of a multitude of algorithms for annotating and comparing biological sequences. Graphical models that have been applied to these problems include hidden Markov models for annotation, tree models for phylogenetics, and pair hidden Markov models for alignment. A single algorithm, the sum-product algorithm, solves many of the inference problems that are associated with different statistical models. This article introduces the polytope propagation algorithm for computing the Newton polytope of an observation from a graphical model. This algorithm is a geometric version of the sum-product algorithm and is used to analyze the parametric behavior of maximum a posteriori inference calculations for graphical models.

Topics in inference and decision-making with partial knowledge

NASA Technical Reports Server (NTRS)

Safavian, S. Rasoul; Landgrebe, David

1990-01-01

Two essential elements needed in the process of inference and decision-making are prior probabilities and likelihood functions. When both of these components are known accurately and precisely, the Bayesian approach provides a consistent and coherent solution to the problems of inference and decision-making. In many situations, however, either one or both of the above components may not be known, or at least may not be known precisely. This problem of partial knowledge about prior probabilities and likelihood functions is addressed. There are at least two ways to cope with this lack of precise knowledge: robust methods, and interval-valued methods. First, ways of modeling imprecision and indeterminacies in prior probabilities and likelihood functions are examined; then how imprecision in the above components carries over to the posterior probabilities is examined. Finally, the problem of decision making with imprecise posterior probabilities and the consequences of such actions are addressed. Application areas where the above problems may occur are in statistical pattern recognition problems, for example, the problem of classification of high-dimensional multispectral remote sensing image data.

Learning Quantitative Sequence-Function Relationships from Massively Parallel Experiments

NASA Astrophysics Data System (ADS)

Atwal, Gurinder S.; Kinney, Justin B.

2016-03-01

A fundamental aspect of biological information processing is the ubiquity of sequence-function relationships—functions that map the sequence of DNA, RNA, or protein to a biochemically relevant activity. Most sequence-function relationships in biology are quantitative, but only recently have experimental techniques for effectively measuring these relationships been developed. The advent of such "massively parallel" experiments presents an exciting opportunity for the concepts and methods of statistical physics to inform the study of biological systems. After reviewing these recent experimental advances, we focus on the problem of how to infer parametric models of sequence-function relationships from the data produced by these experiments. Specifically, we retrace and extend recent theoretical work showing that inference based on mutual information, not the standard likelihood-based approach, is often necessary for accurately learning the parameters of these models. Closely connected with this result is the emergence of "diffeomorphic modes"—directions in parameter space that are far less constrained by data than likelihood-based inference would suggest. Analogous to Goldstone modes in physics, diffeomorphic modes arise from an arbitrarily broken symmetry of the inference problem. An analytically tractable model of a massively parallel experiment is then described, providing an explicit demonstration of these fundamental aspects of statistical inference. This paper concludes with an outlook on the theoretical and computational challenges currently facing studies of quantitative sequence-function relationships.

Evolutionary inference via the Poisson Indel Process.

PubMed

Bouchard-Côté, Alexandre; Jordan, Michael I

2013-01-22

We address the problem of the joint statistical inference of phylogenetic trees and multiple sequence alignments from unaligned molecular sequences. This problem is generally formulated in terms of string-valued evolutionary processes along the branches of a phylogenetic tree. The classic evolutionary process, the TKF91 model [Thorne JL, Kishino H, Felsenstein J (1991) J Mol Evol 33(2):114-124] is a continuous-time Markov chain model composed of insertion, deletion, and substitution events. Unfortunately, this model gives rise to an intractable computational problem: The computation of the marginal likelihood under the TKF91 model is exponential in the number of taxa. In this work, we present a stochastic process, the Poisson Indel Process (PIP), in which the complexity of this computation is reduced to linear. The Poisson Indel Process is closely related to the TKF91 model, differing only in its treatment of insertions, but it has a global characterization as a Poisson process on the phylogeny. Standard results for Poisson processes allow key computations to be decoupled, which yields the favorable computational profile of inference under the PIP model. We present illustrative experiments in which Bayesian inference under the PIP model is compared with separate inference of phylogenies and alignments.

Evolutionary inference via the Poisson Indel Process

PubMed Central

Bouchard-Côté, Alexandre; Jordan, Michael I.

2013-01-01

We address the problem of the joint statistical inference of phylogenetic trees and multiple sequence alignments from unaligned molecular sequences. This problem is generally formulated in terms of string-valued evolutionary processes along the branches of a phylogenetic tree. The classic evolutionary process, the TKF91 model [Thorne JL, Kishino H, Felsenstein J (1991) J Mol Evol 33(2):114–124] is a continuous-time Markov chain model composed of insertion, deletion, and substitution events. Unfortunately, this model gives rise to an intractable computational problem: The computation of the marginal likelihood under the TKF91 model is exponential in the number of taxa. In this work, we present a stochastic process, the Poisson Indel Process (PIP), in which the complexity of this computation is reduced to linear. The Poisson Indel Process is closely related to the TKF91 model, differing only in its treatment of insertions, but it has a global characterization as a Poisson process on the phylogeny. Standard results for Poisson processes allow key computations to be decoupled, which yields the favorable computational profile of inference under the PIP model. We present illustrative experiments in which Bayesian inference under the PIP model is compared with separate inference of phylogenies and alignments. PMID:23275296

Gene-network inference by message passing

NASA Astrophysics Data System (ADS)

Braunstein, A.; Pagnani, A.; Weigt, M.; Zecchina, R.

2008-01-01

The inference of gene-regulatory processes from gene-expression data belongs to the major challenges of computational systems biology. Here we address the problem from a statistical-physics perspective and develop a message-passing algorithm which is able to infer sparse, directed and combinatorial regulatory mechanisms. Using the replica technique, the algorithmic performance can be characterized analytically for artificially generated data. The algorithm is applied to genome-wide expression data of baker's yeast under various environmental conditions. We find clear cases of combinatorial control, and enrichment in common functional annotations of regulated genes and their regulators.

Statistical inference of protein structural alignments using information and compression.

PubMed

Collier, James H; Allison, Lloyd; Lesk, Arthur M; Stuckey, Peter J; Garcia de la Banda, Maria; Konagurthu, Arun S

2017-04-01

Structural molecular biology depends crucially on computational techniques that compare protein three-dimensional structures and generate structural alignments (the assignment of one-to-one correspondences between subsets of amino acids based on atomic coordinates). Despite its importance, the structural alignment problem has not been formulated, much less solved, in a consistent and reliable way. To overcome these difficulties, we present here a statistical framework for the precise inference of structural alignments, built on the Bayesian and information-theoretic principle of Minimum Message Length (MML). The quality of any alignment is measured by its explanatory power-the amount of lossless compression achieved to explain the protein coordinates using that alignment. We have implemented this approach in MMLigner , the first program able to infer statistically significant structural alignments. We also demonstrate the reliability of MMLigner 's alignment results when compared with the state of the art. Importantly, MMLigner can also discover different structural alignments of comparable quality, a challenging problem for oligomers and protein complexes. Source code, binaries and an interactive web version are available at http://lcb.infotech.monash.edu.au/mmligner . arun.konagurthu@monash.edu. Supplementary data are available at Bioinformatics online. © The Author 2017. Published by Oxford University Press. All rights reserved. For Permissions, please e-mail: journals.permissions@oup.com

Statistical inference with quantum measurements: methodologies for nitrogen vacancy centers in diamond

NASA Astrophysics Data System (ADS)

Hincks, Ian; Granade, Christopher; Cory, David G.

2018-01-01

The analysis of photon count data from the standard nitrogen vacancy (NV) measurement process is treated as a statistical inference problem. This has applications toward gaining better and more rigorous error bars for tasks such as parameter estimation (e.g. magnetometry), tomography, and randomized benchmarking. We start by providing a summary of the standard phenomenological model of the NV optical process in terms of Lindblad jump operators. This model is used to derive random variables describing emitted photons during measurement, to which finite visibility, dark counts, and imperfect state preparation are added. NV spin-state measurement is then stated as an abstract statistical inference problem consisting of an underlying biased coin obstructed by three Poisson rates. Relevant frequentist and Bayesian estimators are provided, discussed, and quantitatively compared. We show numerically that the risk of the maximum likelihood estimator is well approximated by the Cramér-Rao bound, for which we provide a simple formula. Of the estimators, we in particular promote the Bayes estimator, owing to its slightly better risk performance, and straightforward error propagation into more complex experiments. This is illustrated on experimental data, where quantum Hamiltonian learning is performed and cross-validated in a fully Bayesian setting, and compared to a more traditional weighted least squares fit.

Boosting Bayesian parameter inference of nonlinear stochastic differential equation models by Hamiltonian scale separation.

PubMed

Albert, Carlo; Ulzega, Simone; Stoop, Ruedi

2016-04-01

Parameter inference is a fundamental problem in data-driven modeling. Given observed data that is believed to be a realization of some parameterized model, the aim is to find parameter values that are able to explain the observed data. In many situations, the dominant sources of uncertainty must be included into the model for making reliable predictions. This naturally leads to stochastic models. Stochastic models render parameter inference much harder, as the aim then is to find a distribution of likely parameter values. In Bayesian statistics, which is a consistent framework for data-driven learning, this so-called posterior distribution can be used to make probabilistic predictions. We propose a novel, exact, and very efficient approach for generating posterior parameter distributions for stochastic differential equation models calibrated to measured time series. The algorithm is inspired by reinterpreting the posterior distribution as a statistical mechanics partition function of an object akin to a polymer, where the measurements are mapped on heavier beads compared to those of the simulated data. To arrive at distribution samples, we employ a Hamiltonian Monte Carlo approach combined with a multiple time-scale integration. A separation of time scales naturally arises if either the number of measurement points or the number of simulation points becomes large. Furthermore, at least for one-dimensional problems, we can decouple the harmonic modes between measurement points and solve the fastest part of their dynamics analytically. Our approach is applicable to a wide range of inference problems and is highly parallelizable.

Discrete Inverse and State Estimation Problems

NASA Astrophysics Data System (ADS)

Wunsch, Carl

2006-06-01

The problems of making inferences about the natural world from noisy observations and imperfect theories occur in almost all scientific disciplines. This book addresses these problems using examples taken from geophysical fluid dynamics. It focuses on discrete formulations, both static and time-varying, known variously as inverse, state estimation or data assimilation problems. Starting with fundamental algebraic and statistical ideas, the book guides the reader through a range of inference tools including the singular value decomposition, Gauss-Markov and minimum variance estimates, Kalman filters and related smoothers, and adjoint (Lagrange multiplier) methods. The final chapters discuss a variety of practical applications to geophysical flow problems. Discrete Inverse and State Estimation Problems is an ideal introduction to the topic for graduate students and researchers in oceanography, meteorology, climate dynamics, and geophysical fluid dynamics. It is also accessible to a wider scientific audience; the only prerequisite is an understanding of linear algebra. Provides a comprehensive introduction to discrete methods of inference from incomplete information Based upon 25 years of practical experience using real data and models Develops sequential and whole-domain analysis methods from simple least-squares Contains many examples and problems, and web-based support through MIT opencourseware

Confidence set inference with a prior quadratic bound

NASA Technical Reports Server (NTRS)

Backus, George E.

1989-01-01

In the uniqueness part of a geophysical inverse problem, the observer wants to predict all likely values of P unknown numerical properties z=(z sub 1,...,z sub p) of the earth from measurement of D other numerical properties y (sup 0) = (y (sub 1) (sup 0), ..., y (sub D (sup 0)), using full or partial knowledge of the statistical distribution of the random errors in y (sup 0). The data space Y containing y(sup 0) is D-dimensional, so when the model space X is infinite-dimensional the linear uniqueness problem usually is insoluble without prior information about the correct earth model x. If that information is a quadratic bound on x, Bayesian inference (BI) and stochastic inversion (SI) inject spurious structure into x, implied by neither the data nor the quadratic bound. Confidence set inference (CSI) provides an alternative inversion technique free of this objection. Confidence set inference is illustrated in the problem of estimating the geomagnetic field B at the core-mantle boundary (CMB) from components of B measured on or above the earth's surface.

Reliability of a Measure of Institutional Discrimination against Minorities

DTIC Science & Technology

1979-12-01

samples are presented. The first is based upon classical statistical theory and the second derives from a series of computer-generated Monte Carlo...Institutional racism and sexism . Englewood Cliffs, N. J.: Prentice-Hall, Inc., 1978. Hays, W. L. and Winkler, R. L. Statistics : probability, inference... statistical measure of the e of institutional discrimination are discussed. Two methods of dealing with the problem of reliability of the measure in small

Hybrid regulatory models: a statistically tractable approach to model regulatory network dynamics.

PubMed

Ocone, Andrea; Millar, Andrew J; Sanguinetti, Guido

2013-04-01

Computational modelling of the dynamics of gene regulatory networks is a central task of systems biology. For networks of small/medium scale, the dominant paradigm is represented by systems of coupled non-linear ordinary differential equations (ODEs). ODEs afford great mechanistic detail and flexibility, but calibrating these models to data is often an extremely difficult statistical problem. Here, we develop a general statistical inference framework for stochastic transcription-translation networks. We use a coarse-grained approach, which represents the system as a network of stochastic (binary) promoter and (continuous) protein variables. We derive an exact inference algorithm and an efficient variational approximation that allows scalable inference and learning of the model parameters. We demonstrate the power of the approach on two biological case studies, showing that the method allows a high degree of flexibility and is capable of testable novel biological predictions. http://homepages.inf.ed.ac.uk/gsanguin/software.html. Supplementary data are available at Bioinformatics online.

Statistical Inference for Big Data Problems in Molecular Biophysics

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ramanathan, Arvind; Savol, Andrej; Burger, Virginia

2012-01-01

We highlight the role of statistical inference techniques in providing biological insights from analyzing long time-scale molecular simulation data. Technologi- cal and algorithmic improvements in computation have brought molecular simu- lations to the forefront of techniques applied to investigating the basis of living systems. While these longer simulations, increasingly complex reaching petabyte scales presently, promise a detailed view into microscopic behavior, teasing out the important information has now become a true challenge on its own. Mining this data for important patterns is critical to automating therapeutic intervention discovery, improving protein design, and fundamentally understanding the mech- anistic basis of cellularmore » homeostasis.« less

Tropical geometry of statistical models.

PubMed

Pachter, Lior; Sturmfels, Bernd

2004-11-16

This article presents a unified mathematical framework for inference in graphical models, building on the observation that graphical models are algebraic varieties. From this geometric viewpoint, observations generated from a model are coordinates of a point in the variety, and the sum-product algorithm is an efficient tool for evaluating specific coordinates. Here, we address the question of how the solutions to various inference problems depend on the model parameters. The proposed answer is expressed in terms of tropical algebraic geometry. The Newton polytope of a statistical model plays a key role. Our results are applied to the hidden Markov model and the general Markov model on a binary tree.

Cox process representation and inference for stochastic reaction-diffusion processes

NASA Astrophysics Data System (ADS)

Schnoerr, David; Grima, Ramon; Sanguinetti, Guido

2016-05-01

Complex behaviour in many systems arises from the stochastic interactions of spatially distributed particles or agents. Stochastic reaction-diffusion processes are widely used to model such behaviour in disciplines ranging from biology to the social sciences, yet they are notoriously difficult to simulate and calibrate to observational data. Here we use ideas from statistical physics and machine learning to provide a solution to the inverse problem of learning a stochastic reaction-diffusion process from data. Our solution relies on a non-trivial connection between stochastic reaction-diffusion processes and spatio-temporal Cox processes, a well-studied class of models from computational statistics. This connection leads to an efficient and flexible algorithm for parameter inference and model selection. Our approach shows excellent accuracy on numeric and real data examples from systems biology and epidemiology. Our work provides both insights into spatio-temporal stochastic systems, and a practical solution to a long-standing problem in computational modelling.

Bayesian inference and decision theory - A framework for decision making in natural resource management

USGS Publications Warehouse

Dorazio, R.M.; Johnson, F.A.

2003-01-01

Bayesian inference and decision theory may be used in the solution of relatively complex problems of natural resource management, owing to recent advances in statistical theory and computing. In particular, Markov chain Monte Carlo algorithms provide a computational framework for fitting models of adequate complexity and for evaluating the expected consequences of alternative management actions. We illustrate these features using an example based on management of waterfowl habitat.

Statistical Inference-Based Cache Management for Mobile Learning

ERIC Educational Resources Information Center

Li, Qing; Zhao, Jianmin; Zhu, Xinzhong

2009-01-01

Supporting efficient data access in the mobile learning environment is becoming a hot research problem in recent years, and the problem becomes tougher when the clients are using light-weight mobile devices such as cell phones whose limited storage space prevents the clients from holding a large cache. A practical solution is to store the cache…

Slow Thinking and Deep Learning: Tversky and Kahneman's Taxi Cabs

ERIC Educational Resources Information Center

Bedwell, Mike

2015-01-01

This article is based on classroom application of a problem story constructed by Amos Tversky in the 1970s. His intention was to evaluate human beings' intuitions about statistical inference. The problem was revisited by his colleague, the Nobel Prize winner Daniel Kahneman. The aim of this article is to show how popular science textbooks can…

Anchoring quartet-based phylogenetic distances and applications to species tree reconstruction.

PubMed

Sayyari, Erfan; Mirarab, Siavash

2016-11-11

Inferring species trees from gene trees using the coalescent-based summary methods has been the subject of much attention, yet new scalable and accurate methods are needed. We introduce DISTIQUE, a new statistically consistent summary method for inferring species trees from gene trees under the coalescent model. We generalize our results to arbitrary phylogenetic inference problems; we show that two arbitrarily chosen leaves, called anchors, can be used to estimate relative distances between all other pairs of leaves by inferring relevant quartet trees. This results in a family of distance-based tree inference methods, with running times ranging between quadratic to quartic in the number of leaves. We show in simulated studies that DISTIQUE has comparable accuracy to leading coalescent-based summary methods and reduced running times.

P values are only an index to evidence: 20th- vs. 21st-century statistical science.

PubMed

Burnham, K P; Anderson, D R

2014-03-01

Early statistical methods focused on pre-data probability statements (i.e., data as random variables) such as P values; these are not really inferences nor are P values evidential. Statistical science clung to these principles throughout much of the 20th century as a wide variety of methods were developed for special cases. Looking back, it is clear that the underlying paradigm (i.e., testing and P values) was weak. As Kuhn (1970) suggests, new paradigms have taken the place of earlier ones: this is a goal of good science. New methods have been developed and older methods extended and these allow proper measures of strength of evidence and multimodel inference. It is time to move forward with sound theory and practice for the difficult practical problems that lie ahead. Given data the useful foundation shifts to post-data probability statements such as model probabilities (Akaike weights) or related quantities such as odds ratios and likelihood intervals. These new methods allow formal inference from multiple models in the a prior set. These quantities are properly evidential. The past century was aimed at finding the "best" model and making inferences from it. The goal in the 21st century is to base inference on all the models weighted by their model probabilities (model averaging). Estimates of precision can include model selection uncertainty leading to variances conditional on the model set. The 21st century will be about the quantification of information, proper measures of evidence, and multi-model inference. Nelder (1999:261) concludes, "The most important task before us in developing statistical science is to demolish the P-value culture, which has taken root to a frightening extent in many areas of both pure and applied science and technology".

The role of causal criteria in causal inferences: Bradford Hill's "aspects of association".

PubMed

Ward, Andrew C

2009-06-17

As noted by Wesley Salmon and many others, causal concepts are ubiquitous in every branch of theoretical science, in the practical disciplines and in everyday life. In the theoretical and practical sciences especially, people often base claims about causal relations on applications of statistical methods to data. However, the source and type of data place important constraints on the choice of statistical methods as well as on the warrant attributed to the causal claims based on the use of such methods. For example, much of the data used by people interested in making causal claims come from non-experimental, observational studies in which random allocations to treatment and control groups are not present. Thus, one of the most important problems in the social and health sciences concerns making justified causal inferences using non-experimental, observational data. In this paper, I examine one method of justifying such inferences that is especially widespread in epidemiology and the health sciences generally - the use of causal criteria. I argue that while the use of causal criteria is not appropriate for either deductive or inductive inferences, they do have an important role to play in inferences to the best explanation. As such, causal criteria, exemplified by what Bradford Hill referred to as "aspects of [statistical] associations", have an indispensible part to play in the goal of making justified causal claims.

The role of causal criteria in causal inferences: Bradford Hill's "aspects of association"

PubMed Central

Ward, Andrew C

2009-01-01

As noted by Wesley Salmon and many others, causal concepts are ubiquitous in every branch of theoretical science, in the practical disciplines and in everyday life. In the theoretical and practical sciences especially, people often base claims about causal relations on applications of statistical methods to data. However, the source and type of data place important constraints on the choice of statistical methods as well as on the warrant attributed to the causal claims based on the use of such methods. For example, much of the data used by people interested in making causal claims come from non-experimental, observational studies in which random allocations to treatment and control groups are not present. Thus, one of the most important problems in the social and health sciences concerns making justified causal inferences using non-experimental, observational data. In this paper, I examine one method of justifying such inferences that is especially widespread in epidemiology and the health sciences generally – the use of causal criteria. I argue that while the use of causal criteria is not appropriate for either deductive or inductive inferences, they do have an important role to play in inferences to the best explanation. As such, causal criteria, exemplified by what Bradford Hill referred to as "aspects of [statistical] associations", have an indispensible part to play in the goal of making justified causal claims. PMID:19534788

Space-Time Data fusion for Remote Sensing Applications

NASA Technical Reports Server (NTRS)

Braverman, Amy; Nguyen, H.; Cressie, N.

2011-01-01

NASA has been collecting massive amounts of remote sensing data about Earth's systems for more than a decade. Missions are selected to be complementary in quantities measured, retrieval techniques, and sampling characteristics, so these datasets are highly synergistic. To fully exploit this, a rigorous methodology for combining data with heterogeneous sampling characteristics is required. For scientific purposes, the methodology must also provide quantitative measures of uncertainty that propagate input-data uncertainty appropriately. We view this as a statistical inference problem. The true but notdirectly- observed quantities form a vector-valued field continuous in space and time. Our goal is to infer those true values or some function of them, and provide to uncertainty quantification for those inferences. We use a spatiotemporal statistical model that relates the unobserved quantities of interest at point-level to the spatially aggregated, observed data. We describe and illustrate our method using CO2 data from two NASA data sets.

Statistical Inference at Work: Statistical Process Control as an Example

ERIC Educational Resources Information Center

Bakker, Arthur; Kent, Phillip; Derry, Jan; Noss, Richard; Hoyles, Celia

2008-01-01

To characterise statistical inference in the workplace this paper compares a prototypical type of statistical inference at work, statistical process control (SPC), with a type of statistical inference that is better known in educational settings, hypothesis testing. Although there are some similarities between the reasoning structure involved in…

Maximum caliber inference of nonequilibrium processes

NASA Astrophysics Data System (ADS)

Otten, Moritz; Stock, Gerhard

2010-07-01

Thirty years ago, Jaynes suggested a general theoretical approach to nonequilibrium statistical mechanics, called maximum caliber (MaxCal) [Annu. Rev. Phys. Chem. 31, 579 (1980)]. MaxCal is a variational principle for dynamics in the same spirit that maximum entropy is a variational principle for equilibrium statistical mechanics. Motivated by the success of maximum entropy inference methods for equilibrium problems, in this work the MaxCal formulation is applied to the inference of nonequilibrium processes. That is, given some time-dependent observables of a dynamical process, one constructs a model that reproduces these input data and moreover, predicts the underlying dynamics of the system. For example, the observables could be some time-resolved measurements of the folding of a protein, which are described by a few-state model of the free energy landscape of the system. MaxCal then calculates the probabilities of an ensemble of trajectories such that on average the data are reproduced. From this probability distribution, any dynamical quantity of the system can be calculated, including population probabilities, fluxes, or waiting time distributions. After briefly reviewing the formalism, the practical numerical implementation of MaxCal in the case of an inference problem is discussed. Adopting various few-state models of increasing complexity, it is demonstrated that the MaxCal principle indeed works as a practical method of inference: The scheme is fairly robust and yields correct results as long as the input data are sufficient. As the method is unbiased and general, it can deal with any kind of time dependency such as oscillatory transients and multitime decays.

Sensitivity to imputation models and assumptions in receiver operating characteristic analysis with incomplete data

PubMed Central

Karakaya, Jale; Karabulut, Erdem; Yucel, Recai M.

2015-01-01

Modern statistical methods using incomplete data have been increasingly applied in a wide variety of substantive problems. Similarly, receiver operating characteristic (ROC) analysis, a method used in evaluating diagnostic tests or biomarkers in medical research, has also been increasingly popular problem in both its development and application. While missing-data methods have been applied in ROC analysis, the impact of model mis-specification and/or assumptions (e.g. missing at random) underlying the missing data has not been thoroughly studied. In this work, we study the performance of multiple imputation (MI) inference in ROC analysis. Particularly, we investigate parametric and non-parametric techniques for MI inference under common missingness mechanisms. Depending on the coherency of the imputation model with the underlying data generation mechanism, our results show that MI generally leads to well-calibrated inferences under ignorable missingness mechanisms. PMID:26379316

Probabilistic numerical methods for PDE-constrained Bayesian inverse problems

NASA Astrophysics Data System (ADS)

Cockayne, Jon; Oates, Chris; Sullivan, Tim; Girolami, Mark

2017-06-01

This paper develops meshless methods for probabilistically describing discretisation error in the numerical solution of partial differential equations. This construction enables the solution of Bayesian inverse problems while accounting for the impact of the discretisation of the forward problem. In particular, this drives statistical inferences to be more conservative in the presence of significant solver error. Theoretical results are presented describing rates of convergence for the posteriors in both the forward and inverse problems. This method is tested on a challenging inverse problem with a nonlinear forward model.

Network inference using informative priors.

PubMed

Mukherjee, Sach; Speed, Terence P

2008-09-23

Recent years have seen much interest in the study of systems characterized by multiple interacting components. A class of statistical models called graphical models, in which graphs are used to represent probabilistic relationships between variables, provides a framework for formal inference regarding such systems. In many settings, the object of inference is the network structure itself. This problem of "network inference" is well known to be a challenging one. However, in scientific settings there is very often existing information regarding network connectivity. A natural idea then is to take account of such information during inference. This article addresses the question of incorporating prior information into network inference. We focus on directed models called Bayesian networks, and use Markov chain Monte Carlo to draw samples from posterior distributions over network structures. We introduce prior distributions on graphs capable of capturing information regarding network features including edges, classes of edges, degree distributions, and sparsity. We illustrate our approach in the context of systems biology, applying our methods to network inference in cancer signaling.

Theory-Based Causal Induction

ERIC Educational Resources Information Center

Griffiths, Thomas L.; Tenenbaum, Joshua B.

2009-01-01

Inducing causal relationships from observations is a classic problem in scientific inference, statistics, and machine learning. It is also a central part of human learning, and a task that people perform remarkably well given its notorious difficulties. People can learn causal structure in various settings, from diverse forms of data: observations…

On the Problems of Construction and Statistical Inference Associated with a Generalization of Canonical Variables.

DTIC Science & Technology

1982-02-01

of them are pre- sented in this paper. As an application, important practical problems similar to the one posed by Gnanadesikan (1977), p. 77 can be... Gnanadesikan and Wilk (1969) to search for a non-linear combination, giving rise to non-linear first principal component. So, a p-dinensional vector can...distribution, Gnanadesikan and Gupta (1970) and earlier Eaton (1967) have considered the problem of ranking the r underlying populations according to the

Combining statistical inference and decisions in ecology

USGS Publications Warehouse

Williams, Perry J.; Hooten, Mevin B.

2016-01-01

Statistical decision theory (SDT) is a sub-field of decision theory that formally incorporates statistical investigation into a decision-theoretic framework to account for uncertainties in a decision problem. SDT provides a unifying analysis of three types of information: statistical results from a data set, knowledge of the consequences of potential choices (i.e., loss), and prior beliefs about a system. SDT links the theoretical development of a large body of statistical methods including point estimation, hypothesis testing, and confidence interval estimation. The theory and application of SDT have mainly been developed and published in the fields of mathematics, statistics, operations research, and other decision sciences, but have had limited exposure in ecology. Thus, we provide an introduction to SDT for ecologists and describe its utility for linking the conventionally separate tasks of statistical investigation and decision making in a single framework. We describe the basic framework of both Bayesian and frequentist SDT, its traditional use in statistics, and discuss its application to decision problems that occur in ecology. We demonstrate SDT with two types of decisions: Bayesian point estimation, and an applied management problem of selecting a prescribed fire rotation for managing a grassland bird species. Central to SDT, and decision theory in general, are loss functions. Thus, we also provide basic guidance and references for constructing loss functions for an SDT problem.

Network inference using informative priors

PubMed Central

Mukherjee, Sach; Speed, Terence P.

2008-01-01

Recent years have seen much interest in the study of systems characterized by multiple interacting components. A class of statistical models called graphical models, in which graphs are used to represent probabilistic relationships between variables, provides a framework for formal inference regarding such systems. In many settings, the object of inference is the network structure itself. This problem of “network inference” is well known to be a challenging one. However, in scientific settings there is very often existing information regarding network connectivity. A natural idea then is to take account of such information during inference. This article addresses the question of incorporating prior information into network inference. We focus on directed models called Bayesian networks, and use Markov chain Monte Carlo to draw samples from posterior distributions over network structures. We introduce prior distributions on graphs capable of capturing information regarding network features including edges, classes of edges, degree distributions, and sparsity. We illustrate our approach in the context of systems biology, applying our methods to network inference in cancer signaling. PMID:18799736

Why We (Usually) Don't Have to Worry about Multiple Comparisons

ERIC Educational Resources Information Center

Gelman, Andrew; Hill, Jennifer; Yajima, Masanao

2012-01-01

Applied researchers often find themselves making statistical inferences in settings that would seem to require multiple comparisons adjustments. We challenge the Type I error paradigm that underlies these corrections. Moreover we posit that the problem of multiple comparisons can disappear entirely when viewed from a hierarchical Bayesian…

Subjective randomness as statistical inference.

PubMed

Griffiths, Thomas L; Daniels, Dylan; Austerweil, Joseph L; Tenenbaum, Joshua B

2018-06-01

Some events seem more random than others. For example, when tossing a coin, a sequence of eight heads in a row does not seem very random. Where do these intuitions about randomness come from? We argue that subjective randomness can be understood as the result of a statistical inference assessing the evidence that an event provides for having been produced by a random generating process. We show how this account provides a link to previous work relating randomness to algorithmic complexity, in which random events are those that cannot be described by short computer programs. Algorithmic complexity is both incomputable and too general to capture the regularities that people can recognize, but viewing randomness as statistical inference provides two paths to addressing these problems: considering regularities generated by simpler computing machines, and restricting the set of probability distributions that characterize regularity. Building on previous work exploring these different routes to a more restricted notion of randomness, we define strong quantitative models of human randomness judgments that apply not just to binary sequences - which have been the focus of much of the previous work on subjective randomness - but also to binary matrices and spatial clustering. Copyright © 2018 Elsevier Inc. All rights reserved.

Stan: Statistical inference

NASA Astrophysics Data System (ADS)

Stan Development Team

2018-01-01

Stan facilitates statistical inference at the frontiers of applied statistics and provides both a modeling language for specifying complex statistical models and a library of statistical algorithms for computing inferences with those models. These components are exposed through interfaces in environments such as R, Python, and the command line.

The Development of Introductory Statistics Students' Informal Inferential Reasoning and Its Relationship to Formal Inferential Reasoning

ERIC Educational Resources Information Center

Jacob, Bridgette L.

2013-01-01

The difficulties introductory statistics students have with formal statistical inference are well known in the field of statistics education. "Informal" statistical inference has been studied as a means to introduce inferential reasoning well before and without the formalities of formal statistical inference. This mixed methods study…

Students' Emergent Articulations of Statistical Models and Modeling in Making Informal Statistical Inferences

ERIC Educational Resources Information Center

Braham, Hana Manor; Ben-Zvi, Dani

2017-01-01

A fundamental aspect of statistical inference is representation of real-world data using statistical models. This article analyzes students' articulations of statistical models and modeling during their first steps in making informal statistical inferences. An integrated modeling approach (IMA) was designed and implemented to help students…

Cortical Hierarchies Perform Bayesian Causal Inference in Multisensory Perception

PubMed Central

Rohe, Tim; Noppeney, Uta

2015-01-01

To form a veridical percept of the environment, the brain needs to integrate sensory signals from a common source but segregate those from independent sources. Thus, perception inherently relies on solving the “causal inference problem.” Behaviorally, humans solve this problem optimally as predicted by Bayesian Causal Inference; yet, the underlying neural mechanisms are unexplored. Combining psychophysics, Bayesian modeling, functional magnetic resonance imaging (fMRI), and multivariate decoding in an audiovisual spatial localization task, we demonstrate that Bayesian Causal Inference is performed by a hierarchy of multisensory processes in the human brain. At the bottom of the hierarchy, in auditory and visual areas, location is represented on the basis that the two signals are generated by independent sources (= segregation). At the next stage, in posterior intraparietal sulcus, location is estimated under the assumption that the two signals are from a common source (= forced fusion). Only at the top of the hierarchy, in anterior intraparietal sulcus, the uncertainty about the causal structure of the world is taken into account and sensory signals are combined as predicted by Bayesian Causal Inference. Characterizing the computational operations of signal interactions reveals the hierarchical nature of multisensory perception in human neocortex. It unravels how the brain accomplishes Bayesian Causal Inference, a statistical computation fundamental for perception and cognition. Our results demonstrate how the brain combines information in the face of uncertainty about the underlying causal structure of the world. PMID:25710328

The statistical analysis of global climate change studies

DOE Office of Scientific and Technical Information (OSTI.GOV)

Hardin, J.W.

1992-01-01

The focus of this work is to contribute to the enhancement of the relationship between climatologists and statisticians. The analysis of global change data has been underway for many years by atmospheric scientists. Much of this analysis includes a heavy reliance on statistics and statistical inference. Some specific climatological analyses are presented and the dependence on statistics is documented before the analysis is undertaken. The first problem presented involves the fluctuation-dissipation theorem and its application to global climate models. This problem has a sound theoretical niche in the literature of both climate modeling and physics, but a statistical analysis inmore » which the data is obtained from the model to show graphically the relationship has not been undertaken. It is under this motivation that the author presents this problem. A second problem concerning the standard errors in estimating global temperatures is purely statistical in nature although very little materials exists for sampling on such a frame. This problem not only has climatological and statistical ramifications, but political ones as well. It is planned to use these results in a further analysis of global warming using actual data collected on the earth. In order to simplify the analysis of these problems, the development of a computer program, MISHA, is presented. This interactive program contains many of the routines, functions, graphics, and map projections needed by the climatologist in order to effectively enter the arena of data visualization.« less

A Bayesian approach to truncated data sets: An application to Malmquist bias in Supernova Cosmology

NASA Astrophysics Data System (ADS)

March, Marisa Cristina

2018-01-01

A problem commonly encountered in statistical analysis of data is that of truncated data sets. A truncated data set is one in which a number of data points are completely missing from a sample, this is in contrast to a censored sample in which partial information is missing from some data points. In astrophysics this problem is commonly seen in a magnitude limited survey such that the survey is incomplete at fainter magnitudes, that is, certain faint objects are simply not observed. The effect of this `missing data' is manifested as Malmquist bias and can result in biases in parameter inference if it is not accounted for. In Frequentist methodologies the Malmquist bias is often corrected for by analysing many simulations and computing the appropriate correction factors. One problem with this methodology is that the corrections are model dependent. In this poster we derive a Bayesian methodology for accounting for truncated data sets in problems of parameter inference and model selection. We first show the methodology for a simple Gaussian linear model and then go on to show the method for accounting for a truncated data set in the case for cosmological parameter inference with a magnitude limited supernova Ia survey.

Modeling Error Distributions of Growth Curve Models through Bayesian Methods

ERIC Educational Resources Information Center

Zhang, Zhiyong

2016-01-01

Growth curve models are widely used in social and behavioral sciences. However, typical growth curve models often assume that the errors are normally distributed although non-normal data may be even more common than normal data. In order to avoid possible statistical inference problems in blindly assuming normality, a general Bayesian framework is…

Combining statistical inference and decisions in ecology.

PubMed

Williams, Perry J; Hooten, Mevin B

2016-09-01

Statistical decision theory (SDT) is a sub-field of decision theory that formally incorporates statistical investigation into a decision-theoretic framework to account for uncertainties in a decision problem. SDT provides a unifying analysis of three types of information: statistical results from a data set, knowledge of the consequences of potential choices (i.e., loss), and prior beliefs about a system. SDT links the theoretical development of a large body of statistical methods, including point estimation, hypothesis testing, and confidence interval estimation. The theory and application of SDT have mainly been developed and published in the fields of mathematics, statistics, operations research, and other decision sciences, but have had limited exposure in ecology. Thus, we provide an introduction to SDT for ecologists and describe its utility for linking the conventionally separate tasks of statistical investigation and decision making in a single framework. We describe the basic framework of both Bayesian and frequentist SDT, its traditional use in statistics, and discuss its application to decision problems that occur in ecology. We demonstrate SDT with two types of decisions: Bayesian point estimation and an applied management problem of selecting a prescribed fire rotation for managing a grassland bird species. Central to SDT, and decision theory in general, are loss functions. Thus, we also provide basic guidance and references for constructing loss functions for an SDT problem. © 2016 by the Ecological Society of America.

Mathematical inference in one point microrheology

NASA Astrophysics Data System (ADS)

Hohenegger, Christel; McKinley, Scott

2016-11-01

Pioneered by the work of Mason and Weitz, one point passive microrheology has been successfully applied to obtaining estimates of the loss and storage modulus of viscoelastic fluids when the mean-square displacement obeys a local power law. Using numerical simulations of a fluctuating viscoelastic fluid model, we study the problem of recovering the mechanical parameters of the fluid's memory kernel using statistical inference like mean-square displacements and increment auto-correlation functions. Seeking a better understanding of the influence of the assumptions made in the inversion process, we mathematically quantify the uncertainty in traditional one point microrheology for simulated data and demonstrate that a large family of memory kernels yields the same statistical signature. We consider both simulated data obtained from a full viscoelastic fluid simulation of the unsteady Stokes equations with fluctuations and from a Generalized Langevin Equation of the particle's motion described by the same memory kernel. From the theory of inverse problems, we propose an alternative method that can be used to recover information about the loss and storage modulus and discuss its limitations and uncertainties. NSF-DMS 1412998.

Fast and Accurate Multivariate Gaussian Modeling of Protein Families: Predicting Residue Contacts and Protein-Interaction Partners

PubMed Central

Feinauer, Christoph; Procaccini, Andrea; Zecchina, Riccardo; Weigt, Martin; Pagnani, Andrea

2014-01-01

In the course of evolution, proteins show a remarkable conservation of their three-dimensional structure and their biological function, leading to strong evolutionary constraints on the sequence variability between homologous proteins. Our method aims at extracting such constraints from rapidly accumulating sequence data, and thereby at inferring protein structure and function from sequence information alone. Recently, global statistical inference methods (e.g. direct-coupling analysis, sparse inverse covariance estimation) have achieved a breakthrough towards this aim, and their predictions have been successfully implemented into tertiary and quaternary protein structure prediction methods. However, due to the discrete nature of the underlying variable (amino-acids), exact inference requires exponential time in the protein length, and efficient approximations are needed for practical applicability. Here we propose a very efficient multivariate Gaussian modeling approach as a variant of direct-coupling analysis: the discrete amino-acid variables are replaced by continuous Gaussian random variables. The resulting statistical inference problem is efficiently and exactly solvable. We show that the quality of inference is comparable or superior to the one achieved by mean-field approximations to inference with discrete variables, as done by direct-coupling analysis. This is true for (i) the prediction of residue-residue contacts in proteins, and (ii) the identification of protein-protein interaction partner in bacterial signal transduction. An implementation of our multivariate Gaussian approach is available at the website http://areeweb.polito.it/ricerca/cmp/code. PMID:24663061

The space of ultrametric phylogenetic trees.

PubMed

Gavryushkin, Alex; Drummond, Alexei J

2016-08-21

The reliability of a phylogenetic inference method from genomic sequence data is ensured by its statistical consistency. Bayesian inference methods produce a sample of phylogenetic trees from the posterior distribution given sequence data. Hence the question of statistical consistency of such methods is equivalent to the consistency of the summary of the sample. More generally, statistical consistency is ensured by the tree space used to analyse the sample. In this paper, we consider two standard parameterisations of phylogenetic time-trees used in evolutionary models: inter-coalescent interval lengths and absolute times of divergence events. For each of these parameterisations we introduce a natural metric space on ultrametric phylogenetic trees. We compare the introduced spaces with existing models of tree space and formulate several formal requirements that a metric space on phylogenetic trees must possess in order to be a satisfactory space for statistical analysis, and justify them. We show that only a few known constructions of the space of phylogenetic trees satisfy these requirements. However, our results suggest that these basic requirements are not enough to distinguish between the two metric spaces we introduce and that the choice between metric spaces requires additional properties to be considered. Particularly, that the summary tree minimising the square distance to the trees from the sample might be different for different parameterisations. This suggests that further fundamental insight is needed into the problem of statistical consistency of phylogenetic inference methods. Copyright © 2016 The Authors. Published by Elsevier Ltd.. All rights reserved.

Assessing risk factors for dental caries: a statistical modeling approach.

PubMed

Trottini, Mario; Bossù, Maurizio; Corridore, Denise; Ierardo, Gaetano; Luzzi, Valeria; Saccucci, Matteo; Polimeni, Antonella

2015-01-01

The problem of identifying potential determinants and predictors of dental caries is of key importance in caries research and it has received considerable attention in the scientific literature. From the methodological side, a broad range of statistical models is currently available to analyze dental caries indices (DMFT, dmfs, etc.). These models have been applied in several studies to investigate the impact of different risk factors on the cumulative severity of dental caries experience. However, in most of the cases (i) these studies focus on a very specific subset of risk factors; and (ii) in the statistical modeling only few candidate models are considered and model selection is at best only marginally addressed. As a result, our understanding of the robustness of the statistical inferences with respect to the choice of the model is very limited; the richness of the set of statistical models available for analysis in only marginally exploited; and inferences could be biased due the omission of potentially important confounding variables in the model's specification. In this paper we argue that these limitations can be overcome considering a general class of candidate models and carefully exploring the model space using standard model selection criteria and measures of global fit and predictive performance of the candidate models. Strengths and limitations of the proposed approach are illustrated with a real data set. In our illustration the model space contains more than 2.6 million models, which require inferences to be adjusted for 'optimism'.

Models for inference in dynamic metacommunity systems

USGS Publications Warehouse

Dorazio, Robert M.; Kery, Marc; Royle, J. Andrew; Plattner, Matthias

2010-01-01

A variety of processes are thought to be involved in the formation and dynamics of species assemblages. For example, various metacommunity theories are based on differences in the relative contributions of dispersal of species among local communities and interactions of species within local communities. Interestingly, metacommunity theories continue to be advanced without much empirical validation. Part of the problem is that statistical models used to analyze typical survey data either fail to specify ecological processes with sufficient complexity or they fail to account for errors in detection of species during sampling. In this paper, we describe a statistical modeling framework for the analysis of metacommunity dynamics that is based on the idea of adopting a unified approach, multispecies occupancy modeling, for computing inferences about individual species, local communities of species, or the entire metacommunity of species. This approach accounts for errors in detection of species during sampling and also allows different metacommunity paradigms to be specified in terms of species- and location-specific probabilities of occurrence, extinction, and colonization: all of which are estimable. In addition, this approach can be used to address inference problems that arise in conservation ecology, such as predicting temporal and spatial changes in biodiversity for use in making conservation decisions. To illustrate, we estimate changes in species composition associated with the species-specific phenologies of flight patterns of butterflies in Switzerland for the purpose of estimating regional differences in biodiversity.

A Bayesian Interpretation of First-Order Phase Transitions

NASA Astrophysics Data System (ADS)

Davis, Sergio; Peralta, Joaquín; Navarrete, Yasmín; González, Diego; Gutiérrez, Gonzalo

2016-03-01

In this work we review the formalism used in describing the thermodynamics of first-order phase transitions from the point of view of maximum entropy inference. We present the concepts of transition temperature, latent heat and entropy difference between phases as emergent from the more fundamental concept of internal energy, after a statistical inference analysis. We explicitly demonstrate this point of view by making inferences on a simple game, resulting in the same formalism as in thermodynamical phase transitions. We show that analogous quantities will inevitably arise in any problem of inferring the result of a yes/no question, given two different states of knowledge and information in the form of expectation values. This exposition may help to clarify the role of these thermodynamical quantities in the context of different first-order phase transitions such as the case of magnetic Hamiltonians (e.g. the Potts model).

The Reasoning behind Informal Statistical Inference

ERIC Educational Resources Information Center

Makar, Katie; Bakker, Arthur; Ben-Zvi, Dani

2011-01-01

Informal statistical inference (ISI) has been a frequent focus of recent research in statistics education. Considering the role that context plays in developing ISI calls into question the need to be more explicit about the reasoning that underpins ISI. This paper uses educational literature on informal statistical inference and philosophical…

Kernel canonical-correlation Granger causality for multiple time series

NASA Astrophysics Data System (ADS)

Wu, Guorong; Duan, Xujun; Liao, Wei; Gao, Qing; Chen, Huafu

2011-04-01

Canonical-correlation analysis as a multivariate statistical technique has been applied to multivariate Granger causality analysis to infer information flow in complex systems. It shows unique appeal and great superiority over the traditional vector autoregressive method, due to the simplified procedure that detects causal interaction between multiple time series, and the avoidance of potential model estimation problems. However, it is limited to the linear case. Here, we extend the framework of canonical correlation to include the estimation of multivariate nonlinear Granger causality for drawing inference about directed interaction. Its feasibility and effectiveness are verified on simulated data.

Nonlinear Inference in Partially Observed Physical Systems and Deep Neural Networks

NASA Astrophysics Data System (ADS)

Rozdeba, Paul J.

The problem of model state and parameter estimation is a significant challenge in nonlinear systems. Due to practical considerations of experimental design, it is often the case that physical systems are partially observed, meaning that data is only available for a subset of the degrees of freedom required to fully model the observed system's behaviors and, ultimately, predict future observations. Estimation in this context is highly complicated by the presence of chaos, stochasticity, and measurement noise in dynamical systems. One of the aims of this dissertation is to simultaneously analyze state and parameter estimation in as a regularized inverse problem, where the introduction of a model makes it possible to reverse the forward problem of partial, noisy observation; and as a statistical inference problem using data assimilation to transfer information from measurements to the model states and parameters. Ultimately these two formulations achieve the same goal. Similar aspects that appear in both are highlighted as a means for better understanding the structure of the nonlinear inference problem. An alternative approach to data assimilation that uses model reduction is then examined as a way to eliminate unresolved nonlinear gating variables from neuron models. In this formulation, only measured variables enter into the model, and the resulting errors are themselves modeled by nonlinear stochastic processes with memory. Finally, variational annealing, a data assimilation method previously applied to dynamical systems, is introduced as a potentially useful tool for understanding deep neural network training in machine learning by exploiting similarities between the two problems.

Estimation versus falsification approaches in sport and exercise science.

PubMed

Wilkinson, Michael; Winter, Edward M

2018-05-22

There has been a recent resurgence in debate about methods for statistical inference in science. The debate addresses statistical concepts and their impact on the value and meaning of analyses' outcomes. In contrast, philosophical underpinnings of approaches and the extent to which analytical tools match philosophical goals of the scientific method have received less attention. This short piece considers application of the scientific method to "what-is-the-influence-of x-on-y" type questions characteristic of sport and exercise science. We consider applications and interpretations of estimation versus falsification based statistical approaches and their value in addressing how much x influences y, and in measurement error and method agreement settings. We compare estimation using magnitude based inference (MBI) with falsification using null hypothesis significance testing (NHST), and highlight the limited value both of falsification and NHST to address problems in sport and exercise science. We recommend adopting an estimation approach, expressing the uncertainty of effects of x on y, and their practical/clinical value against pre-determined effect magnitudes using MBI.

Rational approximations to rational models: alternative algorithms for category learning.

PubMed

Sanborn, Adam N; Griffiths, Thomas L; Navarro, Daniel J

2010-10-01

Rational models of cognition typically consider the abstract computational problems posed by the environment, assuming that people are capable of optimally solving those problems. This differs from more traditional formal models of cognition, which focus on the psychological processes responsible for behavior. A basic challenge for rational models is thus explaining how optimal solutions can be approximated by psychological processes. We outline a general strategy for answering this question, namely to explore the psychological plausibility of approximation algorithms developed in computer science and statistics. In particular, we argue that Monte Carlo methods provide a source of rational process models that connect optimal solutions to psychological processes. We support this argument through a detailed example, applying this approach to Anderson's (1990, 1991) rational model of categorization (RMC), which involves a particularly challenging computational problem. Drawing on a connection between the RMC and ideas from nonparametric Bayesian statistics, we propose 2 alternative algorithms for approximate inference in this model. The algorithms we consider include Gibbs sampling, a procedure appropriate when all stimuli are presented simultaneously, and particle filters, which sequentially approximate the posterior distribution with a small number of samples that are updated as new data become available. Applying these algorithms to several existing datasets shows that a particle filter with a single particle provides a good description of human inferences.

Twenty-five years of maximum-entropy principle

NASA Astrophysics Data System (ADS)

Kapur, J. N.

1983-04-01

The strengths and weaknesses of the maximum entropy principle (MEP) are examined and some challenging problems that remain outstanding at the end of the first quarter century of the principle are discussed. The original formalism of the MEP is presented and its relationship to statistical mechanics is set forth. The use of MEP for characterizing statistical distributions, in statistical inference, nonlinear spectral analysis, transportation models, population density models, models for brand-switching in marketing and vote-switching in elections is discussed. Its application to finance, insurance, image reconstruction, pattern recognition, operations research and engineering, biology and medicine, and nonparametric density estimation is considered.

Deep Learning for Population Genetic Inference.

PubMed

Sheehan, Sara; Song, Yun S

2016-03-01

Given genomic variation data from multiple individuals, computing the likelihood of complex population genetic models is often infeasible. To circumvent this problem, we introduce a novel likelihood-free inference framework by applying deep learning, a powerful modern technique in machine learning. Deep learning makes use of multilayer neural networks to learn a feature-based function from the input (e.g., hundreds of correlated summary statistics of data) to the output (e.g., population genetic parameters of interest). We demonstrate that deep learning can be effectively employed for population genetic inference and learning informative features of data. As a concrete application, we focus on the challenging problem of jointly inferring natural selection and demography (in the form of a population size change history). Our method is able to separate the global nature of demography from the local nature of selection, without sequential steps for these two factors. Studying demography and selection jointly is motivated by Drosophila, where pervasive selection confounds demographic analysis. We apply our method to 197 African Drosophila melanogaster genomes from Zambia to infer both their overall demography, and regions of their genome under selection. We find many regions of the genome that have experienced hard sweeps, and fewer under selection on standing variation (soft sweep) or balancing selection. Interestingly, we find that soft sweeps and balancing selection occur more frequently closer to the centromere of each chromosome. In addition, our demographic inference suggests that previously estimated bottlenecks for African Drosophila melanogaster are too extreme.

Deep Learning for Population Genetic Inference

PubMed Central

Sheehan, Sara; Song, Yun S.

2016-01-01

Given genomic variation data from multiple individuals, computing the likelihood of complex population genetic models is often infeasible. To circumvent this problem, we introduce a novel likelihood-free inference framework by applying deep learning, a powerful modern technique in machine learning. Deep learning makes use of multilayer neural networks to learn a feature-based function from the input (e.g., hundreds of correlated summary statistics of data) to the output (e.g., population genetic parameters of interest). We demonstrate that deep learning can be effectively employed for population genetic inference and learning informative features of data. As a concrete application, we focus on the challenging problem of jointly inferring natural selection and demography (in the form of a population size change history). Our method is able to separate the global nature of demography from the local nature of selection, without sequential steps for these two factors. Studying demography and selection jointly is motivated by Drosophila, where pervasive selection confounds demographic analysis. We apply our method to 197 African Drosophila melanogaster genomes from Zambia to infer both their overall demography, and regions of their genome under selection. We find many regions of the genome that have experienced hard sweeps, and fewer under selection on standing variation (soft sweep) or balancing selection. Interestingly, we find that soft sweeps and balancing selection occur more frequently closer to the centromere of each chromosome. In addition, our demographic inference suggests that previously estimated bottlenecks for African Drosophila melanogaster are too extreme. PMID:27018908

Why Bayesian Psychologists Should Change the Way They Use the Bayes Factor.

PubMed

Hoijtink, Herbert; van Kooten, Pascal; Hulsker, Koenraad

2016-01-01

The discussion following Bem's ( 2011 ) psi research highlights that applications of the Bayes factor in psychological research are not without problems. The first problem is the omission to translate subjective prior knowledge into subjective prior distributions. In the words of Savage ( 1961 ): "they make the Bayesian omelet without breaking the Bayesian egg." The second problem occurs if the Bayesian egg is not broken: the omission to choose default prior distributions such that the ensuing inferences are well calibrated. The third problem is the adherence to inadequate rules for the interpretation of the size of the Bayes factor. The current paper will elaborate these problems and show how to avoid them using the basic hypotheses and statistical model used in the first experiment described in Bem ( 2011 ). It will be argued that a thorough investigation of these problems in the context of more encompassing hypotheses and statistical models is called for if Bayesian psychologists want to add a well-founded Bayes factor to the tool kit of psychological researchers.

Improving stochastic estimates with inference methods: calculating matrix diagonals.

PubMed

Selig, Marco; Oppermann, Niels; Ensslin, Torsten A

2012-02-01

Estimating the diagonal entries of a matrix, that is not directly accessible but only available as a linear operator in the form of a computer routine, is a common necessity in many computational applications, especially in image reconstruction and statistical inference. Here, methods of statistical inference are used to improve the accuracy or the computational costs of matrix probing methods to estimate matrix diagonals. In particular, the generalized Wiener filter methodology, as developed within information field theory, is shown to significantly improve estimates based on only a few sampling probes, in cases in which some form of continuity of the solution can be assumed. The strength, length scale, and precise functional form of the exploited autocorrelation function of the matrix diagonal is determined from the probes themselves. The developed algorithm is successfully applied to mock and real world problems. These performance tests show that, in situations where a matrix diagonal has to be calculated from only a small number of computationally expensive probes, a speedup by a factor of 2 to 10 is possible with the proposed method. © 2012 American Physical Society

Statistical inference approach to structural reconstruction of complex networks from binary time series

NASA Astrophysics Data System (ADS)

Ma, Chuang; Chen, Han-Shuang; Lai, Ying-Cheng; Zhang, Hai-Feng

2018-02-01

Complex networks hosting binary-state dynamics arise in a variety of contexts. In spite of previous works, to fully reconstruct the network structure from observed binary data remains challenging. We articulate a statistical inference based approach to this problem. In particular, exploiting the expectation-maximization (EM) algorithm, we develop a method to ascertain the neighbors of any node in the network based solely on binary data, thereby recovering the full topology of the network. A key ingredient of our method is the maximum-likelihood estimation of the probabilities associated with actual or nonexistent links, and we show that the EM algorithm can distinguish the two kinds of probability values without any ambiguity, insofar as the length of the available binary time series is reasonably long. Our method does not require any a priori knowledge of the detailed dynamical processes, is parameter-free, and is capable of accurate reconstruction even in the presence of noise. We demonstrate the method using combinations of distinct types of binary dynamical processes and network topologies, and provide a physical understanding of the underlying reconstruction mechanism. Our statistical inference based reconstruction method contributes an additional piece to the rapidly expanding "toolbox" of data based reverse engineering of complex networked systems.

A statistical model for interpreting computerized dynamic posturography data

NASA Technical Reports Server (NTRS)

Feiveson, Alan H.; Metter, E. Jeffrey; Paloski, William H.

2002-01-01

Computerized dynamic posturography (CDP) is widely used for assessment of altered balance control. CDP trials are quantified using the equilibrium score (ES), which ranges from zero to 100, as a decreasing function of peak sway angle. The problem of how best to model and analyze ESs from a controlled study is considered. The ES often exhibits a skewed distribution in repeated trials, which can lead to incorrect inference when applying standard regression or analysis of variance models. Furthermore, CDP trials are terminated when a patient loses balance. In these situations, the ES is not observable, but is assigned the lowest possible score--zero. As a result, the response variable has a mixed discrete-continuous distribution, further compromising inference obtained by standard statistical methods. Here, we develop alternative methodology for analyzing ESs under a stochastic model extending the ES to a continuous latent random variable that always exists, but is unobserved in the event of a fall. Loss of balance occurs conditionally, with probability depending on the realized latent ES. After fitting the model by a form of quasi-maximum-likelihood, one may perform statistical inference to assess the effects of explanatory variables. An example is provided, using data from the NIH/NIA Baltimore Longitudinal Study on Aging.

Statistical inference approach to structural reconstruction of complex networks from binary time series.

PubMed

Ma, Chuang; Chen, Han-Shuang; Lai, Ying-Cheng; Zhang, Hai-Feng

2018-02-01

Complex networks hosting binary-state dynamics arise in a variety of contexts. In spite of previous works, to fully reconstruct the network structure from observed binary data remains challenging. We articulate a statistical inference based approach to this problem. In particular, exploiting the expectation-maximization (EM) algorithm, we develop a method to ascertain the neighbors of any node in the network based solely on binary data, thereby recovering the full topology of the network. A key ingredient of our method is the maximum-likelihood estimation of the probabilities associated with actual or nonexistent links, and we show that the EM algorithm can distinguish the two kinds of probability values without any ambiguity, insofar as the length of the available binary time series is reasonably long. Our method does not require any a priori knowledge of the detailed dynamical processes, is parameter-free, and is capable of accurate reconstruction even in the presence of noise. We demonstrate the method using combinations of distinct types of binary dynamical processes and network topologies, and provide a physical understanding of the underlying reconstruction mechanism. Our statistical inference based reconstruction method contributes an additional piece to the rapidly expanding "toolbox" of data based reverse engineering of complex networked systems.

BEAGLE: an application programming interface and high-performance computing library for statistical phylogenetics.

PubMed

Ayres, Daniel L; Darling, Aaron; Zwickl, Derrick J; Beerli, Peter; Holder, Mark T; Lewis, Paul O; Huelsenbeck, John P; Ronquist, Fredrik; Swofford, David L; Cummings, Michael P; Rambaut, Andrew; Suchard, Marc A

2012-01-01

Phylogenetic inference is fundamental to our understanding of most aspects of the origin and evolution of life, and in recent years, there has been a concentration of interest in statistical approaches such as Bayesian inference and maximum likelihood estimation. Yet, for large data sets and realistic or interesting models of evolution, these approaches remain computationally demanding. High-throughput sequencing can yield data for thousands of taxa, but scaling to such problems using serial computing often necessitates the use of nonstatistical or approximate approaches. The recent emergence of graphics processing units (GPUs) provides an opportunity to leverage their excellent floating-point computational performance to accelerate statistical phylogenetic inference. A specialized library for phylogenetic calculation would allow existing software packages to make more effective use of available computer hardware, including GPUs. Adoption of a common library would also make it easier for other emerging computing architectures, such as field programmable gate arrays, to be used in the future. We present BEAGLE, an application programming interface (API) and library for high-performance statistical phylogenetic inference. The API provides a uniform interface for performing phylogenetic likelihood calculations on a variety of compute hardware platforms. The library includes a set of efficient implementations and can currently exploit hardware including GPUs using NVIDIA CUDA, central processing units (CPUs) with Streaming SIMD Extensions and related processor supplementary instruction sets, and multicore CPUs via OpenMP. To demonstrate the advantages of a common API, we have incorporated the library into several popular phylogenetic software packages. The BEAGLE library is free open source software licensed under the Lesser GPL and available from http://beagle-lib.googlecode.com. An example client program is available as public domain software.

BEAGLE: An Application Programming Interface and High-Performance Computing Library for Statistical Phylogenetics

PubMed Central

Ayres, Daniel L.; Darling, Aaron; Zwickl, Derrick J.; Beerli, Peter; Holder, Mark T.; Lewis, Paul O.; Huelsenbeck, John P.; Ronquist, Fredrik; Swofford, David L.; Cummings, Michael P.; Rambaut, Andrew; Suchard, Marc A.

2012-01-01

Abstract Phylogenetic inference is fundamental to our understanding of most aspects of the origin and evolution of life, and in recent years, there has been a concentration of interest in statistical approaches such as Bayesian inference and maximum likelihood estimation. Yet, for large data sets and realistic or interesting models of evolution, these approaches remain computationally demanding. High-throughput sequencing can yield data for thousands of taxa, but scaling to such problems using serial computing often necessitates the use of nonstatistical or approximate approaches. The recent emergence of graphics processing units (GPUs) provides an opportunity to leverage their excellent floating-point computational performance to accelerate statistical phylogenetic inference. A specialized library for phylogenetic calculation would allow existing software packages to make more effective use of available computer hardware, including GPUs. Adoption of a common library would also make it easier for other emerging computing architectures, such as field programmable gate arrays, to be used in the future. We present BEAGLE, an application programming interface (API) and library for high-performance statistical phylogenetic inference. The API provides a uniform interface for performing phylogenetic likelihood calculations on a variety of compute hardware platforms. The library includes a set of efficient implementations and can currently exploit hardware including GPUs using NVIDIA CUDA, central processing units (CPUs) with Streaming SIMD Extensions and related processor supplementary instruction sets, and multicore CPUs via OpenMP. To demonstrate the advantages of a common API, we have incorporated the library into several popular phylogenetic software packages. The BEAGLE library is free open source software licensed under the Lesser GPL and available from http://beagle-lib.googlecode.com. An example client program is available as public domain software. PMID:21963610

High-dimensional inference with the generalized Hopfield model: principal component analysis and corrections.

PubMed

Cocco, S; Monasson, R; Sessak, V

2011-05-01

We consider the problem of inferring the interactions between a set of N binary variables from the knowledge of their frequencies and pairwise correlations. The inference framework is based on the Hopfield model, a special case of the Ising model where the interaction matrix is defined through a set of patterns in the variable space, and is of rank much smaller than N. We show that maximum likelihood inference is deeply related to principal component analysis when the amplitude of the pattern components ξ is negligible compared to √N. Using techniques from statistical mechanics, we calculate the corrections to the patterns to the first order in ξ/√N. We stress the need to generalize the Hopfield model and include both attractive and repulsive patterns in order to correctly infer networks with sparse and strong interactions. We present a simple geometrical criterion to decide how many attractive and repulsive patterns should be considered as a function of the sampling noise. We moreover discuss how many sampled configurations are required for a good inference, as a function of the system size N and of the amplitude ξ. The inference approach is illustrated on synthetic and biological data.

Design of experiments and data analysis challenges in calibration for forensics applications

DOE PAGES

Anderson-Cook, Christine M.; Burr, Thomas L.; Hamada, Michael S.; ...

2015-07-15

Forensic science aims to infer characteristics of source terms using measured observables. Our focus is on statistical design of experiments and data analysis challenges arising in nuclear forensics. More specifically, we focus on inferring aspects of experimental conditions (of a process to produce product Pu oxide powder), such as temperature, nitric acid concentration, and Pu concentration, using measured features of the product Pu oxide powder. The measured features, Y, include trace chemical concentrations and particle morphology such as particle size and shape of the produced Pu oxide power particles. Making inferences about the nature of inputs X that were usedmore » to create nuclear materials having particular characteristics, Y, is an inverse problem. Therefore, statistical analysis can be used to identify the best set (or sets) of Xs for a new set of observed responses Y. One can fit a model (or models) such as Υ = f(Χ) + error, for each of the responses, based on a calibration experiment and then “invert” to solve for the best set of Xs for a new set of Ys. This perspectives paper uses archived experimental data to consider aspects of data collection and experiment design for the calibration data to maximize the quality of the predicted Ys in the forward models; that is, we assume that well-estimated forward models are effective in the inverse problem. In addition, we consider how to identify a best solution for the inferred X, and evaluate the quality of the result and its robustness to a variety of initial assumptions, and different correlation structures between the responses. In addition, we also briefly review recent advances in metrology issues related to characterizing particle morphology measurements used in the response vector, Y.« less

Design of experiments and data analysis challenges in calibration for forensics applications

DOE Office of Scientific and Technical Information (OSTI.GOV)

Anderson-Cook, Christine M.; Burr, Thomas L.; Hamada, Michael S.

Forensic science aims to infer characteristics of source terms using measured observables. Our focus is on statistical design of experiments and data analysis challenges arising in nuclear forensics. More specifically, we focus on inferring aspects of experimental conditions (of a process to produce product Pu oxide powder), such as temperature, nitric acid concentration, and Pu concentration, using measured features of the product Pu oxide powder. The measured features, Y, include trace chemical concentrations and particle morphology such as particle size and shape of the produced Pu oxide power particles. Making inferences about the nature of inputs X that were usedmore » to create nuclear materials having particular characteristics, Y, is an inverse problem. Therefore, statistical analysis can be used to identify the best set (or sets) of Xs for a new set of observed responses Y. One can fit a model (or models) such as Υ = f(Χ) + error, for each of the responses, based on a calibration experiment and then “invert” to solve for the best set of Xs for a new set of Ys. This perspectives paper uses archived experimental data to consider aspects of data collection and experiment design for the calibration data to maximize the quality of the predicted Ys in the forward models; that is, we assume that well-estimated forward models are effective in the inverse problem. In addition, we consider how to identify a best solution for the inferred X, and evaluate the quality of the result and its robustness to a variety of initial assumptions, and different correlation structures between the responses. In addition, we also briefly review recent advances in metrology issues related to characterizing particle morphology measurements used in the response vector, Y.« less

Confidence set inference with a prior quadratic bound

NASA Technical Reports Server (NTRS)

Backus, George E.

1988-01-01

In the uniqueness part of a geophysical inverse problem, the observer wants to predict all likely values of P unknown numerical properties z = (z sub 1,...,z sub p) of the earth from measurement of D other numerical properties y(0)=(y sub 1(0),...,y sub D(0)) knowledge of the statistical distribution of the random errors in y(0). The data space Y containing y(0) is D-dimensional, so when the model space X is infinite-dimensional the linear uniqueness problem usually is insoluble without prior information about the correct earth model x. If that information is a quadratic bound on x (e.g., energy or dissipation rate), Bayesian inference (BI) and stochastic inversion (SI) inject spurious structure into x, implied by neither the data nor the quadratic bound. Confidence set inference (CSI) provides an alternative inversion technique free of this objection. CSI is illustrated in the problem of estimating the geomagnetic field B at the core-mantle boundary (CMB) from components of B measured on or above the earth's surface. Neither the heat flow nor the energy bound is strong enough to permit estimation of B(r) at single points on the CMB, but the heat flow bound permits estimation of uniform averages of B(r) over discs on the CMB, and both bounds permit weighted disc-averages with continous weighting kernels. Both bounds also permit estimation of low-degree Gauss coefficients at the CMB. The heat flow bound resolves them up to degree 8 if the crustal field at satellite altitudes must be treated as a systematic error, but can resolve to degree 11 under the most favorable statistical treatment of the crust. These two limits produce circles of confusion on the CMB with diameters of 25 deg and 19 deg respectively.

Inferring explicit weighted consensus networks to represent alternative evolutionary histories

PubMed Central

2013-01-01

Background The advent of molecular biology techniques and constant increase in availability of genetic material have triggered the development of many phylogenetic tree inference methods. However, several reticulate evolution processes, such as horizontal gene transfer and hybridization, have been shown to blur the species evolutionary history by causing discordance among phylogenies inferred from different genes. Methods To tackle this problem, we hereby describe a new method for inferring and representing alternative (reticulate) evolutionary histories of species as an explicit weighted consensus network which can be constructed from a collection of gene trees with or without prior knowledge of the species phylogeny. Results We provide a way of building a weighted phylogenetic network for each of the following reticulation mechanisms: diploid hybridization, intragenic recombination and complete or partial horizontal gene transfer. We successfully tested our method on some synthetic and real datasets to infer the above-mentioned evolutionary events which may have influenced the evolution of many species. Conclusions Our weighted consensus network inference method allows one to infer, visualize and validate statistically major conflicting signals induced by the mechanisms of reticulate evolution. The results provided by the new method can be used to represent the inferred conflicting signals by means of explicit and easy-to-interpret phylogenetic networks. PMID:24359207

Models for inference in dynamic metacommunity systems

USGS Publications Warehouse

Dorazio, R.M.; Kery, M.; Royle, J. Andrew; Plattner, M.

2010-01-01

A variety of processes are thought to be involved in the formation and dynamics of species assemblages. For example, various metacommunity theories are based on differences in the relative contributions of dispersal of species among local communities and interactions of species within local communities. Interestingly, metacommunity theories continue to be advanced without much empirical validation. Part of the problem is that statistical models used to analyze typical survey data either fail to specify ecological processes with sufficient complexity or they fail to account for errors in detection of species during sampling. In this paper, we describe a statistical modeling framework for the analysis of metacommunity dynamics that is based on the idea of adopting a unified approach, multispecies occupancy modeling, for computing inferences about individual species, local communities of species, or the entire metacommunity of species. This approach accounts for errors in detection of species during sampling and also allows different metacommunity paradigms to be specified in terms of species-and location-specific probabilities of occurrence, extinction, and colonization: all of which are estimable. In addition, this approach can be used to address inference problems that arise in conservation ecology, such as predicting temporal and spatial changes in biodiversity for use in making conservation decisions. To illustrate, we estimate changes in species composition associated with the species-specific phenologies of flight patterns of butterflies in Switzerland for the purpose of estimating regional differences in biodiversity. ?? 2010 by the Ecological Society of America.

Invited Commentary: The Need for Cognitive Science in Methodology.

PubMed

Greenland, Sander

2017-09-15

There is no complete solution for the problem of abuse of statistics, but methodological training needs to cover cognitive biases and other psychosocial factors affecting inferences. The present paper discusses 3 common cognitive distortions: 1) dichotomania, the compulsion to perceive quantities as dichotomous even when dichotomization is unnecessary and misleading, as in inferences based on whether a P value is "statistically significant"; 2) nullism, the tendency to privilege the hypothesis of no difference or no effect when there is no scientific basis for doing so, as when testing only the null hypothesis; and 3) statistical reification, treating hypothetical data distributions and statistical models as if they reflect known physical laws rather than speculative assumptions for thought experiments. As commonly misused, null-hypothesis significance testing combines these cognitive problems to produce highly distorted interpretation and reporting of study results. Interval estimation has so far proven to be an inadequate solution because it involves dichotomization, an avenue for nullism. Sensitivity and bias analyses have been proposed to address reproducibility problems (Am J Epidemiol. 2017;186(6):646-647); these methods can indeed address reification, but they can also introduce new distortions via misleading specifications for bias parameters. P values can be reframed to lessen distortions by presenting them without reference to a cutoff, providing them for relevant alternatives to the null, and recognizing their dependence on all assumptions used in their computation; they nonetheless require rescaling for measuring evidence. I conclude that methodological development and training should go beyond coverage of mechanistic biases (e.g., confounding, selection bias, measurement error) to cover distortions of conclusions produced by statistical methods and psychosocial forces. © The Author(s) 2017. Published by Oxford University Press on behalf of the Johns Hopkins Bloomberg School of Public Health. All rights reserved. For permissions, please e-mail: journals.permissions@oup.com.

The effects of spatial autoregressive dependencies on inference in ordinary least squares: a geometric approach

NASA Astrophysics Data System (ADS)

Smith, Tony E.; Lee, Ka Lok

2012-01-01

There is a common belief that the presence of residual spatial autocorrelation in ordinary least squares (OLS) regression leads to inflated significance levels in beta coefficients and, in particular, inflated levels relative to the more efficient spatial error model (SEM). However, our simulations show that this is not always the case. Hence, the purpose of this paper is to examine this question from a geometric viewpoint. The key idea is to characterize the OLS test statistic in terms of angle cosines and examine the geometric implications of this characterization. Our first result is to show that if the explanatory variables in the regression exhibit no spatial autocorrelation, then the distribution of test statistics for individual beta coefficients in OLS is independent of any spatial autocorrelation in the error term. Hence, inferences about betas exhibit all the optimality properties of the classic uncorrelated error case. However, a second more important series of results show that if spatial autocorrelation is present in both the dependent and explanatory variables, then the conventional wisdom is correct. In particular, even when an explanatory variable is statistically independent of the dependent variable, such joint spatial dependencies tend to produce "spurious correlation" that results in over-rejection of the null hypothesis. The underlying geometric nature of this problem is clarified by illustrative examples. The paper concludes with a brief discussion of some possible remedies for this problem.

Using the Coefficient of Confidence to Make the Philosophical Switch from a Posteriori to a Priori Inferential Statistics

ERIC Educational Resources Information Center

Trafimow, David

2017-01-01

There has been much controversy over the null hypothesis significance testing procedure, with much of the criticism centered on the problem of inverse inference. Specifically, p gives the probability of the finding (or one more extreme) given the null hypothesis, whereas the null hypothesis significance testing procedure involves drawing a…

On a full Bayesian inference for force reconstruction problems

NASA Astrophysics Data System (ADS)

Aucejo, M.; De Smet, O.

2018-05-01

In a previous paper, the authors introduced a flexible methodology for reconstructing mechanical sources in the frequency domain from prior local information on both their nature and location over a linear and time invariant structure. The proposed approach was derived from Bayesian statistics, because of its ability in mathematically accounting for experimenter's prior knowledge. However, since only the Maximum a Posteriori estimate was computed, the posterior uncertainty about the regularized solution given the measured vibration field, the mechanical model and the regularization parameter was not assessed. To answer this legitimate question, this paper fully exploits the Bayesian framework to provide, from a Markov Chain Monte Carlo algorithm, credible intervals and other statistical measures (mean, median, mode) for all the parameters of the force reconstruction problem.

Design-based Sample and Probability Law-Assumed Sample: Their Role in Scientific Investigation.

ERIC Educational Resources Information Center

Ojeda, Mario Miguel; Sahai, Hardeo

2002-01-01

Discusses some key statistical concepts in probabilistic and non-probabilistic sampling to provide an overview for understanding the inference process. Suggests a statistical model constituting the basis of statistical inference and provides a brief review of the finite population descriptive inference and a quota sampling inferential theory.…

The Importance of Statistical Modeling in Data Analysis and Inference

ERIC Educational Resources Information Center

Rollins, Derrick, Sr.

2017-01-01

Statistical inference simply means to draw a conclusion based on information that comes from data. Error bars are the most commonly used tool for data analysis and inference in chemical engineering data studies. This work demonstrates, using common types of data collection studies, the importance of specifying the statistical model for sound…

Maximum profile likelihood estimation of differential equation parameters through model based smoothing state estimates.

PubMed

Campbell, D A; Chkrebtii, O

2013-12-01

Statistical inference for biochemical models often faces a variety of characteristic challenges. In this paper we examine state and parameter estimation for the JAK-STAT intracellular signalling mechanism, which exemplifies the implementation intricacies common in many biochemical inference problems. We introduce an extension to the Generalized Smoothing approach for estimating delay differential equation models, addressing selection of complexity parameters, choice of the basis system, and appropriate optimization strategies. Motivated by the JAK-STAT system, we further extend the generalized smoothing approach to consider a nonlinear observation process with additional unknown parameters, and highlight how the approach handles unobserved states and unevenly spaced observations. The methodology developed is generally applicable to problems of estimation for differential equation models with delays, unobserved states, nonlinear observation processes, and partially observed histories. Crown Copyright © 2013. Published by Elsevier Inc. All rights reserved.

Inferring Demographic History Using Two-Locus Statistics.

PubMed

Ragsdale, Aaron P; Gutenkunst, Ryan N

2017-06-01

Population demographic history may be learned from contemporary genetic variation data. Methods based on aggregating the statistics of many single loci into an allele frequency spectrum (AFS) have proven powerful, but such methods ignore potentially informative patterns of linkage disequilibrium (LD) between neighboring loci. To leverage such patterns, we developed a composite-likelihood framework for inferring demographic history from aggregated statistics of pairs of loci. Using this framework, we show that two-locus statistics are more sensitive to demographic history than single-locus statistics such as the AFS. In particular, two-locus statistics escape the notorious confounding of depth and duration of a bottleneck, and they provide a means to estimate effective population size based on the recombination rather than mutation rate. We applied our approach to a Zambian population of Drosophila melanogaster Notably, using both single- and two-locus statistics, we inferred a substantially lower ancestral effective population size than previous works and did not infer a bottleneck history. Together, our results demonstrate the broad potential for two-locus statistics to enable powerful population genetic inference. Copyright © 2017 by the Genetics Society of America.

Estimating size and scope economies in the Portuguese water sector using the Bayesian stochastic frontier analysis.

PubMed

Carvalho, Pedro; Marques, Rui Cunha

2016-02-15

This study aims to search for economies of size and scope in the Portuguese water sector applying Bayesian and classical statistics to make inference in stochastic frontier analysis (SFA). This study proves the usefulness and advantages of the application of Bayesian statistics for making inference in SFA over traditional SFA which just uses classical statistics. The resulting Bayesian methods allow overcoming some problems that arise in the application of the traditional SFA, such as the bias in small samples and skewness of residuals. In the present case study of the water sector in Portugal, these Bayesian methods provide more plausible and acceptable results. Based on the results obtained we found that there are important economies of output density, economies of size, economies of vertical integration and economies of scope in the Portuguese water sector, pointing out to the huge advantages in undertaking mergers by joining the retail and wholesale components and by joining the drinking water and wastewater services. Copyright © 2015 Elsevier B.V. All rights reserved.

BCM: toolkit for Bayesian analysis of Computational Models using samplers.

PubMed

Thijssen, Bram; Dijkstra, Tjeerd M H; Heskes, Tom; Wessels, Lodewyk F A

2016-10-21

Computational models in biology are characterized by a large degree of uncertainty. This uncertainty can be analyzed with Bayesian statistics, however, the sampling algorithms that are frequently used for calculating Bayesian statistical estimates are computationally demanding, and each algorithm has unique advantages and disadvantages. It is typically unclear, before starting an analysis, which algorithm will perform well on a given computational model. We present BCM, a toolkit for the Bayesian analysis of Computational Models using samplers. It provides efficient, multithreaded implementations of eleven algorithms for sampling from posterior probability distributions and for calculating marginal likelihoods. BCM includes tools to simplify the process of model specification and scripts for visualizing the results. The flexible architecture allows it to be used on diverse types of biological computational models. In an example inference task using a model of the cell cycle based on ordinary differential equations, BCM is significantly more efficient than existing software packages, allowing more challenging inference problems to be solved. BCM represents an efficient one-stop-shop for computational modelers wishing to use sampler-based Bayesian statistics.

Introduction to bioinformatics.

PubMed

Can, Tolga

2014-01-01

Bioinformatics is an interdisciplinary field mainly involving molecular biology and genetics, computer science, mathematics, and statistics. Data intensive, large-scale biological problems are addressed from a computational point of view. The most common problems are modeling biological processes at the molecular level and making inferences from collected data. A bioinformatics solution usually involves the following steps: Collect statistics from biological data. Build a computational model. Solve a computational modeling problem. Test and evaluate a computational algorithm. This chapter gives a brief introduction to bioinformatics by first providing an introduction to biological terminology and then discussing some classical bioinformatics problems organized by the types of data sources. Sequence analysis is the analysis of DNA and protein sequences for clues regarding function and includes subproblems such as identification of homologs, multiple sequence alignment, searching sequence patterns, and evolutionary analyses. Protein structures are three-dimensional data and the associated problems are structure prediction (secondary and tertiary), analysis of protein structures for clues regarding function, and structural alignment. Gene expression data is usually represented as matrices and analysis of microarray data mostly involves statistics analysis, classification, and clustering approaches. Biological networks such as gene regulatory networks, metabolic pathways, and protein-protein interaction networks are usually modeled as graphs and graph theoretic approaches are used to solve associated problems such as construction and analysis of large-scale networks.

Bayesian Parameter Inference and Model Selection by Population Annealing in Systems Biology

PubMed Central

Murakami, Yohei

2014-01-01

Parameter inference and model selection are very important for mathematical modeling in systems biology. Bayesian statistics can be used to conduct both parameter inference and model selection. Especially, the framework named approximate Bayesian computation is often used for parameter inference and model selection in systems biology. However, Monte Carlo methods needs to be used to compute Bayesian posterior distributions. In addition, the posterior distributions of parameters are sometimes almost uniform or very similar to their prior distributions. In such cases, it is difficult to choose one specific value of parameter with high credibility as the representative value of the distribution. To overcome the problems, we introduced one of the population Monte Carlo algorithms, population annealing. Although population annealing is usually used in statistical mechanics, we showed that population annealing can be used to compute Bayesian posterior distributions in the approximate Bayesian computation framework. To deal with un-identifiability of the representative values of parameters, we proposed to run the simulations with the parameter ensemble sampled from the posterior distribution, named “posterior parameter ensemble”. We showed that population annealing is an efficient and convenient algorithm to generate posterior parameter ensemble. We also showed that the simulations with the posterior parameter ensemble can, not only reproduce the data used for parameter inference, but also capture and predict the data which was not used for parameter inference. Lastly, we introduced the marginal likelihood in the approximate Bayesian computation framework for Bayesian model selection. We showed that population annealing enables us to compute the marginal likelihood in the approximate Bayesian computation framework and conduct model selection depending on the Bayes factor. PMID:25089832

Statistical Inference in Graphical Models

DTIC Science & Technology

2008-06-17

fuse probability theory and graph theory in such a way as to permit efficient rep- resentation and computation with probability distributions. They...message passing. 59 viii 1. INTRODUCTION In approaching real-world problems, we often need to deal with uncertainty. Probability and statis- tics provide a...dynamic programming methods. However, for many sensors of interest, the signal-to-noise ratio does not allow such a treatment. Another source of

Evidence and Clinical Trials.

NASA Astrophysics Data System (ADS)

Goodman, Steven N.

1989-11-01

This dissertation explores the use of a mathematical measure of statistical evidence, the log likelihood ratio, in clinical trials. The methods and thinking behind the use of an evidential measure are contrasted with traditional methods of analyzing data, which depend primarily on a p-value as an estimate of the statistical strength of an observed data pattern. It is contended that neither the behavioral dictates of Neyman-Pearson hypothesis testing methods, nor the coherency dictates of Bayesian methods are realistic models on which to base inference. The use of the likelihood alone is applied to four aspects of trial design or conduct: the calculation of sample size, the monitoring of data, testing for the equivalence of two treatments, and meta-analysis--the combining of results from different trials. Finally, a more general model of statistical inference, using belief functions, is used to see if it is possible to separate the assessment of evidence from our background knowledge. It is shown that traditional and Bayesian methods can be modeled as two ends of a continuum of structured background knowledge, methods which summarize evidence at the point of maximum likelihood assuming no structure, and Bayesian methods assuming complete knowledge. Both schools are seen to be missing a concept of ignorance- -uncommitted belief. This concept provides the key to understanding the problem of sampling to a foregone conclusion and the role of frequency properties in statistical inference. The conclusion is that statistical evidence cannot be defined independently of background knowledge, and that frequency properties of an estimator are an indirect measure of uncommitted belief. Several likelihood summaries need to be used in clinical trials, with the quantitative disparity between summaries being an indirect measure of our ignorance. This conclusion is linked with parallel ideas in the philosophy of science and cognitive psychology.

Reasoning about Informal Statistical Inference: One Statistician's View

ERIC Educational Resources Information Center

Rossman, Allan J.

2008-01-01

This paper identifies key concepts and issues associated with the reasoning of informal statistical inference. I focus on key ideas of inference that I think all students should learn, including at secondary level as well as tertiary. I argue that a fundamental component of inference is to go beyond the data at hand, and I propose that statistical…

Data-driven inference for the spatial scan statistic.

PubMed

Almeida, Alexandre C L; Duarte, Anderson R; Duczmal, Luiz H; Oliveira, Fernando L P; Takahashi, Ricardo H C

2011-08-02

Kulldorff's spatial scan statistic for aggregated area maps searches for clusters of cases without specifying their size (number of areas) or geographic location in advance. Their statistical significance is tested while adjusting for the multiple testing inherent in such a procedure. However, as is shown in this work, this adjustment is not done in an even manner for all possible cluster sizes. A modification is proposed to the usual inference test of the spatial scan statistic, incorporating additional information about the size of the most likely cluster found. A new interpretation of the results of the spatial scan statistic is done, posing a modified inference question: what is the probability that the null hypothesis is rejected for the original observed cases map with a most likely cluster of size k, taking into account only those most likely clusters of size k found under null hypothesis for comparison? This question is especially important when the p-value computed by the usual inference process is near the alpha significance level, regarding the correctness of the decision based in this inference. A practical procedure is provided to make more accurate inferences about the most likely cluster found by the spatial scan statistic.

Assessment of statistical education in Indonesia: Preliminary results and initiation to simulation-based inference

NASA Astrophysics Data System (ADS)

Saputra, K. V. I.; Cahyadi, L.; Sembiring, U. A.

2018-01-01

Start in this paper, we assess our traditional elementary statistics education and also we introduce elementary statistics with simulation-based inference. To assess our statistical class, we adapt the well-known CAOS (Comprehensive Assessment of Outcomes in Statistics) test that serves as an external measure to assess the student’s basic statistical literacy. This test generally represents as an accepted measure of statistical literacy. We also introduce a new teaching method on elementary statistics class. Different from the traditional elementary statistics course, we will introduce a simulation-based inference method to conduct hypothesis testing. From the literature, it has shown that this new teaching method works very well in increasing student’s understanding of statistics.

Apes are intuitive statisticians.

PubMed

Rakoczy, Hannes; Clüver, Annette; Saucke, Liane; Stoffregen, Nicole; Gräbener, Alice; Migura, Judith; Call, Josep

2014-04-01

Inductive learning and reasoning, as we use it both in everyday life and in science, is characterized by flexible inferences based on statistical information: inferences from populations to samples and vice versa. Many forms of such statistical reasoning have been found to develop late in human ontogeny, depending on formal education and language, and to be fragile even in adults. New revolutionary research, however, suggests that even preverbal human infants make use of intuitive statistics. Here, we conducted the first investigation of such intuitive statistical reasoning with non-human primates. In a series of 7 experiments, Bonobos, Chimpanzees, Gorillas and Orangutans drew flexible statistical inferences from populations to samples. These inferences, furthermore, were truly based on statistical information regarding the relative frequency distributions in a population, and not on absolute frequencies. Intuitive statistics in its most basic form is thus an evolutionarily more ancient rather than a uniquely human capacity. Copyright © 2014 Elsevier B.V. All rights reserved.

Astrophysical data analysis with information field theory

NASA Astrophysics Data System (ADS)

Enßlin, Torsten

2014-12-01

Non-parametric imaging and data analysis in astrophysics and cosmology can be addressed by information field theory (IFT), a means of Bayesian, data based inference on spatially distributed signal fields. IFT is a statistical field theory, which permits the construction of optimal signal recovery algorithms. It exploits spatial correlations of the signal fields even for nonlinear and non-Gaussian signal inference problems. The alleviation of a perception threshold for recovering signals of unknown correlation structure by using IFT will be discussed in particular as well as a novel improvement on instrumental self-calibration schemes. IFT can be applied to many areas. Here, applications in in cosmology (cosmic microwave background, large-scale structure) and astrophysics (galactic magnetism, radio interferometry) are presented.

Cluster mass inference via random field theory.

PubMed

Zhang, Hui; Nichols, Thomas E; Johnson, Timothy D

2009-01-01

Cluster extent and voxel intensity are two widely used statistics in neuroimaging inference. Cluster extent is sensitive to spatially extended signals while voxel intensity is better for intense but focal signals. In order to leverage strength from both statistics, several nonparametric permutation methods have been proposed to combine the two methods. Simulation studies have shown that of the different cluster permutation methods, the cluster mass statistic is generally the best. However, to date, there is no parametric cluster mass inference available. In this paper, we propose a cluster mass inference method based on random field theory (RFT). We develop this method for Gaussian images, evaluate it on Gaussian and Gaussianized t-statistic images and investigate its statistical properties via simulation studies and real data. Simulation results show that the method is valid under the null hypothesis and demonstrate that it can be more powerful than the cluster extent inference method. Further, analyses with a single subject and a group fMRI dataset demonstrate better power than traditional cluster size inference, and good accuracy relative to a gold-standard permutation test.

Sequential Monte Carlo for inference of latent ARMA time-series with innovations correlated in time

NASA Astrophysics Data System (ADS)

Urteaga, Iñigo; Bugallo, Mónica F.; Djurić, Petar M.

2017-12-01

We consider the problem of sequential inference of latent time-series with innovations correlated in time and observed via nonlinear functions. We accommodate time-varying phenomena with diverse properties by means of a flexible mathematical representation of the data. We characterize statistically such time-series by a Bayesian analysis of their densities. The density that describes the transition of the state from time t to the next time instant t+1 is used for implementation of novel sequential Monte Carlo (SMC) methods. We present a set of SMC methods for inference of latent ARMA time-series with innovations correlated in time for different assumptions in knowledge of parameters. The methods operate in a unified and consistent manner for data with diverse memory properties. We show the validity of the proposed approach by comprehensive simulations of the challenging stochastic volatility model.

Inverse Ising problem in continuous time: A latent variable approach

NASA Astrophysics Data System (ADS)

Donner, Christian; Opper, Manfred

2017-12-01

We consider the inverse Ising problem: the inference of network couplings from observed spin trajectories for a model with continuous time Glauber dynamics. By introducing two sets of auxiliary latent random variables we render the likelihood into a form which allows for simple iterative inference algorithms with analytical updates. The variables are (1) Poisson variables to linearize an exponential term which is typical for point process likelihoods and (2) Pólya-Gamma variables, which make the likelihood quadratic in the coupling parameters. Using the augmented likelihood, we derive an expectation-maximization (EM) algorithm to obtain the maximum likelihood estimate of network parameters. Using a third set of latent variables we extend the EM algorithm to sparse couplings via L1 regularization. Finally, we develop an efficient approximate Bayesian inference algorithm using a variational approach. We demonstrate the performance of our algorithms on data simulated from an Ising model. For data which are simulated from a more biologically plausible network with spiking neurons, we show that the Ising model captures well the low order statistics of the data and how the Ising couplings are related to the underlying synaptic structure of the simulated network.

A Test by Any Other Name: P Values, Bayes Factors, and Statistical Inference.

PubMed

Stern, Hal S

2016-01-01

Procedures used for statistical inference are receiving increased scrutiny as the scientific community studies the factors associated with insuring reproducible research. This note addresses recent negative attention directed at p values, the relationship of confidence intervals and tests, and the role of Bayesian inference and Bayes factors, with an eye toward better understanding these different strategies for statistical inference. We argue that researchers and data analysts too often resort to binary decisions (e.g., whether to reject or accept the null hypothesis) in settings where this may not be required.

Using Guided Reinvention to Develop Teachers' Understanding of Hypothesis Testing Concepts

ERIC Educational Resources Information Center

Dolor, Jason; Noll, Jennifer

2015-01-01

Statistics education reform efforts emphasize the importance of informal inference in the learning of statistics. Research suggests statistics teachers experience similar difficulties understanding statistical inference concepts as students and how teacher knowledge can impact student learning. This study investigates how teachers reinvented an…

Multiple Illuminant Colour Estimation via Statistical Inference on Factor Graphs.

PubMed

Mutimbu, Lawrence; Robles-Kelly, Antonio

2016-08-31

This paper presents a method to recover a spatially varying illuminant colour estimate from scenes lit by multiple light sources. Starting with the image formation process, we formulate the illuminant recovery problem in a statistically datadriven setting. To do this, we use a factor graph defined across the scale space of the input image. In the graph, we utilise a set of illuminant prototypes computed using a data driven approach. As a result, our method delivers a pixelwise illuminant colour estimate being devoid of libraries or user input. The use of a factor graph also allows for the illuminant estimates to be recovered making use of a maximum a posteriori (MAP) inference process. Moreover, we compute the probability marginals by performing a Delaunay triangulation on our factor graph. We illustrate the utility of our method for pixelwise illuminant colour recovery on widely available datasets and compare against a number of alternatives. We also show sample colour correction results on real-world images.

Permutation-based inference for the AUC: A unified approach for continuous and discontinuous data.

PubMed

Pauly, Markus; Asendorf, Thomas; Konietschke, Frank

2016-11-01

We investigate rank-based studentized permutation methods for the nonparametric Behrens-Fisher problem, that is, inference methods for the area under the ROC curve. We hereby prove that the studentized permutation distribution of the Brunner-Munzel rank statistic is asymptotically standard normal, even under the alternative. Thus, incidentally providing the hitherto missing theoretical foundation for the Neubert and Brunner studentized permutation test. In particular, we do not only show its consistency, but also that confidence intervals for the underlying treatment effects can be computed by inverting this permutation test. In addition, we derive permutation-based range-preserving confidence intervals. Extensive simulation studies show that the permutation-based confidence intervals appear to maintain the preassigned coverage probability quite accurately (even for rather small sample sizes). For a convenient application of the proposed methods, a freely available software package for the statistical software R has been developed. A real data example illustrates the application. © 2016 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

Statistical Inference of a RANS closure for a Jet-in-Crossflow simulation

NASA Astrophysics Data System (ADS)

Heyse, Jan; Edeling, Wouter; Iaccarino, Gianluca

2016-11-01

The jet-in-crossflow is found in several engineering applications, such as discrete film cooling for turbine blades, where a coolant injected through hols in the blade's surface protects the component from the hot gases leaving the combustion chamber. Experimental measurements using MRI techniques have been completed for a single hole injection into a turbulent crossflow, providing full 3D averaged velocity field. For such flows of engineering interest, Reynolds-Averaged Navier-Stokes (RANS) turbulence closure models are often the only viable computational option. However, RANS models are known to provide poor predictions in the region close to the injection point. Since these models are calibrated on simple canonical flow problems, the obtained closure coefficient estimates are unlikely to extrapolate well to more complex flows. We will therefore calibrate the parameters of a RANS model using statistical inference techniques informed by the experimental jet-in-crossflow data. The obtained probabilistic parameter estimates can in turn be used to compute flow fields with quantified uncertainty. Stanford Graduate Fellowship in Science and Engineering.

Reconstruction of a Real World Social Network using the Potts Model and Loopy Belief Propagation.

PubMed

Bisconti, Cristian; Corallo, Angelo; Fortunato, Laura; Gentile, Antonio A; Massafra, Andrea; Pellè, Piergiuseppe

2015-01-01

The scope of this paper is to test the adoption of a statistical model derived from Condensed Matter Physics, for the reconstruction of the structure of a social network. The inverse Potts model, traditionally applied to recursive observations of quantum states in an ensemble of particles, is here addressed to observations of the members' states in an organization and their (anti)correlations, thus inferring interactions as links among the members. Adopting proper (Bethe) approximations, such an inverse problem is showed to be tractable. Within an operational framework, this network-reconstruction method is tested for a small real-world social network, the Italian parliament. In this study case, it is easy to track statuses of the parliament members, using (co)sponsorships of law proposals as the initial dataset. In previous studies of similar activity-based networks, the graph structure was inferred directly from activity co-occurrences: here we compare our statistical reconstruction with such standard methods, outlining discrepancies and advantages.

Reconstruction of a Real World Social Network using the Potts Model and Loopy Belief Propagation

PubMed Central

Bisconti, Cristian; Corallo, Angelo; Fortunato, Laura; Gentile, Antonio A.; Massafra, Andrea; Pellè, Piergiuseppe

2015-01-01

The scope of this paper is to test the adoption of a statistical model derived from Condensed Matter Physics, for the reconstruction of the structure of a social network. The inverse Potts model, traditionally applied to recursive observations of quantum states in an ensemble of particles, is here addressed to observations of the members' states in an organization and their (anti)correlations, thus inferring interactions as links among the members. Adopting proper (Bethe) approximations, such an inverse problem is showed to be tractable. Within an operational framework, this network-reconstruction method is tested for a small real-world social network, the Italian parliament. In this study case, it is easy to track statuses of the parliament members, using (co)sponsorships of law proposals as the initial dataset. In previous studies of similar activity-based networks, the graph structure was inferred directly from activity co-occurrences: here we compare our statistical reconstruction with such standard methods, outlining discrepancies and advantages. PMID:26617539

Hierarchical Probabilistic Inference of Cosmic Shear

NASA Astrophysics Data System (ADS)

Schneider, Michael D.; Hogg, David W.; Marshall, Philip J.; Dawson, William A.; Meyers, Joshua; Bard, Deborah J.; Lang, Dustin

2015-07-01

Point estimators for the shearing of galaxy images induced by gravitational lensing involve a complex inverse problem in the presence of noise, pixelization, and model uncertainties. We present a probabilistic forward modeling approach to gravitational lensing inference that has the potential to mitigate the biased inferences in most common point estimators and is practical for upcoming lensing surveys. The first part of our statistical framework requires specification of a likelihood function for the pixel data in an imaging survey given parameterized models for the galaxies in the images. We derive the lensing shear posterior by marginalizing over all intrinsic galaxy properties that contribute to the pixel data (i.e., not limited to galaxy ellipticities) and learn the distributions for the intrinsic galaxy properties via hierarchical inference with a suitably flexible conditional probabilitiy distribution specification. We use importance sampling to separate the modeling of small imaging areas from the global shear inference, thereby rendering our algorithm computationally tractable for large surveys. With simple numerical examples we demonstrate the improvements in accuracy from our importance sampling approach, as well as the significance of the conditional distribution specification for the intrinsic galaxy properties when the data are generated from an unknown number of distinct galaxy populations with different morphological characteristics.

Natural language processing and inference rules as strategies for updating problem list in an electronic health record.

PubMed

Plazzotta, Fernando; Otero, Carlos; Luna, Daniel; de Quiros, Fernan Gonzalez Bernaldo

2013-01-01

Physicians do not always keep the problem list accurate, complete and updated. To analyze natural language processing (NLP) techniques and inference rules as strategies to maintain completeness and accuracy of the problem list in EHRs. Non systematic literature review in PubMed, in the last 10 years. Strategies to maintain the EHRs problem list were analyzed in two ways: inputting and removing problems from the problem list. NLP and inference rules have acceptable performance for inputting problems into the problem list. No studies using these techniques for removing problems were published Conclusion: Both tools, NLP and inference rules have had acceptable results as tools for maintain the completeness and accuracy of the problem list.

Evaluating the Use of Random Distribution Theory to Introduce Statistical Inference Concepts to Business Students

ERIC Educational Resources Information Center

Larwin, Karen H.; Larwin, David A.

2011-01-01

Bootstrapping methods and random distribution methods are increasingly recommended as better approaches for teaching students about statistical inference in introductory-level statistics courses. The authors examined the effect of teaching undergraduate business statistics students using random distribution and bootstrapping simulations. It is the…

On using summary statistics from an external calibration sample to correct for covariate measurement error.

PubMed

Guo, Ying; Little, Roderick J; McConnell, Daniel S

2012-01-01

Covariate measurement error is common in epidemiologic studies. Current methods for correcting measurement error with information from external calibration samples are insufficient to provide valid adjusted inferences. We consider the problem of estimating the regression of an outcome Y on covariates X and Z, where Y and Z are observed, X is unobserved, but a variable W that measures X with error is observed. Information about measurement error is provided in an external calibration sample where data on X and W (but not Y and Z) are recorded. We describe a method that uses summary statistics from the calibration sample to create multiple imputations of the missing values of X in the regression sample, so that the regression coefficients of Y on X and Z and associated standard errors can be estimated using simple multiple imputation combining rules, yielding valid statistical inferences under the assumption of a multivariate normal distribution. The proposed method is shown by simulation to provide better inferences than existing methods, namely the naive method, classical calibration, and regression calibration, particularly for correction for bias and achieving nominal confidence levels. We also illustrate our method with an example using linear regression to examine the relation between serum reproductive hormone concentrations and bone mineral density loss in midlife women in the Michigan Bone Health and Metabolism Study. Existing methods fail to adjust appropriately for bias due to measurement error in the regression setting, particularly when measurement error is substantial. The proposed method corrects this deficiency.

Family farming workers mental health in a microrregion in southern Brazil.

PubMed

Poletto, Ângela Regina; Gontijo, Leila Amaral

2012-01-01

This research aims at investigating family farming workers' of Ituporanga microregion mental health problems and sociodemographical feature and work process association. The sample corresponded to 447 family farming workers in Ituporanga, i. e., part of the overall population lives in the 1.578 rural properties of the city (IBGE, 2007). A questionnaire with socio-demographic and work process variables was used for data collection concerning mental health problems along with the Self Report Questionnaire (SRQ-20). Inference descriptive statistics with central trend measures and variability was used for data analysis. By means of binary logistic regression the probability of an event, i.e. the presence of mental health problems occur as a result of predicting variables. Level of significance 5% was adopted in all statistical procedures. The investigation revealed the prevalence of 33,8% of mental health problems. It was observed that women prevailed with 39,7% (n = 91), in contrast with men with 26,1% (n = 46), being such association statistically significant (X² = 8,225, df = 1, p = 0,004, phi= -0,143). Socio-demographical and work process variables showed predictors of mental health problems, such as: (sex, age, use of agrochemicals, working hours outside and during harvest time, being family intoxication the most important. Mental health problems showed mostly associated to the use of agro-chemicals and farmers being intoxicated.

Application of Transformations in Parametric Inference

ERIC Educational Resources Information Center

Brownstein, Naomi; Pensky, Marianna

2008-01-01

The objective of the present paper is to provide a simple approach to statistical inference using the method of transformations of variables. We demonstrate performance of this powerful tool on examples of constructions of various estimation procedures, hypothesis testing, Bayes analysis and statistical inference for the stress-strength systems.…

Statistical Inference for Data Adaptive Target Parameters.

PubMed

Hubbard, Alan E; Kherad-Pajouh, Sara; van der Laan, Mark J

2016-05-01

Consider one observes n i.i.d. copies of a random variable with a probability distribution that is known to be an element of a particular statistical model. In order to define our statistical target we partition the sample in V equal size sub-samples, and use this partitioning to define V splits in an estimation sample (one of the V subsamples) and corresponding complementary parameter-generating sample. For each of the V parameter-generating samples, we apply an algorithm that maps the sample to a statistical target parameter. We define our sample-split data adaptive statistical target parameter as the average of these V-sample specific target parameters. We present an estimator (and corresponding central limit theorem) of this type of data adaptive target parameter. This general methodology for generating data adaptive target parameters is demonstrated with a number of practical examples that highlight new opportunities for statistical learning from data. This new framework provides a rigorous statistical methodology for both exploratory and confirmatory analysis within the same data. Given that more research is becoming "data-driven", the theory developed within this paper provides a new impetus for a greater involvement of statistical inference into problems that are being increasingly addressed by clever, yet ad hoc pattern finding methods. To suggest such potential, and to verify the predictions of the theory, extensive simulation studies, along with a data analysis based on adaptively determined intervention rules are shown and give insight into how to structure such an approach. The results show that the data adaptive target parameter approach provides a general framework and resulting methodology for data-driven science.

Computational approaches to protein inference in shotgun proteomics

PubMed Central

2012-01-01

Shotgun proteomics has recently emerged as a powerful approach to characterizing proteomes in biological samples. Its overall objective is to identify the form and quantity of each protein in a high-throughput manner by coupling liquid chromatography with tandem mass spectrometry. As a consequence of its high throughput nature, shotgun proteomics faces challenges with respect to the analysis and interpretation of experimental data. Among such challenges, the identification of proteins present in a sample has been recognized as an important computational task. This task generally consists of (1) assigning experimental tandem mass spectra to peptides derived from a protein database, and (2) mapping assigned peptides to proteins and quantifying the confidence of identified proteins. Protein identification is fundamentally a statistical inference problem with a number of methods proposed to address its challenges. In this review we categorize current approaches into rule-based, combinatorial optimization and probabilistic inference techniques, and present them using integer programing and Bayesian inference frameworks. We also discuss the main challenges of protein identification and propose potential solutions with the goal of spurring innovative research in this area. PMID:23176300

The relation between statistical power and inference in fMRI

PubMed Central

Wager, Tor D.; Yarkoni, Tal

2017-01-01

Statistically underpowered studies can result in experimental failure even when all other experimental considerations have been addressed impeccably. In fMRI the combination of a large number of dependent variables, a relatively small number of observations (subjects), and a need to correct for multiple comparisons can decrease statistical power dramatically. This problem has been clearly addressed yet remains controversial—especially in regards to the expected effect sizes in fMRI, and especially for between-subjects effects such as group comparisons and brain-behavior correlations. We aimed to clarify the power problem by considering and contrasting two simulated scenarios of such possible brain-behavior correlations: weak diffuse effects and strong localized effects. Sampling from these scenarios shows that, particularly in the weak diffuse scenario, common sample sizes (n = 20–30) display extremely low statistical power, poorly represent the actual effects in the full sample, and show large variation on subsequent replications. Empirical data from the Human Connectome Project resembles the weak diffuse scenario much more than the localized strong scenario, which underscores the extent of the power problem for many studies. Possible solutions to the power problem include increasing the sample size, using less stringent thresholds, or focusing on a region-of-interest. However, these approaches are not always feasible and some have major drawbacks. The most prominent solutions that may help address the power problem include model-based (multivariate) prediction methods and meta-analyses with related synthesis-oriented approaches. PMID:29155843

Statistical limitations in functional neuroimaging. I. Non-inferential methods and statistical models.

PubMed Central

Petersson, K M; Nichols, T E; Poline, J B; Holmes, A P

1999-01-01

Functional neuroimaging (FNI) provides experimental access to the intact living brain making it possible to study higher cognitive functions in humans. In this review and in a companion paper in this issue, we discuss some common methods used to analyse FNI data. The emphasis in both papers is on assumptions and limitations of the methods reviewed. There are several methods available to analyse FNI data indicating that none is optimal for all purposes. In order to make optimal use of the methods available it is important to know the limits of applicability. For the interpretation of FNI results it is also important to take into account the assumptions, approximations and inherent limitations of the methods used. This paper gives a brief overview over some non-inferential descriptive methods and common statistical models used in FNI. Issues relating to the complex problem of model selection are discussed. In general, proper model selection is a necessary prerequisite for the validity of the subsequent statistical inference. The non-inferential section describes methods that, combined with inspection of parameter estimates and other simple measures, can aid in the process of model selection and verification of assumptions. The section on statistical models covers approaches to global normalization and some aspects of univariate, multivariate, and Bayesian models. Finally, approaches to functional connectivity and effective connectivity are discussed. In the companion paper we review issues related to signal detection and statistical inference. PMID:10466149

Statistical inference for tumor growth inhibition T/C ratio.

PubMed

Wu, Jianrong

2010-09-01

The tumor growth inhibition T/C ratio is commonly used to quantify treatment effects in drug screening tumor xenograft experiments. The T/C ratio is converted to an antitumor activity rating using an arbitrary cutoff point and often without any formal statistical inference. Here, we applied a nonparametric bootstrap method and a small sample likelihood ratio statistic to make a statistical inference of the T/C ratio, including both hypothesis testing and a confidence interval estimate. Furthermore, sample size and power are also discussed for statistical design of tumor xenograft experiments. Tumor xenograft data from an actual experiment were analyzed to illustrate the application.

Data Analysis with Graphical Models: Software Tools

NASA Technical Reports Server (NTRS)

Buntine, Wray L.

1994-01-01

Probabilistic graphical models (directed and undirected Markov fields, and combined in chain graphs) are used widely in expert systems, image processing and other areas as a framework for representing and reasoning with probabilities. They come with corresponding algorithms for performing probabilistic inference. This paper discusses an extension to these models by Spiegelhalter and Gilks, plates, used to graphically model the notion of a sample. This offers a graphical specification language for representing data analysis problems. When combined with general methods for statistical inference, this also offers a unifying framework for prototyping and/or generating data analysis algorithms from graphical specifications. This paper outlines the framework and then presents some basic tools for the task: a graphical version of the Pitman-Koopman Theorem for the exponential family, problem decomposition, and the calculation of exact Bayes factors. Other tools already developed, such as automatic differentiation, Gibbs sampling, and use of the EM algorithm, make this a broad basis for the generation of data analysis software.

Investigating Mathematics Teachers' Thoughts of Statistical Inference

ERIC Educational Resources Information Center

Yang, Kai-Lin

2012-01-01

Research on statistical cognition and application suggests that statistical inference concepts are commonly misunderstood by students and even misinterpreted by researchers. Although some research has been done on students' misunderstanding or misconceptions of confidence intervals (CIs), few studies explore either students' or mathematics…

Lessons from Inferentialism for Statistics Education

ERIC Educational Resources Information Center

Bakker, Arthur; Derry, Jan

2011-01-01

This theoretical paper relates recent interest in informal statistical inference (ISI) to the semantic theory termed inferentialism, a significant development in contemporary philosophy, which places inference at the heart of human knowing. This theory assists epistemological reflection on challenges in statistics education encountered when…

Statistical Inference and Patterns of Inequality in the Global North

ERIC Educational Resources Information Center

Moran, Timothy Patrick

2006-01-01

Cross-national inequality trends have historically been a crucial field of inquiry across the social sciences, and new methodological techniques of statistical inference have recently improved the ability to analyze these trends over time. This paper applies Monte Carlo, bootstrap inference methods to the income surveys of the Luxembourg Income…

Statistical inference and Aristotle's Rhetoric.

PubMed

Macdonald, Ranald R

2004-11-01

Formal logic operates in a closed system where all the information relevant to any conclusion is present, whereas this is not the case when one reasons about events and states of the world. Pollard and Richardson drew attention to the fact that the reasoning behind statistical tests does not lead to logically justifiable conclusions. In this paper statistical inferences are defended not by logic but by the standards of everyday reasoning. Aristotle invented formal logic, but argued that people mostly get at the truth with the aid of enthymemes--incomplete syllogisms which include arguing from examples, analogies and signs. It is proposed that statistical tests work in the same way--in that they are based on examples, invoke the analogy of a model and use the size of the effect under test as a sign that the chance hypothesis is unlikely. Of existing theories of statistical inference only a weak version of Fisher's takes this into account. Aristotle anticipated Fisher by producing an argument of the form that there were too many cases in which an outcome went in a particular direction for that direction to be plausibly attributed to chance. We can therefore conclude that Aristotle would have approved of statistical inference and there is a good reason for calling this form of statistical inference classical.

Hydrological modelling of the Chaohe Basin in China: Statistical model formulation and Bayesian inference

NASA Astrophysics Data System (ADS)

Yang, Jing; Reichert, Peter; Abbaspour, Karim C.; Yang, Hong

2007-07-01

SummaryCalibration of hydrologic models is very difficult because of measurement errors in input and response, errors in model structure, and the large number of non-identifiable parameters of distributed models. The difficulties even increase in arid regions with high seasonal variation of precipitation, where the modelled residuals often exhibit high heteroscedasticity and autocorrelation. On the other hand, support of water management by hydrologic models is important in arid regions, particularly if there is increasing water demand due to urbanization. The use and assessment of model results for this purpose require a careful calibration and uncertainty analysis. Extending earlier work in this field, we developed a procedure to overcome (i) the problem of non-identifiability of distributed parameters by introducing aggregate parameters and using Bayesian inference, (ii) the problem of heteroscedasticity of errors by combining a Box-Cox transformation of results and data with seasonally dependent error variances, (iii) the problems of autocorrelated errors, missing data and outlier omission with a continuous-time autoregressive error model, and (iv) the problem of the seasonal variation of error correlations with seasonally dependent characteristic correlation times. The technique was tested with the calibration of the hydrologic sub-model of the Soil and Water Assessment Tool (SWAT) in the Chaohe Basin in North China. The results demonstrated the good performance of this approach to uncertainty analysis, particularly with respect to the fulfilment of statistical assumptions of the error model. A comparison with an independent error model and with error models that only considered a subset of the suggested techniques clearly showed the superiority of the approach based on all the features (i)-(iv) mentioned above.

Generic Feature Selection with Short Fat Data

PubMed Central

Clarke, B.; Chu, J.-H.

2014-01-01

SUMMARY Consider a regression problem in which there are many more explanatory variables than data points, i.e., p ≫ n. Essentially, without reducing the number of variables inference is impossible. So, we group the p explanatory variables into blocks by clustering, evaluate statistics on the blocks and then regress the response on these statistics under a penalized error criterion to obtain estimates of the regression coefficients. We examine the performance of this approach for a variety of choices of n, p, classes of statistics, clustering algorithms, penalty terms, and data types. When n is not large, the discrimination over number of statistics is weak, but computations suggest regressing on approximately [n/K] statistics where K is the number of blocks formed by a clustering algorithm. Small deviations from this are observed when the blocks of variables are of very different sizes. Larger deviations are observed when the penalty term is an Lq norm with high enough q. PMID:25346546

Non-extensive Statistics to the Cosmological Lithium Problem

NASA Astrophysics Data System (ADS)

Hou, S. Q.; He, J. J.; Parikh, A.; Kahl, D.; Bertulani, C. A.; Kajino, T.; Mathews, G. J.; Zhao, G.

2017-01-01

Big Bang nucleosynthesis (BBN) theory predicts the abundances of the light elements D, 3He, 4He, and 7Li produced in the early universe. The primordial abundances of D and 4He inferred from observational data are in good agreement with predictions, however, BBN theory overestimates the primordial 7Li abundance by about a factor of three. This is the so-called “cosmological lithium problem.” Solutions to this problem using conventional astrophysics and nuclear physics have not been successful over the past few decades, probably indicating the presence of new physics during the era of BBN. We have investigated the impact on BBN predictions of adopting a generalized distribution to describe the velocities of nucleons in the framework of Tsallis non-extensive statistics. This generalized velocity distribution is characterized by a parameter q, and reduces to the usually assumed Maxwell-Boltzmann distribution for q = 1. We find excellent agreement between predicted and observed primordial abundances of D, 4He, and 7Li for 1.069 ≤ q ≤ 1.082, suggesting a possible new solution to the cosmological lithium problem.

Software for Data Analysis with Graphical Models

NASA Technical Reports Server (NTRS)

Buntine, Wray L.; Roy, H. Scott

1994-01-01

Probabilistic graphical models are being used widely in artificial intelligence and statistics, for instance, in diagnosis and expert systems, as a framework for representing and reasoning with probabilities and independencies. They come with corresponding algorithms for performing statistical inference. This offers a unifying framework for prototyping and/or generating data analysis algorithms from graphical specifications. This paper illustrates the framework with an example and then presents some basic techniques for the task: problem decomposition and the calculation of exact Bayes factors. Other tools already developed, such as automatic differentiation, Gibbs sampling, and use of the EM algorithm, make this a broad basis for the generation of data analysis software.

Recursive regularization for inferring gene networks from time-course gene expression profiles

PubMed Central

Shimamura, Teppei; Imoto, Seiya; Yamaguchi, Rui; Fujita, André; Nagasaki, Masao; Miyano, Satoru

2009-01-01

Background Inferring gene networks from time-course microarray experiments with vector autoregressive (VAR) model is the process of identifying functional associations between genes through multivariate time series. This problem can be cast as a variable selection problem in Statistics. One of the promising methods for variable selection is the elastic net proposed by Zou and Hastie (2005). However, VAR modeling with the elastic net succeeds in increasing the number of true positives while it also results in increasing the number of false positives. Results By incorporating relative importance of the VAR coefficients into the elastic net, we propose a new class of regularization, called recursive elastic net, to increase the capability of the elastic net and estimate gene networks based on the VAR model. The recursive elastic net can reduce the number of false positives gradually by updating the importance. Numerical simulations and comparisons demonstrate that the proposed method succeeds in reducing the number of false positives drastically while keeping the high number of true positives in the network inference and achieves two or more times higher true discovery rate (the proportion of true positives among the selected edges) than the competing methods even when the number of time points is small. We also compared our method with various reverse-engineering algorithms on experimental data of MCF-7 breast cancer cells stimulated with two ErbB ligands, EGF and HRG. Conclusion The recursive elastic net is a powerful tool for inferring gene networks from time-course gene expression profiles. PMID:19386091

CADDIS Volume 4. Data Analysis: Biological and Environmental Data Requirements

EPA Pesticide Factsheets

Overview of PECBO Module, using scripts to infer environmental conditions from biological observations, statistically estimating species-environment relationships, methods for inferring environmental conditions, statistical scripts in module.

Statistical methods for the beta-binomial model in teratology.

PubMed Central

Yamamoto, E; Yanagimoto, T

1994-01-01

The beta-binomial model is widely used for analyzing teratological data involving littermates. Recent developments in statistical analyses of teratological data are briefly reviewed with emphasis on the model. For statistical inference of the parameters in the beta-binomial distribution, separation of the likelihood introduces an likelihood inference. This leads to reducing biases of estimators and also to improving accuracy of empirical significance levels of tests. Separate inference of the parameters can be conducted in a unified way. PMID:8187716

On Some Assumptions of the Null Hypothesis Statistical Testing

ERIC Educational Resources Information Center

Patriota, Alexandre Galvão

2017-01-01

Bayesian and classical statistical approaches are based on different types of logical principles. In order to avoid mistaken inferences and misguided interpretations, the practitioner must respect the inference rules embedded into each statistical method. Ignoring these principles leads to the paradoxical conclusions that the hypothesis…

Towards a web-based decision support tool for selecting appropriate statistical test in medical and biological sciences.

PubMed

Suner, Aslı; Karakülah, Gökhan; Dicle, Oğuz

2014-01-01

Statistical hypothesis testing is an essential component of biological and medical studies for making inferences and estimations from the collected data in the study; however, the misuse of statistical tests is widely common. In order to prevent possible errors in convenient statistical test selection, it is currently possible to consult available test selection algorithms developed for various purposes. However, the lack of an algorithm presenting the most common statistical tests used in biomedical research in a single flowchart causes several problems such as shifting users among the algorithms, poor decision support in test selection and lack of satisfaction of potential users. Herein, we demonstrated a unified flowchart; covers mostly used statistical tests in biomedical domain, to provide decision aid to non-statistician users while choosing the appropriate statistical test for testing their hypothesis. We also discuss some of the findings while we are integrating the flowcharts into each other to develop a single but more comprehensive decision algorithm.

Kernel learning at the first level of inference.

PubMed

Cawley, Gavin C; Talbot, Nicola L C

2014-05-01

Kernel learning methods, whether Bayesian or frequentist, typically involve multiple levels of inference, with the coefficients of the kernel expansion being determined at the first level and the kernel and regularisation parameters carefully tuned at the second level, a process known as model selection. Model selection for kernel machines is commonly performed via optimisation of a suitable model selection criterion, often based on cross-validation or theoretical performance bounds. However, if there are a large number of kernel parameters, as for instance in the case of automatic relevance determination (ARD), there is a substantial risk of over-fitting the model selection criterion, resulting in poor generalisation performance. In this paper we investigate the possibility of learning the kernel, for the Least-Squares Support Vector Machine (LS-SVM) classifier, at the first level of inference, i.e. parameter optimisation. The kernel parameters and the coefficients of the kernel expansion are jointly optimised at the first level of inference, minimising a training criterion with an additional regularisation term acting on the kernel parameters. The key advantage of this approach is that the values of only two regularisation parameters need be determined in model selection, substantially alleviating the problem of over-fitting the model selection criterion. The benefits of this approach are demonstrated using a suite of synthetic and real-world binary classification benchmark problems, where kernel learning at the first level of inference is shown to be statistically superior to the conventional approach, improves on our previous work (Cawley and Talbot, 2007) and is competitive with Multiple Kernel Learning approaches, but with reduced computational expense. Copyright © 2014 Elsevier Ltd. All rights reserved.

Direct evidence for a dual process model of deductive inference.

PubMed

Markovits, Henry; Brunet, Marie-Laurence; Thompson, Valerie; Brisson, Janie

2013-07-01

In 2 experiments, we tested a strong version of a dual process theory of conditional inference (cf. Verschueren et al., 2005a, 2005b) that assumes that most reasoners have 2 strategies available, the choice of which is determined by situational variables, cognitive capacity, and metacognitive control. The statistical strategy evaluates inferences probabilistically, accepting those with high conditional probability. The counterexample strategy rejects inferences when a counterexample shows the inference to be invalid. To discriminate strategy use, we presented reasoners with conditional statements (if p, then q) and explicit statistical information about the relative frequency of the probability of p/q (50% vs. 90%). A statistical strategy would accept the more probable inferences more frequently, whereas the counterexample one would reject both. In Experiment 1, reasoners under time pressure used the statistical strategy more, but switched to the counterexample strategy when time constraints were removed; the former took less time than the latter. These data are consistent with the hypothesis that the statistical strategy is the default heuristic. Under a free-time condition, reasoners preferred the counterexample strategy and kept it when put under time pressure. Thus, it is not simply a lack of capacity that produces a statistical strategy; instead, it seems that time pressure disrupts the ability to make good metacognitive choices. In line with this conclusion, in a 2nd experiment, we measured reasoners' confidence in their performance; those under time pressure were less confident in the statistical than the counterexample strategy and more likely to switch strategies under free-time conditions. PsycINFO Database Record (c) 2013 APA, all rights reserved.

The APA Task Force on Statistical Inference (TFSI) Report as a Framework for Teaching and Evaluating Students' Understandings of Study Validity.

ERIC Educational Resources Information Center

Thompson, Bruce

Web-based statistical instruction, like all statistical instruction, ought to focus on teaching the essence of the research endeavor: the exercise of reflective judgment. Using the framework of the recent report of the American Psychological Association (APA) Task Force on Statistical Inference (Wilkinson and the APA Task Force on Statistical…

Deterministic physical systems under uncertain initial conditions: the case of maximum entropy applied to projectile motion

NASA Astrophysics Data System (ADS)

Montecinos, Alejandra; Davis, Sergio; Peralta, Joaquín

2018-07-01

The kinematics and dynamics of deterministic physical systems have been a foundation of our understanding of the world since Galileo and Newton. For real systems, however, uncertainty is largely present via external forces such as friction or lack of precise knowledge about the initial conditions of the system. In this work we focus on the latter case and describe the use of inference methodologies in solving the statistical properties of classical systems subject to uncertain initial conditions. In particular we describe the application of the formalism of maximum entropy (MaxEnt) inference to the problem of projectile motion, given information about the average horizontal range over many realizations. By using MaxEnt we can invert the problem and use the provided information on the average range to reduce the original uncertainty in the initial conditions. Also, additional insight into the initial condition's probabilities, and the projectile path distribution itself, can be achieved based on the value of the average horizontal range. The wide applicability of this procedure, as well as its ease of use, reveals a useful tool with which to revisit a large number of physics problems, from classrooms to frontier research.

Data Analysis Techniques for Physical Scientists

NASA Astrophysics Data System (ADS)

Pruneau, Claude A.

2017-10-01

Preface; How to read this book; 1. The scientific method; Part I. Foundation in Probability and Statistics: 2. Probability; 3. Probability models; 4. Classical inference I: estimators; 5. Classical inference II: optimization; 6. Classical inference III: confidence intervals and statistical tests; 7. Bayesian inference; Part II. Measurement Techniques: 8. Basic measurements; 9. Event reconstruction; 10. Correlation functions; 11. The multiple facets of correlation functions; 12. Data correction methods; Part III. Simulation Techniques: 13. Monte Carlo methods; 14. Collision and detector modeling; List of references; Index.

CADDIS Volume 4. Data Analysis: Predicting Environmental Conditions from Biological Observations (PECBO Appendix)

EPA Pesticide Factsheets

Overview of PECBO Module, using scripts to infer environmental conditions from biological observations, statistically estimating species-environment relationships, methods for inferring environmental conditions, statistical scripts in module.

Efficient inference for genetic association studies with multiple outcomes.

PubMed

Ruffieux, Helene; Davison, Anthony C; Hager, Jorg; Irincheeva, Irina

2017-10-01

Combined inference for heterogeneous high-dimensional data is critical in modern biology, where clinical and various kinds of molecular data may be available from a single study. Classical genetic association studies regress a single clinical outcome on many genetic variants one by one, but there is an increasing demand for joint analysis of many molecular outcomes and genetic variants in order to unravel functional interactions. Unfortunately, most existing approaches to joint modeling are either too simplistic to be powerful or are impracticable for computational reasons. Inspired by Richardson and others (2010, Bayesian Statistics 9), we consider a sparse multivariate regression model that allows simultaneous selection of predictors and associated responses. As Markov chain Monte Carlo (MCMC) inference on such models can be prohibitively slow when the number of genetic variants exceeds a few thousand, we propose a variational inference approach which produces posterior information very close to that of MCMC inference, at a much reduced computational cost. Extensive numerical experiments show that our approach outperforms popular variable selection methods and tailored Bayesian procedures, dealing within hours with problems involving hundreds of thousands of genetic variants and tens to hundreds of clinical or molecular outcomes. © The Author 2017. Published by Oxford University Press. All rights reserved. For permissions, please e-mail: journals.permissions@oup.com.

Inference on the Strength of Balancing Selection for Epistatically Interacting Loci

PubMed Central

Buzbas, Erkan Ozge; Joyce, Paul; Rosenberg, Noah A.

2011-01-01

Existing inference methods for estimating the strength of balancing selection in multi-locus genotypes rely on the assumption that there are no epistatic interactions between loci. Complex systems in which balancing selection is prevalent, such as sets of human immune system genes, are known to contain components that interact epistatically. Therefore, current methods may not produce reliable inference on the strength of selection at these loci. In this paper, we address this problem by presenting statistical methods that can account for epistatic interactions in making inference about balancing selection. A theoretical result due to Fearnhead (2006) is used to build a multi-locus Wright-Fisher model of balancing selection, allowing for epistatic interactions among loci. Antagonistic and synergistic types of interactions are examined. The joint posterior distribution of the selection and mutation parameters is sampled by Markov chain Monte Carlo methods, and the plausibility of models is assessed via Bayes factors. As a component of the inference process, an algorithm to generate multi-locus allele frequencies under balancing selection models with epistasis is also presented. Recent evidence on interactions among a set of human immune system genes is introduced as a motivating biological system for the epistatic model, and data on these genes are used to demonstrate the methods. PMID:21277883

HIERARCHICAL PROBABILISTIC INFERENCE OF COSMIC SHEAR

DOE Office of Scientific and Technical Information (OSTI.GOV)

Schneider, Michael D.; Dawson, William A.; Hogg, David W.

2015-07-01

Point estimators for the shearing of galaxy images induced by gravitational lensing involve a complex inverse problem in the presence of noise, pixelization, and model uncertainties. We present a probabilistic forward modeling approach to gravitational lensing inference that has the potential to mitigate the biased inferences in most common point estimators and is practical for upcoming lensing surveys. The first part of our statistical framework requires specification of a likelihood function for the pixel data in an imaging survey given parameterized models for the galaxies in the images. We derive the lensing shear posterior by marginalizing over all intrinsic galaxymore » properties that contribute to the pixel data (i.e., not limited to galaxy ellipticities) and learn the distributions for the intrinsic galaxy properties via hierarchical inference with a suitably flexible conditional probabilitiy distribution specification. We use importance sampling to separate the modeling of small imaging areas from the global shear inference, thereby rendering our algorithm computationally tractable for large surveys. With simple numerical examples we demonstrate the improvements in accuracy from our importance sampling approach, as well as the significance of the conditional distribution specification for the intrinsic galaxy properties when the data are generated from an unknown number of distinct galaxy populations with different morphological characteristics.« less

Dynamic State Estimation of Terrestrial and Solar Plasmas

NASA Astrophysics Data System (ADS)

Kamalabadi, Farzad

A pervasive problem in virtually all branches of space science is the estimation of multi-dimensional state parameters of a dynamical system from a collection of indirect, often incomplete, and imprecise measurements. Subsequent scientific inference is predicated on rigorous analysis, interpretation, and understanding of physical observations and on the reliability of the associated quantitative statistical bounds and performance characteristics of the algorithms used. In this work, we focus on these dynamic state estimation problems and illustrate their importance in the context of two timely activities in space remote sensing. First, we discuss the estimation of multi-dimensional ionospheric state parameters from UV spectral imaging measurements anticipated to be acquired the recently selected NASA Heliophysics mission, Ionospheric Connection Explorer (ICON). Next, we illustrate that similar state-space formulations provide the means for the estimation of 3D, time-dependent densities and temperatures in the solar corona from a series of white-light and EUV measurements. We demonstrate that, while a general framework for the stochastic formulation of the state estimation problem is suited for systematic inference of the parameters of a hidden Markov process, several challenges must be addressed in the assimilation of an increasing volume and diversity of space observations. These challenges are: (1) the computational tractability when faced with voluminous and multimodal data, (2) the inherent limitations of the underlying models which assume, often incorrectly, linear dynamics and Gaussian noise, and (3) the unavailability or inaccuracy of transition probabilities and noise statistics. We argue that pursuing answers to these questions necessitates cross-disciplinary research that enables progress toward systematically reconciling observational and theoretical understanding of the space environment.

Causal Inference from Big Data: Theoretical Foundations and the Data-fusion Problem

DTIC Science & Technology

2015-06-01

both treatment and response. Some of these factors may be unmeasurable, such as genetic trait or lifestyle, while others are measurable, such as gender...several tasks in Artificial Intelligence [22, 23] and Statistics [24, 25] as well as in the empirical sciences (e.g., Genetics [26, 27], Economics [28...conditions are likely to be different. Special cases of transportability can be found in the literature under different rubrics such as “external validity

Inference of Vohradský's Models of Genetic Networks by Solving Two-Dimensional Function Optimization Problems

PubMed Central

Kimura, Shuhei; Sato, Masanao; Okada-Hatakeyama, Mariko

2013-01-01

The inference of a genetic network is a problem in which mutual interactions among genes are inferred from time-series of gene expression levels. While a number of models have been proposed to describe genetic networks, this study focuses on a mathematical model proposed by Vohradský. Because of its advantageous features, several researchers have proposed the inference methods based on Vohradský's model. When trying to analyze large-scale networks consisting of dozens of genes, however, these methods must solve high-dimensional non-linear function optimization problems. In order to resolve the difficulty of estimating the parameters of the Vohradský's model, this study proposes a new method that defines the problem as several two-dimensional function optimization problems. Through numerical experiments on artificial genetic network inference problems, we showed that, although the computation time of the proposed method is not the shortest, the method has the ability to estimate parameters of Vohradský's models more effectively with sufficiently short computation times. This study then applied the proposed method to an actual inference problem of the bacterial SOS DNA repair system, and succeeded in finding several reasonable regulations. PMID:24386175

Statistical Inferences from Formaldehyde Dna-Protein Cross-Link Data

EPA Science Inventory

Physiologically-based pharmacokinetic (PBPK) modeling has reached considerable sophistication in its application in the pharmacological and environmental health areas. Yet, mature methodologies for making statistical inferences have not been routinely incorporated in these applic...

Introducing Statistical Inference to Biology Students through Bootstrapping and Randomization

ERIC Educational Resources Information Center

Lock, Robin H.; Lock, Patti Frazer

2008-01-01

Bootstrap methods and randomization tests are increasingly being used as alternatives to standard statistical procedures in biology. They also serve as an effective introduction to the key ideas of statistical inference in introductory courses for biology students. We discuss the use of such simulation based procedures in an integrated curriculum…

Developing Young Children's Emergent Inferential Practices in Statistics

ERIC Educational Resources Information Center

Makar, Katie

2016-01-01

Informal statistical inference has now been researched at all levels of schooling and initial tertiary study. Work in informal statistical inference is least understood in the early years, where children have had little if any exposure to data handling. A qualitative study in Australia was carried out through a series of teaching experiments with…

Localized Smart-Interpretation

NASA Astrophysics Data System (ADS)

Lundh Gulbrandsen, Mats; Mejer Hansen, Thomas; Bach, Torben; Pallesen, Tom

2014-05-01

The complex task of setting up a geological model consists not only of combining available geological information into a conceptual plausible model, but also requires consistency with availably data, e.g. geophysical data. However, in many cases the direct geological information, e.g borehole samples, are very sparse, so in order to create a geological model, the geologist needs to rely on the geophysical data. The problem is however, that the amount of geophysical data in many cases are so vast that it is practically impossible to integrate all of them in the manual interpretation process. This means that a lot of the information available from the geophysical surveys are unexploited, which is a problem, due to the fact that the resulting geological model does not fulfill its full potential and hence are less trustworthy. We suggest an approach to geological modeling that 1. allow all geophysical data to be considered when building the geological model 2. is fast 3. allow quantification of geological modeling. The method is constructed to build a statistical model, f(d,m), describing the relation between what the geologists interpret, d, and what the geologist knows, m. The para- meter m reflects any available information that can be quantified, such as geophysical data, the result of a geophysical inversion, elevation maps, etc... The parameter d reflects an actual interpretation, such as for example the depth to the base of a ground water reservoir. First we infer a statistical model f(d,m), by examining sets of actual interpretations made by a geological expert, [d1, d2, ...], and the information used to perform the interpretation; [m1, m2, ...]. This makes it possible to quantify how the geological expert performs interpolation through f(d,m). As the geological expert proceeds interpreting, the number of interpreted datapoints from which the statistical model is inferred increases, and therefore the accuracy of the statistical model increases. When a model f(d,m) successfully has been inferred, we are able to simulate how the geological expert would perform an interpretation given some external information m, through f(d|m). We will demonstrate this method applied on geological interpretation and densely sampled airborne electromagnetic data. In short, our goal is to build a statistical model describing how a geological expert performs geological interpretation given some geophysical data. We then wish to use this statistical model to perform semi automatic interpretation, everywhere where such geophysical data exist, in a manner consistent with the choices made by a geological expert. Benefits of such a statistical model are that 1. it provides a quantification of how a geological expert performs interpretation based on available diverse data 2. all available geophysical information can be used 3. it allows much faster interpretation of large data sets.

A new probe of the magnetic field power spectrum in cosmic web filaments

NASA Astrophysics Data System (ADS)

Hales, Christopher A.; Greiner, Maksim; Ensslin, Torsten A.

2015-08-01

Establishing the properties of magnetic fields on scales larger than galaxy clusters is critical for resolving the unknown origin and evolution of galactic and cluster magnetism. More generally, observations of magnetic fields on cosmic scales are needed for assessing the impacts of magnetism on cosmology, particle physics, and structure formation over the full history of the Universe. However, firm observational evidence for magnetic fields in large scale structure remains elusive. In an effort to address this problem, we have developed a novel statistical method to infer the magnetic field power spectrum in cosmic web filaments using observation of the two-point correlation of Faraday rotation measures from a dense grid of extragalactic radio sources. Here we describe our approach, which embeds and extends the pioneering work of Kolatt (1998) within the context of Information Field Theory (a statistical theory for Bayesian inference on spatially distributed signals; Enfllin et al., 2009). We describe prospects for observation, for example with forthcoming data from the ultra-deep JVLA CHILES Con Pol survey and future surveys with the SKA.

Comparison of cosmology and seabed acoustics measurements using statistical inference from maximum entropy

NASA Astrophysics Data System (ADS)

Knobles, David; Stotts, Steven; Sagers, Jason

2012-03-01

Why can one obtain from similar measurements a greater amount of information about cosmological parameters than seabed parameters in ocean waveguides? The cosmological measurements are in the form of a power spectrum constructed from spatial correlations of temperature fluctuations within the microwave background radiation. The seabed acoustic measurements are in the form of spatial correlations along the length of a spatial aperture. This study explores the above question from the perspective of posterior probability distributions obtained from maximizing a relative entropy functional. An answer is in part that the seabed in shallow ocean environments generally has large temporal and spatial inhomogeneities, whereas the early universe was a nearly homogeneous cosmological soup with small but important fluctuations. Acoustic propagation models used in shallow water acoustics generally do not capture spatial and temporal variability sufficiently well, which leads to model error dominating the statistical inference problem. This is not the case in cosmology. Further, the physics of the acoustic modes in cosmology is that of a standing wave with simple initial conditions, whereas for underwater acoustics it is a traveling wave in a strongly inhomogeneous bounded medium.

A Quantum Probability Model of Causal Reasoning

PubMed Central

Trueblood, Jennifer S.; Busemeyer, Jerome R.

2012-01-01

People can often outperform statistical methods and machine learning algorithms in situations that involve making inferences about the relationship between causes and effects. While people are remarkably good at causal reasoning in many situations, there are several instances where they deviate from expected responses. This paper examines three situations where judgments related to causal inference problems produce unexpected results and describes a quantum inference model based on the axiomatic principles of quantum probability theory that can explain these effects. Two of the three phenomena arise from the comparison of predictive judgments (i.e., the conditional probability of an effect given a cause) with diagnostic judgments (i.e., the conditional probability of a cause given an effect). The third phenomenon is a new finding examining order effects in predictive causal judgments. The quantum inference model uses the notion of incompatibility among different causes to account for all three phenomena. Psychologically, the model assumes that individuals adopt different points of view when thinking about different causes. The model provides good fits to the data and offers a coherent account for all three causal reasoning effects thus proving to be a viable new candidate for modeling human judgment. PMID:22593747

TARGETED SEQUENTIAL DESIGN FOR TARGETED LEARNING INFERENCE OF THE OPTIMAL TREATMENT RULE AND ITS MEAN REWARD.

PubMed

Chambaz, Antoine; Zheng, Wenjing; van der Laan, Mark J

2017-01-01

This article studies the targeted sequential inference of an optimal treatment rule (TR) and its mean reward in the non-exceptional case, i.e. , assuming that there is no stratum of the baseline covariates where treatment is neither beneficial nor harmful, and under a companion margin assumption. Our pivotal estimator, whose definition hinges on the targeted minimum loss estimation (TMLE) principle, actually infers the mean reward under the current estimate of the optimal TR. This data-adaptive statistical parameter is worthy of interest on its own. Our main result is a central limit theorem which enables the construction of confidence intervals on both mean rewards under the current estimate of the optimal TR and under the optimal TR itself. The asymptotic variance of the estimator takes the form of the variance of an efficient influence curve at a limiting distribution, allowing to discuss the efficiency of inference. As a by product, we also derive confidence intervals on two cumulated pseudo-regrets, a key notion in the study of bandits problems. A simulation study illustrates the procedure. One of the corner-stones of the theoretical study is a new maximal inequality for martingales with respect to the uniform entropy integral.

Testing Transitivity of Preferences on Two-Alternative Forced Choice Data

PubMed Central

Regenwetter, Michel; Dana, Jason; Davis-Stober, Clintin P.

2010-01-01

As Duncan Luce and other prominent scholars have pointed out on several occasions, testing algebraic models against empirical data raises difficult conceptual, mathematical, and statistical challenges. Empirical data often result from statistical sampling processes, whereas algebraic theories are nonprobabilistic. Many probabilistic specifications lead to statistical boundary problems and are subject to nontrivial order constrained statistical inference. The present paper discusses Luce's challenge for a particularly prominent axiom: Transitivity. The axiom of transitivity is a central component in many algebraic theories of preference and choice. We offer the currently most complete solution to the challenge in the case of transitivity of binary preference on the theory side and two-alternative forced choice on the empirical side, explicitly for up to five, and implicitly for up to seven, choice alternatives. We also discuss the relationship between our proposed solution and weak stochastic transitivity. We recommend to abandon the latter as a model of transitive individual preferences. PMID:21833217

TIME-DOMAIN METHODS FOR DIFFUSIVE TRANSPORT IN SOFT MATTER

PubMed Central

Fricks, John; Yao, Lingxing; Elston, Timothy C.; Gregory Forest, And M.

2015-01-01

Passive microrheology [12] utilizes measurements of noisy, entropic fluctuations (i.e., diffusive properties) of micron-scale spheres in soft matter to infer bulk frequency-dependent loss and storage moduli. Here, we are concerned exclusively with diffusion of Brownian particles in viscoelastic media, for which the Mason-Weitz theoretical-experimental protocol is ideal, and the more challenging inference of bulk viscoelastic moduli is decoupled. The diffusive theory begins with a generalized Langevin equation (GLE) with a memory drag law specified by a kernel [7, 16, 22, 23]. We start with a discrete formulation of the GLE as an autoregressive stochastic process governing microbead paths measured by particle tracking. For the inverse problem (recovery of the memory kernel from experimental data) we apply time series analysis (maximum likelihood estimators via the Kalman filter) directly to bead position data, an alternative to formulas based on mean-squared displacement statistics in frequency space. For direct modeling, we present statistically exact GLE algorithms for individual particle paths as well as statistical correlations for displacement and velocity. Our time-domain methods rest upon a generalization of well-known results for a single-mode exponential kernel [1, 7, 22, 23] to an arbitrary M-mode exponential series, for which the GLE is transformed to a vector Ornstein-Uhlenbeck process. PMID:26412904

Problem Solving as Probabilistic Inference with Subgoaling: Explaining Human Successes and Pitfalls in the Tower of Hanoi

PubMed Central

Donnarumma, Francesco; Maisto, Domenico; Pezzulo, Giovanni

2016-01-01

How do humans and other animals face novel problems for which predefined solutions are not available? Human problem solving links to flexible reasoning and inference rather than to slow trial-and-error learning. It has received considerable attention since the early days of cognitive science, giving rise to well known cognitive architectures such as SOAR and ACT-R, but its computational and brain mechanisms remain incompletely known. Furthermore, it is still unclear whether problem solving is a “specialized” domain or module of cognition, in the sense that it requires computations that are fundamentally different from those supporting perception and action systems. Here we advance a novel view of human problem solving as probabilistic inference with subgoaling. In this perspective, key insights from cognitive architectures are retained such as the importance of using subgoals to split problems into subproblems. However, here the underlying computations use probabilistic inference methods analogous to those that are increasingly popular in the study of perception and action systems. To test our model we focus on the widely used Tower of Hanoi (ToH) task, and show that our proposed method can reproduce characteristic idiosyncrasies of human problem solvers: their sensitivity to the “community structure” of the ToH and their difficulties in executing so-called “counterintuitive” movements. Our analysis reveals that subgoals have two key roles in probabilistic inference and problem solving. First, prior beliefs on (likely) useful subgoals carve the problem space and define an implicit metric for the problem at hand—a metric to which humans are sensitive. Second, subgoals are used as waypoints in the probabilistic problem solving inference and permit to find effective solutions that, when unavailable, lead to problem solving deficits. Our study thus suggests that a probabilistic inference scheme enhanced with subgoals provides a comprehensive framework to study problem solving and its deficits. PMID:27074140

Problem Solving as Probabilistic Inference with Subgoaling: Explaining Human Successes and Pitfalls in the Tower of Hanoi.

PubMed

Donnarumma, Francesco; Maisto, Domenico; Pezzulo, Giovanni

2016-04-01

How do humans and other animals face novel problems for which predefined solutions are not available? Human problem solving links to flexible reasoning and inference rather than to slow trial-and-error learning. It has received considerable attention since the early days of cognitive science, giving rise to well known cognitive architectures such as SOAR and ACT-R, but its computational and brain mechanisms remain incompletely known. Furthermore, it is still unclear whether problem solving is a "specialized" domain or module of cognition, in the sense that it requires computations that are fundamentally different from those supporting perception and action systems. Here we advance a novel view of human problem solving as probabilistic inference with subgoaling. In this perspective, key insights from cognitive architectures are retained such as the importance of using subgoals to split problems into subproblems. However, here the underlying computations use probabilistic inference methods analogous to those that are increasingly popular in the study of perception and action systems. To test our model we focus on the widely used Tower of Hanoi (ToH) task, and show that our proposed method can reproduce characteristic idiosyncrasies of human problem solvers: their sensitivity to the "community structure" of the ToH and their difficulties in executing so-called "counterintuitive" movements. Our analysis reveals that subgoals have two key roles in probabilistic inference and problem solving. First, prior beliefs on (likely) useful subgoals carve the problem space and define an implicit metric for the problem at hand-a metric to which humans are sensitive. Second, subgoals are used as waypoints in the probabilistic problem solving inference and permit to find effective solutions that, when unavailable, lead to problem solving deficits. Our study thus suggests that a probabilistic inference scheme enhanced with subgoals provides a comprehensive framework to study problem solving and its deficits.

Inferring Small Scale Dynamics from Aircraft Measurements of Tracers

NASA Technical Reports Server (NTRS)

Sparling, L. C.; Einaudi, Franco (Technical Monitor)

2000-01-01

The millions of ER-2 and DC-8 aircraft measurements of long-lived tracers in the Upper Troposphere/Lower Stratosphere (UT/LS) hold enormous potential as a source of statistical information about subgrid scale dynamics. Extracting this information however can be extremely difficult because the measurements are made along a 1-D transect through fields that are highly anisotropic in all three dimensions. Some of the challenges and limitations posed by both the instrumentation and platform are illustrated within the context of the problem of using the data to obtain an estimate of the dissipation scale. This presentation will also include some tutorial remarks about the conditional and two-point statistics used in the analysis.

Using Alien Coins to Test Whether Simple Inference Is Bayesian

ERIC Educational Resources Information Center

Cassey, Peter; Hawkins, Guy E.; Donkin, Chris; Brown, Scott D.

2016-01-01

Reasoning and inference are well-studied aspects of basic cognition that have been explained as statistically optimal Bayesian inference. Using a simplified experimental design, we conducted quantitative comparisons between Bayesian inference and human inference at the level of individuals. In 3 experiments, with more than 13,000 participants, we…

Students' Expressions of Uncertainty in Making Informal Inference When Engaged in a Statistical Investigation Using TinkerPlots

ERIC Educational Resources Information Center

Henriques, Ana; Oliveira, Hélia

2016-01-01

This paper reports on the results of a study investigating the potential to embed Informal Statistical Inference in statistical investigations, using TinkerPlots, for assisting 8th grade students' informal inferential reasoning to emerge, particularly their articulations of uncertainty. Data collection included students' written work on a…

Estimation of variance in Cox's regression model with shared gamma frailties.

PubMed

Andersen, P K; Klein, J P; Knudsen, K M; Tabanera y Palacios, R

1997-12-01

The Cox regression model with a shared frailty factor allows for unobserved heterogeneity or for statistical dependence between the observed survival times. Estimation in this model when the frailties are assumed to follow a gamma distribution is reviewed, and we address the problem of obtaining variance estimates for regression coefficients, frailty parameter, and cumulative baseline hazards using the observed nonparametric information matrix. A number of examples are given comparing this approach with fully parametric inference in models with piecewise constant baseline hazards.

Hard, harder, hardest: principal stratification, statistical identifiability, and the inherent difficulty of finding surrogate endpoints.

PubMed

Wolfson, Julian; Henn, Lisa

2014-01-01

In many areas of clinical investigation there is great interest in identifying and validating surrogate endpoints, biomarkers that can be measured a relatively short time after a treatment has been administered and that can reliably predict the effect of treatment on the clinical outcome of interest. However, despite dramatic advances in the ability to measure biomarkers, the recent history of clinical research is littered with failed surrogates. In this paper, we present a statistical perspective on why identifying surrogate endpoints is so difficult. We view the problem from the framework of causal inference, with a particular focus on the technique of principal stratification (PS), an approach which is appealing because the resulting estimands are not biased by unmeasured confounding. In many settings, PS estimands are not statistically identifiable and their degree of non-identifiability can be thought of as representing the statistical difficulty of assessing the surrogate value of a biomarker. In this work, we examine the identifiability issue and present key simplifying assumptions and enhanced study designs that enable the partial or full identification of PS estimands. We also present example situations where these assumptions and designs may or may not be feasible, providing insight into the problem characteristics which make the statistical evaluation of surrogate endpoints so challenging.

Hard, harder, hardest: principal stratification, statistical identifiability, and the inherent difficulty of finding surrogate endpoints

PubMed Central

2014-01-01

In many areas of clinical investigation there is great interest in identifying and validating surrogate endpoints, biomarkers that can be measured a relatively short time after a treatment has been administered and that can reliably predict the effect of treatment on the clinical outcome of interest. However, despite dramatic advances in the ability to measure biomarkers, the recent history of clinical research is littered with failed surrogates. In this paper, we present a statistical perspective on why identifying surrogate endpoints is so difficult. We view the problem from the framework of causal inference, with a particular focus on the technique of principal stratification (PS), an approach which is appealing because the resulting estimands are not biased by unmeasured confounding. In many settings, PS estimands are not statistically identifiable and their degree of non-identifiability can be thought of as representing the statistical difficulty of assessing the surrogate value of a biomarker. In this work, we examine the identifiability issue and present key simplifying assumptions and enhanced study designs that enable the partial or full identification of PS estimands. We also present example situations where these assumptions and designs may or may not be feasible, providing insight into the problem characteristics which make the statistical evaluation of surrogate endpoints so challenging. PMID:25342953

A method and knowledge base for automated inference of patient problems from structured data in an electronic medical record.

PubMed

Wright, Adam; Pang, Justine; Feblowitz, Joshua C; Maloney, Francine L; Wilcox, Allison R; Ramelson, Harley Z; Schneider, Louise I; Bates, David W

2011-01-01

Accurate knowledge of a patient's medical problems is critical for clinical decision making, quality measurement, research, billing and clinical decision support. Common structured sources of problem information include the patient problem list and billing data; however, these sources are often inaccurate or incomplete. To develop and validate methods of automatically inferring patient problems from clinical and billing data, and to provide a knowledge base for inferring problems. We identified 17 target conditions and designed and validated a set of rules for identifying patient problems based on medications, laboratory results, billing codes, and vital signs. A panel of physicians provided input on a preliminary set of rules. Based on this input, we tested candidate rules on a sample of 100,000 patient records to assess their performance compared to gold standard manual chart review. The physician panel selected a final rule for each condition, which was validated on an independent sample of 100,000 records to assess its accuracy. Seventeen rules were developed for inferring patient problems. Analysis using a validation set of 100,000 randomly selected patients showed high sensitivity (range: 62.8-100.0%) and positive predictive value (range: 79.8-99.6%) for most rules. Overall, the inference rules performed better than using either the problem list or billing data alone. We developed and validated a set of rules for inferring patient problems. These rules have a variety of applications, including clinical decision support, care improvement, augmentation of the problem list, and identification of patients for research cohorts.

Bayesian inference with historical data-based informative priors improves detection of differentially expressed genes

PubMed Central

Li, Ben; Sun, Zhaonan; He, Qing; Zhu, Yu; Qin, Zhaohui S.

2016-01-01

Motivation: Modern high-throughput biotechnologies such as microarray are capable of producing a massive amount of information for each sample. However, in a typical high-throughput experiment, only limited number of samples were assayed, thus the classical ‘large p, small n’ problem. On the other hand, rapid propagation of these high-throughput technologies has resulted in a substantial collection of data, often carried out on the same platform and using the same protocol. It is highly desirable to utilize the existing data when performing analysis and inference on a new dataset. Results: Utilizing existing data can be carried out in a straightforward fashion under the Bayesian framework in which the repository of historical data can be exploited to build informative priors and used in new data analysis. In this work, using microarray data, we investigate the feasibility and effectiveness of deriving informative priors from historical data and using them in the problem of detecting differentially expressed genes. Through simulation and real data analysis, we show that the proposed strategy significantly outperforms existing methods including the popular and state-of-the-art Bayesian hierarchical model-based approaches. Our work illustrates the feasibility and benefits of exploiting the increasingly available genomics big data in statistical inference and presents a promising practical strategy for dealing with the ‘large p, small n’ problem. Availability and implementation: Our method is implemented in R package IPBT, which is freely available from https://github.com/benliemory/IPBT. Contact: yuzhu@purdue.edu; zhaohui.qin@emory.edu Supplementary information: Supplementary data are available at Bioinformatics online. PMID:26519502

Using genetic data to strengthen causal inference in observational research.

PubMed

Pingault, Jean-Baptiste; O'Reilly, Paul F; Schoeler, Tabea; Ploubidis, George B; Rijsdijk, Frühling; Dudbridge, Frank

2018-06-05

Causal inference is essential across the biomedical, behavioural and social sciences.By progressing from confounded statistical associations to evidence of causal relationships, causal inference can reveal complex pathways underlying traits and diseases and help to prioritize targets for intervention. Recent progress in genetic epidemiology - including statistical innovation, massive genotyped data sets and novel computational tools for deep data mining - has fostered the intense development of methods exploiting genetic data and relatedness to strengthen causal inference in observational research. In this Review, we describe how such genetically informed methods differ in their rationale, applicability and inherent limitations and outline how they should be integrated in the future to offer a rich causal inference toolbox.

Risk, statistical inference, and the law of evidence: the use of epidemiological data in toxic tort cases.

PubMed

Brannigan, V M; Bier, V M; Berg, C

1992-09-01

Toxic torts are product liability cases dealing with alleged injuries due to chemical or biological hazards such as radiation, thalidomide, or Agent Orange. Toxic tort cases typically rely more heavily than other product liability cases on indirect or statistical proof of injury. There have been numerous theoretical analyses of statistical proof of injury in toxic tort cases. However, there have been only a handful of actual legal decisions regarding the use of such statistical evidence, and most of those decisions have been inconclusive. Recently, a major case from the Fifth Circuit, involving allegations that Benedectin (a morning sickness drug) caused birth defects, was decided entirely on the basis of statistical inference. This paper examines both the conceptual basis of that decision, and also the relationships among statistical inference, scientific evidence, and the rules of product liability in general.

NON-EXTENSIVE STATISTICS TO THE COSMOLOGICAL LITHIUM PROBLEM

DOE Office of Scientific and Technical Information (OSTI.GOV)

Hou, S. Q.; He, J. J.; Parikh, A.

Big Bang nucleosynthesis (BBN) theory predicts the abundances of the light elements D, {sup 3}He, {sup 4}He, and {sup 7}Li produced in the early universe. The primordial abundances of D and {sup 4}He inferred from observational data are in good agreement with predictions, however, BBN theory overestimates the primordial {sup 7}Li abundance by about a factor of three. This is the so-called “cosmological lithium problem.” Solutions to this problem using conventional astrophysics and nuclear physics have not been successful over the past few decades, probably indicating the presence of new physics during the era of BBN. We have investigated themore » impact on BBN predictions of adopting a generalized distribution to describe the velocities of nucleons in the framework of Tsallis non-extensive statistics. This generalized velocity distribution is characterized by a parameter q , and reduces to the usually assumed Maxwell–Boltzmann distribution for q  = 1. We find excellent agreement between predicted and observed primordial abundances of D, {sup 4}He, and {sup 7}Li for 1.069 ≤  q  ≤ 1.082, suggesting a possible new solution to the cosmological lithium problem.« less

On the inherent competition between valid and spurious inductive inferences in Boolean data

NASA Astrophysics Data System (ADS)

Andrecut, M.

Inductive inference is the process of extracting general rules from specific observations. This problem also arises in the analysis of biological networks, such as genetic regulatory networks, where the interactions are complex and the observations are incomplete. A typical task in these problems is to extract general interaction rules as combinations of Boolean covariates, that explain a measured response variable. The inductive inference process can be considered as an incompletely specified Boolean function synthesis problem. This incompleteness of the problem will also generate spurious inferences, which are a serious threat to valid inductive inference rules. Using random Boolean data as a null model, here we attempt to measure the competition between valid and spurious inductive inference rules from a given data set. We formulate two greedy search algorithms, which synthesize a given Boolean response variable in a sparse disjunct normal form, and respectively a sparse generalized algebraic normal form of the variables from the observation data, and we evaluate numerically their performance.

Adaptive design optimization: a mutual information-based approach to model discrimination in cognitive science.

PubMed

Cavagnaro, Daniel R; Myung, Jay I; Pitt, Mark A; Kujala, Janne V

2010-04-01

Discriminating among competing statistical models is a pressing issue for many experimentalists in the field of cognitive science. Resolving this issue begins with designing maximally informative experiments. To this end, the problem to be solved in adaptive design optimization is identifying experimental designs under which one can infer the underlying model in the fewest possible steps. When the models under consideration are nonlinear, as is often the case in cognitive science, this problem can be impossible to solve analytically without simplifying assumptions. However, as we show in this letter, a full solution can be found numerically with the help of a Bayesian computational trick derived from the statistics literature, which recasts the problem as a probability density simulation in which the optimal design is the mode of the density. We use a utility function based on mutual information and give three intuitive interpretations of the utility function in terms of Bayesian posterior estimates. As a proof of concept, we offer a simple example application to an experiment on memory retention.

Making statistical inferences about software reliability

NASA Technical Reports Server (NTRS)

Miller, Douglas R.

1988-01-01

Failure times of software undergoing random debugging can be modelled as order statistics of independent but nonidentically distributed exponential random variables. Using this model inferences can be made about current reliability and, if debugging continues, future reliability. This model also shows the difficulty inherent in statistical verification of very highly reliable software such as that used by digital avionics in commercial aircraft.

Comparing Trend and Gap Statistics across Tests: Distributional Change Using Ordinal Methods and Bayesian Inference

ERIC Educational Resources Information Center

Denbleyker, John Nickolas

2012-01-01

The shortcomings of the proportion above cut (PAC) statistic used so prominently in the educational landscape renders it a very problematic measure for making correct inferences with student test data. The limitations of PAC-based statistics are more pronounced with cross-test comparisons due to their dependency on cut-score locations. A better…

Aspects of First Year Statistics Students' Reasoning When Performing Intuitive Analysis of Variance: Effects of Within- and Between-Group Variability

ERIC Educational Resources Information Center

Trumpower, David L.

2015-01-01

Making inferences about population differences based on samples of data, that is, performing intuitive analysis of variance (IANOVA), is common in everyday life. However, the intuitive reasoning of individuals when making such inferences (even following statistics instruction), often differs from the normative logic of formal statistics. The…

The Problem of Auto-Correlation in Parasitology

PubMed Central

Pollitt, Laura C.; Reece, Sarah E.; Mideo, Nicole; Nussey, Daniel H.; Colegrave, Nick

2012-01-01

Explaining the contribution of host and pathogen factors in driving infection dynamics is a major ambition in parasitology. There is increasing recognition that analyses based on single summary measures of an infection (e.g., peak parasitaemia) do not adequately capture infection dynamics and so, the appropriate use of statistical techniques to analyse dynamics is necessary to understand infections and, ultimately, control parasites. However, the complexities of within-host environments mean that tracking and analysing pathogen dynamics within infections and among hosts poses considerable statistical challenges. Simple statistical models make assumptions that will rarely be satisfied in data collected on host and parasite parameters. In particular, model residuals (unexplained variance in the data) should not be correlated in time or space. Here we demonstrate how failure to account for such correlations can result in incorrect biological inference from statistical analysis. We then show how mixed effects models can be used as a powerful tool to analyse such repeated measures data in the hope that this will encourage better statistical practices in parasitology. PMID:22511865

Difference to Inference: teaching logical and statistical reasoning through on-line interactivity.

PubMed

Malloy, T E

2001-05-01

Difference to Inference is an on-line JAVA program that simulates theory testing and falsification through research design and data collection in a game format. The program, based on cognitive and epistemological principles, is designed to support learning of the thinking skills underlying deductive and inductive logic and statistical reasoning. Difference to Inference has database connectivity so that game scores can be counted as part of course grades.

The coverage of a random sample from a biological community.

PubMed

Engen, S

1975-03-01

A taxonomic group will frequently have a large number of species with small abundances. When a sample is drawn at random from this group, one is therefore faced with the problem that a large proportion of the species will not be discovered. A general definition of quantitative measures of "sample coverage" is proposed, and the problem of statistical inference is considered for two special cases, (1) the actual total relative abundance of those species that are represented in the sample, and (2) their relative contribution to the information index of diversity. The analysis is based on a extended version of the negative binomial species frequency model. The results are tabulated.

Analyzing Single-Molecule Time Series via Nonparametric Bayesian Inference

PubMed Central

Hines, Keegan E.; Bankston, John R.; Aldrich, Richard W.

2015-01-01

The ability to measure the properties of proteins at the single-molecule level offers an unparalleled glimpse into biological systems at the molecular scale. The interpretation of single-molecule time series has often been rooted in statistical mechanics and the theory of Markov processes. While existing analysis methods have been useful, they are not without significant limitations including problems of model selection and parameter nonidentifiability. To address these challenges, we introduce the use of nonparametric Bayesian inference for the analysis of single-molecule time series. These methods provide a flexible way to extract structure from data instead of assuming models beforehand. We demonstrate these methods with applications to several diverse settings in single-molecule biophysics. This approach provides a well-constrained and rigorously grounded method for determining the number of biophysical states underlying single-molecule data. PMID:25650922

Comparing nonparametric Bayesian tree priors for clonal reconstruction of tumors.

PubMed

Deshwar, Amit G; Vembu, Shankar; Morris, Quaid

2015-01-01

Statistical machine learning methods, especially nonparametric Bayesian methods, have become increasingly popular to infer clonal population structure of tumors. Here we describe the treeCRP, an extension of the Chinese restaurant process (CRP), a popular construction used in nonparametric mixture models, to infer the phylogeny and genotype of major subclonal lineages represented in the population of cancer cells. We also propose new split-merge updates tailored to the subclonal reconstruction problem that improve the mixing time of Markov chains. In comparisons with the tree-structured stick breaking prior used in PhyloSub, we demonstrate superior mixing and running time using the treeCRP with our new split-merge procedures. We also show that given the same number of samples, TSSB and treeCRP have similar ability to recover the subclonal structure of a tumor…

A statistical inference approach for the retrieval of the atmospheric ozone profile from simulated satellite measurements of solar backscattered ultraviolet radiation

NASA Technical Reports Server (NTRS)

Bonavito, N. L.; Gordon, C. L.; Inguva, R.; Serafino, G. N.; Barnes, R. A.

1994-01-01

NASA's Mission to Planet Earth (MTPE) will address important interdisciplinary and environmental issues such as global warming, ozone depletion, deforestation, acid rain, and the like with its long term satellite observations of the Earth and with its comprehensive Data and Information System. Extensive sets of satellite observations supporting MTPE will be provided by the Earth Observing System (EOS), while more specific process related observations will be provided by smaller Earth Probes. MTPE will use data from ground and airborne scientific investigations to supplement and validate the global observations obtained from satellite imagery, while the EOS satellites will support interdisciplinary research and model development. This is important for understanding the processes that control the global environment and for improving the prediction of events. In this paper we illustrate the potential for powerful artificial intelligence (AI) techniques when used in the analysis of the formidable problems that exist in the NASA Earth Science programs and of those to be encountered in the future MTPE and EOS programs. These techniques, based on the logical and probabilistic reasoning aspects of plausible inference, strongly emphasize the synergetic relation between data and information. As such, they are ideally suited for the analysis of the massive data streams to be provided by both MTPE and EOS. To demonstrate this, we address both the satellite imagery and model enhancement issues for the problem of ozone profile retrieval through a method based on plausible scientific inferencing. Since in the retrieval problem, the atmospheric ozone profile that is consistent with a given set of measured radiances may not be unique, an optimum statistical method is used to estimate a 'best' profile solution from the radiances and from additional a priori information.

Foundational Principles for Large-Scale Inference: Illustrations Through Correlation Mining.

PubMed

Hero, Alfred O; Rajaratnam, Bala

2016-01-01

When can reliable inference be drawn in fue "Big Data" context? This paper presents a framework for answering this fundamental question in the context of correlation mining, wifu implications for general large scale inference. In large scale data applications like genomics, connectomics, and eco-informatics fue dataset is often variable-rich but sample-starved: a regime where the number n of acquired samples (statistical replicates) is far fewer than fue number p of observed variables (genes, neurons, voxels, or chemical constituents). Much of recent work has focused on understanding the computational complexity of proposed methods for "Big Data". Sample complexity however has received relatively less attention, especially in the setting when the sample size n is fixed, and the dimension p grows without bound. To address fuis gap, we develop a unified statistical framework that explicitly quantifies the sample complexity of various inferential tasks. Sampling regimes can be divided into several categories: 1) the classical asymptotic regime where fue variable dimension is fixed and fue sample size goes to infinity; 2) the mixed asymptotic regime where both variable dimension and sample size go to infinity at comparable rates; 3) the purely high dimensional asymptotic regime where the variable dimension goes to infinity and the sample size is fixed. Each regime has its niche but only the latter regime applies to exa cale data dimension. We illustrate this high dimensional framework for the problem of correlation mining, where it is the matrix of pairwise and partial correlations among the variables fua t are of interest. Correlation mining arises in numerous applications and subsumes the regression context as a special case. we demonstrate various regimes of correlation mining based on the unifying perspective of high dimensional learning rates and sample complexity for different structured covariance models and different inference tasks.

A method and knowledge base for automated inference of patient problems from structured data in an electronic medical record

PubMed Central

Pang, Justine; Feblowitz, Joshua C; Maloney, Francine L; Wilcox, Allison R; Ramelson, Harley Z; Schneider, Louise I; Bates, David W

2011-01-01

Background Accurate knowledge of a patient's medical problems is critical for clinical decision making, quality measurement, research, billing and clinical decision support. Common structured sources of problem information include the patient problem list and billing data; however, these sources are often inaccurate or incomplete. Objective To develop and validate methods of automatically inferring patient problems from clinical and billing data, and to provide a knowledge base for inferring problems. Study design and methods We identified 17 target conditions and designed and validated a set of rules for identifying patient problems based on medications, laboratory results, billing codes, and vital signs. A panel of physicians provided input on a preliminary set of rules. Based on this input, we tested candidate rules on a sample of 100 000 patient records to assess their performance compared to gold standard manual chart review. The physician panel selected a final rule for each condition, which was validated on an independent sample of 100 000 records to assess its accuracy. Results Seventeen rules were developed for inferring patient problems. Analysis using a validation set of 100 000 randomly selected patients showed high sensitivity (range: 62.8–100.0%) and positive predictive value (range: 79.8–99.6%) for most rules. Overall, the inference rules performed better than using either the problem list or billing data alone. Conclusion We developed and validated a set of rules for inferring patient problems. These rules have a variety of applications, including clinical decision support, care improvement, augmentation of the problem list, and identification of patients for research cohorts. PMID:21613643

Inference as Prediction

ERIC Educational Resources Information Center

Watson, Jane

2007-01-01

Inference, or decision making, is seen in curriculum documents as the final step in a statistical investigation. For a formal statistical enquiry this may be associated with sophisticated tests involving probability distributions. For young students without the mathematical background to perform such tests, it is still possible to draw informal…

A Framework for Thinking about Informal Statistical Inference

ERIC Educational Resources Information Center

Makar, Katie; Rubin, Andee

2009-01-01

Informal inferential reasoning has shown some promise in developing students' deeper understanding of statistical processes. This paper presents a framework to think about three key principles of informal inference--generalizations "beyond the data," probabilistic language, and data as evidence. The authors use primary school classroom…

Sensitivity to the Sampling Process Emerges From the Principle of Efficiency.

PubMed

Jara-Ettinger, Julian; Sun, Felix; Schulz, Laura; Tenenbaum, Joshua B

2018-05-01

Humans can seamlessly infer other people's preferences, based on what they do. Broadly, two types of accounts have been proposed to explain different aspects of this ability. The first account focuses on spatial information: Agents' efficient navigation in space reveals what they like. The second account focuses on statistical information: Uncommon choices reveal stronger preferences. Together, these two lines of research suggest that we have two distinct capacities for inferring preferences. Here we propose that this is not the case, and that spatial-based and statistical-based preference inferences can be explained by the assumption that agents are efficient alone. We show that people's sensitivity to spatial and statistical information when they infer preferences is best predicted by a computational model of the principle of efficiency, and that this model outperforms dual-system models, even when the latter are fit to participant judgments. Our results suggest that, as adults, a unified understanding of agency under the principle of efficiency underlies our ability to infer preferences. Copyright © 2018 Cognitive Science Society, Inc.

Decision-theoretic saliency: computational principles, biological plausibility, and implications for neurophysiology and psychophysics.

PubMed

Gao, Dashan; Vasconcelos, Nuno

2009-01-01

A decision-theoretic formulation of visual saliency, first proposed for top-down processing (object recognition) (Gao & Vasconcelos, 2005a), is extended to the problem of bottom-up saliency. Under this formulation, optimality is defined in the minimum probability of error sense, under a constraint of computational parsimony. The saliency of the visual features at a given location of the visual field is defined as the power of those features to discriminate between the stimulus at the location and a null hypothesis. For bottom-up saliency, this is the set of visual features that surround the location under consideration. Discrimination is defined in an information-theoretic sense and the optimal saliency detector derived for a class of stimuli that complies with known statistical properties of natural images. It is shown that under the assumption that saliency is driven by linear filtering, the optimal detector consists of what is usually referred to as the standard architecture of V1: a cascade of linear filtering, divisive normalization, rectification, and spatial pooling. The optimal detector is also shown to replicate the fundamental properties of the psychophysics of saliency: stimulus pop-out, saliency asymmetries for stimulus presence versus absence, disregard of feature conjunctions, and Weber's law. Finally, it is shown that the optimal saliency architecture can be applied to the solution of generic inference problems. In particular, for the class of stimuli studied, it performs the three fundamental operations of statistical inference: assessment of probabilities, implementation of Bayes decision rule, and feature selection.

Statistical inference for extended or shortened phase II studies based on Simon's two-stage designs.

PubMed

Zhao, Junjun; Yu, Menggang; Feng, Xi-Ping

2015-06-07

Simon's two-stage designs are popular choices for conducting phase II clinical trials, especially in the oncology trials to reduce the number of patients placed on ineffective experimental therapies. Recently Koyama and Chen (2008) discussed how to conduct proper inference for such studies because they found that inference procedures used with Simon's designs almost always ignore the actual sampling plan used. In particular, they proposed an inference method for studies when the actual second stage sample sizes differ from planned ones. We consider an alternative inference method based on likelihood ratio. In particular, we order permissible sample paths under Simon's two-stage designs using their corresponding conditional likelihood. In this way, we can calculate p-values using the common definition: the probability of obtaining a test statistic value at least as extreme as that observed under the null hypothesis. In addition to providing inference for a couple of scenarios where Koyama and Chen's method can be difficult to apply, the resulting estimate based on our method appears to have certain advantage in terms of inference properties in many numerical simulations. It generally led to smaller biases and narrower confidence intervals while maintaining similar coverages. We also illustrated the two methods in a real data setting. Inference procedures used with Simon's designs almost always ignore the actual sampling plan. Reported P-values, point estimates and confidence intervals for the response rate are not usually adjusted for the design's adaptiveness. Proper statistical inference procedures should be used.

Efficient fuzzy Bayesian inference algorithms for incorporating expert knowledge in parameter estimation

NASA Astrophysics Data System (ADS)

Rajabi, Mohammad Mahdi; Ataie-Ashtiani, Behzad

2016-05-01

Bayesian inference has traditionally been conceived as the proper framework for the formal incorporation of expert knowledge in parameter estimation of groundwater models. However, conventional Bayesian inference is incapable of taking into account the imprecision essentially embedded in expert provided information. In order to solve this problem, a number of extensions to conventional Bayesian inference have been introduced in recent years. One of these extensions is 'fuzzy Bayesian inference' which is the result of integrating fuzzy techniques into Bayesian statistics. Fuzzy Bayesian inference has a number of desirable features which makes it an attractive approach for incorporating expert knowledge in the parameter estimation process of groundwater models: (1) it is well adapted to the nature of expert provided information, (2) it allows to distinguishably model both uncertainty and imprecision, and (3) it presents a framework for fusing expert provided information regarding the various inputs of the Bayesian inference algorithm. However an important obstacle in employing fuzzy Bayesian inference in groundwater numerical modeling applications is the computational burden, as the required number of numerical model simulations often becomes extremely exhaustive and often computationally infeasible. In this paper, a novel approach of accelerating the fuzzy Bayesian inference algorithm is proposed which is based on using approximate posterior distributions derived from surrogate modeling, as a screening tool in the computations. The proposed approach is first applied to a synthetic test case of seawater intrusion (SWI) in a coastal aquifer. It is shown that for this synthetic test case, the proposed approach decreases the number of required numerical simulations by an order of magnitude. Then the proposed approach is applied to a real-world test case involving three-dimensional numerical modeling of SWI in Kish Island, located in the Persian Gulf. An expert elicitation methodology is developed and applied to the real-world test case in order to provide a road map for the use of fuzzy Bayesian inference in groundwater modeling applications.

Massive optimal data compression and density estimation for scalable, likelihood-free inference in cosmology

NASA Astrophysics Data System (ADS)

Alsing, Justin; Wandelt, Benjamin; Feeney, Stephen

2018-07-01

Many statistical models in cosmology can be simulated forwards but have intractable likelihood functions. Likelihood-free inference methods allow us to perform Bayesian inference from these models using only forward simulations, free from any likelihood assumptions or approximations. Likelihood-free inference generically involves simulating mock data and comparing to the observed data; this comparison in data space suffers from the curse of dimensionality and requires compression of the data to a small number of summary statistics to be tractable. In this paper, we use massive asymptotically optimal data compression to reduce the dimensionality of the data space to just one number per parameter, providing a natural and optimal framework for summary statistic choice for likelihood-free inference. Secondly, we present the first cosmological application of Density Estimation Likelihood-Free Inference (DELFI), which learns a parametrized model for joint distribution of data and parameters, yielding both the parameter posterior and the model evidence. This approach is conceptually simple, requires less tuning than traditional Approximate Bayesian Computation approaches to likelihood-free inference and can give high-fidelity posteriors from orders of magnitude fewer forward simulations. As an additional bonus, it enables parameter inference and Bayesian model comparison simultaneously. We demonstrate DELFI with massive data compression on an analysis of the joint light-curve analysis supernova data, as a simple validation case study. We show that high-fidelity posterior inference is possible for full-scale cosmological data analyses with as few as ˜104 simulations, with substantial scope for further improvement, demonstrating the scalability of likelihood-free inference to large and complex cosmological data sets.

Applying a multiobjective metaheuristic inspired by honey bees to phylogenetic inference.

PubMed

Santander-Jiménez, Sergio; Vega-Rodríguez, Miguel A

2013-10-01

The development of increasingly popular multiobjective metaheuristics has allowed bioinformaticians to deal with optimization problems in computational biology where multiple objective functions must be taken into account. One of the most relevant research topics that can benefit from these techniques is phylogenetic inference. Throughout the years, different researchers have proposed their own view about the reconstruction of ancestral evolutionary relationships among species. As a result, biologists often report different phylogenetic trees from a same dataset when considering distinct optimality principles. In this work, we detail a multiobjective swarm intelligence approach based on the novel Artificial Bee Colony algorithm for inferring phylogenies. The aim of this paper is to propose a complementary view of phylogenetics according to the maximum parsimony and maximum likelihood criteria, in order to generate a set of phylogenetic trees that represent a compromise between these principles. Experimental results on a variety of nucleotide data sets and statistical studies highlight the relevance of the proposal with regard to other multiobjective algorithms and state-of-the-art biological methods. Copyright © 2013 Elsevier Ireland Ltd. All rights reserved.

Bayesian Nonparametric Inference – Why and How

PubMed Central

Müller, Peter; Mitra, Riten

2013-01-01

We review inference under models with nonparametric Bayesian (BNP) priors. The discussion follows a set of examples for some common inference problems. The examples are chosen to highlight problems that are challenging for standard parametric inference. We discuss inference for density estimation, clustering, regression and for mixed effects models with random effects distributions. While we focus on arguing for the need for the flexibility of BNP models, we also review some of the more commonly used BNP models, thus hopefully answering a bit of both questions, why and how to use BNP. PMID:24368932

Gaussian copula as a likelihood function for environmental models

NASA Astrophysics Data System (ADS)

Wani, O.; Espadas, G.; Cecinati, F.; Rieckermann, J.

2017-12-01

Parameter estimation of environmental models always comes with uncertainty. To formally quantify this parametric uncertainty, a likelihood function needs to be formulated, which is defined as the probability of observations given fixed values of the parameter set. A likelihood function allows us to infer parameter values from observations using Bayes' theorem. The challenge is to formulate a likelihood function that reliably describes the error generating processes which lead to the observed monitoring data, such as rainfall and runoff. If the likelihood function is not representative of the error statistics, the parameter inference will give biased parameter values. Several uncertainty estimation methods that are currently being used employ Gaussian processes as a likelihood function, because of their favourable analytical properties. Box-Cox transformation is suggested to deal with non-symmetric and heteroscedastic errors e.g. for flow data which are typically more uncertain in high flows than in periods with low flows. Problem with transformations is that the results are conditional on hyper-parameters, for which it is difficult to formulate the analyst's belief a priori. In an attempt to address this problem, in this research work we suggest learning the nature of the error distribution from the errors made by the model in the "past" forecasts. We use a Gaussian copula to generate semiparametric error distributions . 1) We show that this copula can be then used as a likelihood function to infer parameters, breaking away from the practice of using multivariate normal distributions. Based on the results from a didactical example of predicting rainfall runoff, 2) we demonstrate that the copula captures the predictive uncertainty of the model. 3) Finally, we find that the properties of autocorrelation and heteroscedasticity of errors are captured well by the copula, eliminating the need to use transforms. In summary, our findings suggest that copulas are an interesting departure from the usage of fully parametric distributions as likelihood functions - and they could help us to better capture the statistical properties of errors and make more reliable predictions.

Stationarity: Wanted dead or alive?

USGS Publications Warehouse

Lins, Larry F.; Cohn, Timothy A.

2011-01-01

Aligning engineering practice with natural process behavior would appear, on its face, to be a prudent and reasonable course of action. However, if we do not understand the long-term characteristics of hydroclimatic processes, how does one find the prudent and reasonable course needed for water management? We consider this question in light of three aspects of existing and unresolved issues affecting hydroclimatic variability and statistical inference: Hurst-Kolmogorov phenomena; the complications long-term persistence introduces with respect to statistical understanding; and the dependence of process understanding on arbitrary sampling choices. These problems are not easily addressed. In such circumstances, humility may be more important than physics; a simple model with well-understood flaws may be preferable to a sophisticated model whose correspondence to reality is uncertain.

Does bad inference drive out good?

PubMed

Marozzi, Marco

2015-07-01

The (mis)use of statistics in practice is widely debated, and a field where the debate is particularly active is medicine. Many scholars emphasize that a large proportion of published medical research contains statistical errors. It has been noted that top class journals like Nature Medicine and The New England Journal of Medicine publish a considerable proportion of papers that contain statistical errors and poorly document the application of statistical methods. This paper joins the debate on the (mis)use of statistics in the medical literature. Even though the validation process of a statistical result may be quite elusive, a careful assessment of underlying assumptions is central in medicine as well as in other fields where a statistical method is applied. Unfortunately, a careful assessment of underlying assumptions is missing in many papers, including those published in top class journals. In this paper, it is shown that nonparametric methods are good alternatives to parametric methods when the assumptions for the latter ones are not satisfied. A key point to solve the problem of the misuse of statistics in the medical literature is that all journals have their own statisticians to review the statistical method/analysis section in each submitted paper. © 2015 Wiley Publishing Asia Pty Ltd.

Statistical mechanics of complex neural systems and high dimensional data

NASA Astrophysics Data System (ADS)

Advani, Madhu; Lahiri, Subhaneil; Ganguli, Surya

2013-03-01

Recent experimental advances in neuroscience have opened new vistas into the immense complexity of neuronal networks. This proliferation of data challenges us on two parallel fronts. First, how can we form adequate theoretical frameworks for understanding how dynamical network processes cooperate across widely disparate spatiotemporal scales to solve important computational problems? Second, how can we extract meaningful models of neuronal systems from high dimensional datasets? To aid in these challenges, we give a pedagogical review of a collection of ideas and theoretical methods arising at the intersection of statistical physics, computer science and neurobiology. We introduce the interrelated replica and cavity methods, which originated in statistical physics as powerful ways to quantitatively analyze large highly heterogeneous systems of many interacting degrees of freedom. We also introduce the closely related notion of message passing in graphical models, which originated in computer science as a distributed algorithm capable of solving large inference and optimization problems involving many coupled variables. We then show how both the statistical physics and computer science perspectives can be applied in a wide diversity of contexts to problems arising in theoretical neuroscience and data analysis. Along the way we discuss spin glasses, learning theory, illusions of structure in noise, random matrices, dimensionality reduction and compressed sensing, all within the unified formalism of the replica method. Moreover, we review recent conceptual connections between message passing in graphical models, and neural computation and learning. Overall, these ideas illustrate how statistical physics and computer science might provide a lens through which we can uncover emergent computational functions buried deep within the dynamical complexities of neuronal networks.

Spurious correlations and inference in landscape genetics

Treesearch

Samuel A. Cushman; Erin L. Landguth

2010-01-01

Reliable interpretation of landscape genetic analyses depends on statistical methods that have high power to identify the correct process driving gene flow while rejecting incorrect alternative hypotheses. Little is known about statistical power and inference in individual-based landscape genetics. Our objective was to evaluate the power of causalmodelling with partial...

The Philosophical Foundations of Prescriptive Statements and Statistical Inference

ERIC Educational Resources Information Center

Sun, Shuyan; Pan, Wei

2011-01-01

From the perspectives of the philosophy of science and statistical inference, we discuss the challenges of making prescriptive statements in quantitative research articles. We first consider the prescriptive nature of educational research and argue that prescriptive statements are a necessity in educational research. The logic of deduction,…

Diagnosis of Misalignment in Overhung Rotor using the K-S Statistic and A2 Test

NASA Astrophysics Data System (ADS)

Garikapati, Diwakar; Pacharu, RaviKumar; Munukurthi, Rama Satya Satyanarayana

2018-02-01

Vibration measurement at the bearings of rotating machinery has become a useful technique for diagnosing incipient fault conditions. In particular, vibration measurement can be used to detect unbalance in rotor, bearing failure, gear problems or misalignment between a motor shaft and coupled shaft. This is a particular problem encountered in turbines, ID fans and FD fans used for power generation. For successful fault diagnosis, it is important to adopt motor current signature analysis (MCSA) techniques capable of identifying the faults. It is also useful to develop techniques for inferring information such as the severity of fault. It is proposed that modeling the cumulative distribution function of motor current signals with respect to appropriate theoretical distributions, and quantifying the goodness of fit with the Kolmogorov-Smirnov (KS) statistic and A2 test offers a suitable signal feature for diagnosis. This paper demonstrates the successful comparison of the K-S feature and A2 test for discriminating the misalignment fault from normal function.

Evidence reasoning method for constructing conditional probability tables in a Bayesian network of multimorbidity.

PubMed

Du, Yuanwei; Guo, Yubin

2015-01-01

The intrinsic mechanism of multimorbidity is difficult to recognize and prediction and diagnosis are difficult to carry out accordingly. Bayesian networks can help to diagnose multimorbidity in health care, but it is difficult to obtain the conditional probability table (CPT) because of the lack of clinically statistical data. Today, expert knowledge and experience are increasingly used in training Bayesian networks in order to help predict or diagnose diseases, but the CPT in Bayesian networks is usually irrational or ineffective for ignoring realistic constraints especially in multimorbidity. In order to solve these problems, an evidence reasoning (ER) approach is employed to extract and fuse inference data from experts using a belief distribution and recursive ER algorithm, based on which evidence reasoning method for constructing conditional probability tables in Bayesian network of multimorbidity is presented step by step. A multimorbidity numerical example is used to demonstrate the method and prove its feasibility and application. Bayesian network can be determined as long as the inference assessment is inferred by each expert according to his/her knowledge or experience. Our method is more effective than existing methods for extracting expert inference data accurately and is fused effectively for constructing CPTs in a Bayesian network of multimorbidity.

Exploring the Connection Between Sampling Problems in Bayesian Inference and Statistical Mechanics

NASA Technical Reports Server (NTRS)

Pohorille, Andrew

2006-01-01

The Bayesian and statistical mechanical communities often share the same objective in their work - estimating and integrating probability distribution functions (pdfs) describing stochastic systems, models or processes. Frequently, these pdfs are complex functions of random variables exhibiting multiple, well separated local minima. Conventional strategies for sampling such pdfs are inefficient, sometimes leading to an apparent non-ergodic behavior. Several recently developed techniques for handling this problem have been successfully applied in statistical mechanics. In the multicanonical and Wang-Landau Monte Carlo (MC) methods, the correct pdfs are recovered from uniform sampling of the parameter space by iteratively establishing proper weighting factors connecting these distributions. Trivial generalizations allow for sampling from any chosen pdf. The closely related transition matrix method relies on estimating transition probabilities between different states. All these methods proved to generate estimates of pdfs with high statistical accuracy. In another MC technique, parallel tempering, several random walks, each corresponding to a different value of a parameter (e.g. "temperature"), are generated and occasionally exchanged using the Metropolis criterion. This method can be considered as a statistically correct version of simulated annealing. An alternative approach is to represent the set of independent variables as a Hamiltonian system. Considerab!e progress has been made in understanding how to ensure that the system obeys the equipartition theorem or, equivalently, that coupling between the variables is correctly described. Then a host of techniques developed for dynamical systems can be used. Among them, probably the most powerful is the Adaptive Biasing Force method, in which thermodynamic integration and biased sampling are combined to yield very efficient estimates of pdfs. The third class of methods deals with transitions between states described by rate constants. These problems are isomorphic with chemical kinetics problems. Recently, several efficient techniques for this purpose have been developed based on the approach originally proposed by Gillespie. Although the utility of the techniques mentioned above for Bayesian problems has not been determined, further research along these lines is warranted

A Selective Overview of Variable Selection in High Dimensional Feature Space

PubMed Central

Fan, Jianqing

2010-01-01

High dimensional statistical problems arise from diverse fields of scientific research and technological development. Variable selection plays a pivotal role in contemporary statistical learning and scientific discoveries. The traditional idea of best subset selection methods, which can be regarded as a specific form of penalized likelihood, is computationally too expensive for many modern statistical applications. Other forms of penalized likelihood methods have been successfully developed over the last decade to cope with high dimensionality. They have been widely applied for simultaneously selecting important variables and estimating their effects in high dimensional statistical inference. In this article, we present a brief account of the recent developments of theory, methods, and implementations for high dimensional variable selection. What limits of the dimensionality such methods can handle, what the role of penalty functions is, and what the statistical properties are rapidly drive the advances of the field. The properties of non-concave penalized likelihood and its roles in high dimensional statistical modeling are emphasized. We also review some recent advances in ultra-high dimensional variable selection, with emphasis on independence screening and two-scale methods. PMID:21572976

Robust Strategy for Rocket Engine Health Monitoring

NASA Technical Reports Server (NTRS)

Santi, L. Michael

2001-01-01

Monitoring the health of rocket engine systems is essentially a two-phase process. The acquisition phase involves sensing physical conditions at selected locations, converting physical inputs to electrical signals, conditioning the signals as appropriate to establish scale or filter interference, and recording results in a form that is easy to interpret. The inference phase involves analysis of results from the acquisition phase, comparison of analysis results to established health measures, and assessment of health indications. A variety of analytical tools may be employed in the inference phase of health monitoring. These tools can be separated into three broad categories: statistical, rule based, and model based. Statistical methods can provide excellent comparative measures of engine operating health. They require well-characterized data from an ensemble of "typical" engines, or "golden" data from a specific test assumed to define the operating norm in order to establish reliable comparative measures. Statistical methods are generally suitable for real-time health monitoring because they do not deal with the physical complexities of engine operation. The utility of statistical methods in rocket engine health monitoring is hindered by practical limits on the quantity and quality of available data. This is due to the difficulty and high cost of data acquisition, the limited number of available test engines, and the problem of simulating flight conditions in ground test facilities. In addition, statistical methods incur a penalty for disregarding flow complexity and are therefore limited in their ability to define performance shift causality. Rule based methods infer the health state of the engine system based on comparison of individual measurements or combinations of measurements with defined health norms or rules. This does not mean that rule based methods are necessarily simple. Although binary yes-no health assessment can sometimes be established by relatively simple rules, the causality assignment needed for refined health monitoring often requires an exceptionally complex rule base involving complicated logical maps. Structuring the rule system to be clear and unambiguous can be difficult, and the expert input required to maintain a large logic network and associated rule base can be prohibitive.

Knowledge dimensions in hypothesis test problems

NASA Astrophysics Data System (ADS)

Krishnan, Saras; Idris, Noraini

2012-05-01

The reformation in statistics education over the past two decades has predominantly shifted the focus of statistical teaching and learning from procedural understanding to conceptual understanding. The emphasis of procedural understanding is on the formulas and calculation procedures. Meanwhile, conceptual understanding emphasizes students knowing why they are using a particular formula or executing a specific procedure. In addition, the Revised Bloom's Taxonomy offers a twodimensional framework to describe learning objectives comprising of the six revised cognition levels of original Bloom's taxonomy and four knowledge dimensions. Depending on the level of complexities, the four knowledge dimensions essentially distinguish basic understanding from the more connected understanding. This study identifiesthe factual, procedural and conceptual knowledgedimensions in hypothesis test problems. Hypothesis test being an important tool in making inferences about a population from sample informationis taught in many introductory statistics courses. However, researchers find that students in these courses still have difficulty in understanding the underlying concepts of hypothesis test. Past studies also show that even though students can perform the hypothesis testing procedure, they may not understand the rationale of executing these steps or know how to apply them in novel contexts. Besides knowing the procedural steps in conducting a hypothesis test, students must have fundamental statistical knowledge and deep understanding of the underlying inferential concepts such as sampling distribution and central limit theorem. By identifying the knowledge dimensions of hypothesis test problems in this study, suitable instructional and assessment strategies can be developed in future to enhance students' learning of hypothesis test as a valuable inferential tool.

Robust biological parametric mapping: an improved technique for multimodal brain image analysis

NASA Astrophysics Data System (ADS)

Yang, Xue; Beason-Held, Lori; Resnick, Susan M.; Landman, Bennett A.

2011-03-01

Mapping the quantitative relationship between structure and function in the human brain is an important and challenging problem. Numerous volumetric, surface, region of interest and voxelwise image processing techniques have been developed to statistically assess potential correlations between imaging and non-imaging metrics. Recently, biological parametric mapping has extended the widely popular statistical parametric approach to enable application of the general linear model to multiple image modalities (both for regressors and regressands) along with scalar valued observations. This approach offers great promise for direct, voxelwise assessment of structural and functional relationships with multiple imaging modalities. However, as presented, the biological parametric mapping approach is not robust to outliers and may lead to invalid inferences (e.g., artifactual low p-values) due to slight mis-registration or variation in anatomy between subjects. To enable widespread application of this approach, we introduce robust regression and robust inference in the neuroimaging context of application of the general linear model. Through simulation and empirical studies, we demonstrate that our robust approach reduces sensitivity to outliers without substantial degradation in power. The robust approach and associated software package provides a reliable way to quantitatively assess voxelwise correlations between structural and functional neuroimaging modalities.

Estimating pseudocounts and fold changes for digital expression measurements.

PubMed

Erhard, Florian

2018-06-19

Fold changes from count based high-throughput experiments such as RNA-seq suffer from a zero-frequency problem. To circumvent division by zero, so-called pseudocounts are added to make all observed counts strictly positive. The magnitude of pseudocounts for digital expression measurements and on which stage of the analysis they are introduced remained an arbitrary choice. Moreover, in the strict sense, fold changes are not quantities that can be computed. Instead, due to the stochasticity involved in the experiments, they must be estimated by statistical inference. Here, we build on a statistical framework for fold changes, where pseudocounts correspond to the parameters of the prior distribution used for Bayesian inference of the fold change. We show that arbirary and widely used choices for applying pseudocounts can lead to biased results. As a statistical rigorous alternative, we propose and test an empirical Bayes procedure to choose appropriate pseudocounts. Moreover, we introduce the novel estimator Ψ LFC for fold changes showing favorable properties with small counts and smaller deviations from the truth in simulations and real data compared to existing methods. Our results have direct implications for entities with few reads in sequencing experiments, and indirectly also affect results for entities with many reads. Ψ LFC is available as an R package under https://github.com/erhard-lab/lfc (Apache 2.0 license); R scripts to generate all figures are available at zenodo (doi:10.5281/zenodo.1163029).

Working towards a scalable model of problem-based learning instruction in undergraduate engineering education

NASA Astrophysics Data System (ADS)

Mantri, Archana

2014-05-01

The intent of the study presented in this paper is to show that the model of problem-based learning (PBL) can be made scalable by designing curriculum around a set of open-ended problems (OEPs). The detailed statistical analysis of the data collected to measure the effects of traditional and PBL instructions for three courses in Electronics and Communication Engineering, namely Analog Electronics, Digital Electronics and Pulse, Digital & Switching Circuits is presented here. It measures the effects of pedagogy, gender and cognitive styles on the knowledge, skill and attitude of the students. The study was conducted two times with content designed around same set of OEPs but with two different trained facilitators for all the three courses. The repeatability of results for effects of the independent parameters on dependent parameters is studied and inferences are drawn.

Intuitive statistics by 8-month-old infants

PubMed Central

Xu, Fei; Garcia, Vashti

2008-01-01

Human learners make inductive inferences based on small amounts of data: we generalize from samples to populations and vice versa. The academic discipline of statistics formalizes these intuitive statistical inferences. What is the origin of this ability? We report six experiments investigating whether 8-month-old infants are “intuitive statisticians.” Our results showed that, given a sample, the infants were able to make inferences about the population from which the sample had been drawn. Conversely, given information about the entire population of relatively small size, the infants were able to make predictions about the sample. Our findings provide evidence that infants possess a powerful mechanism for inductive learning, either using heuristics or basic principles of probability. This ability to make inferences based on samples or information about the population develops early and in the absence of schooling or explicit teaching. Human infants may be rational learners from very early in development. PMID:18378901

Assessing colour-dependent occupation statistics inferred from galaxy group catalogues

NASA Astrophysics Data System (ADS)

Campbell, Duncan; van den Bosch, Frank C.; Hearin, Andrew; Padmanabhan, Nikhil; Berlind, Andreas; Mo, H. J.; Tinker, Jeremy; Yang, Xiaohu

2015-09-01

We investigate the ability of current implementations of galaxy group finders to recover colour-dependent halo occupation statistics. To test the fidelity of group catalogue inferred statistics, we run three different group finders used in the literature over a mock that includes galaxy colours in a realistic manner. Overall, the resulting mock group catalogues are remarkably similar, and most colour-dependent statistics are recovered with reasonable accuracy. However, it is also clear that certain systematic errors arise as a consequence of correlated errors in group membership determination, central/satellite designation, and halo mass assignment. We introduce a new statistic, the halo transition probability (HTP), which captures the combined impact of all these errors. As a rule of thumb, errors tend to equalize the properties of distinct galaxy populations (i.e. red versus blue galaxies or centrals versus satellites), and to result in inferred occupation statistics that are more accurate for red galaxies than for blue galaxies. A statistic that is particularly poorly recovered from the group catalogues is the red fraction of central galaxies as a function of halo mass. Group finders do a good job in recovering galactic conformity, but also have a tendency to introduce weak conformity when none is present. We conclude that proper inference of colour-dependent statistics from group catalogues is best achieved using forward modelling (i.e. running group finders over mock data) or by implementing a correction scheme based on the HTP, as long as the latter is not too strongly model dependent.

Bayesian inference with historical data-based informative priors improves detection of differentially expressed genes.

PubMed

Li, Ben; Sun, Zhaonan; He, Qing; Zhu, Yu; Qin, Zhaohui S

2016-03-01

Modern high-throughput biotechnologies such as microarray are capable of producing a massive amount of information for each sample. However, in a typical high-throughput experiment, only limited number of samples were assayed, thus the classical 'large p, small n' problem. On the other hand, rapid propagation of these high-throughput technologies has resulted in a substantial collection of data, often carried out on the same platform and using the same protocol. It is highly desirable to utilize the existing data when performing analysis and inference on a new dataset. Utilizing existing data can be carried out in a straightforward fashion under the Bayesian framework in which the repository of historical data can be exploited to build informative priors and used in new data analysis. In this work, using microarray data, we investigate the feasibility and effectiveness of deriving informative priors from historical data and using them in the problem of detecting differentially expressed genes. Through simulation and real data analysis, we show that the proposed strategy significantly outperforms existing methods including the popular and state-of-the-art Bayesian hierarchical model-based approaches. Our work illustrates the feasibility and benefits of exploiting the increasingly available genomics big data in statistical inference and presents a promising practical strategy for dealing with the 'large p, small n' problem. Our method is implemented in R package IPBT, which is freely available from https://github.com/benliemory/IPBT CONTACT: yuzhu@purdue.edu; zhaohui.qin@emory.edu Supplementary data are available at Bioinformatics online. © The Author 2015. Published by Oxford University Press. All rights reserved. For Permissions, please e-mail: journals.permissions@oup.com.

Social networks help to infer causality in the tumor microenvironment.

PubMed

Crespo, Isaac; Doucey, Marie-Agnès; Xenarios, Ioannis

2016-03-15

Networks have become a popular way to conceptualize a system of interacting elements, such as electronic circuits, social communication, metabolism or gene regulation. Network inference, analysis, and modeling techniques have been developed in different areas of science and technology, such as computer science, mathematics, physics, and biology, with an active interdisciplinary exchange of concepts and approaches. However, some concepts seem to belong to a specific field without a clear transferability to other domains. At the same time, it is increasingly recognized that within some biological systems--such as the tumor microenvironment--where different types of resident and infiltrating cells interact to carry out their functions, the complexity of the system demands a theoretical framework, such as statistical inference, graph analysis and dynamical models, in order to asses and study the information derived from high-throughput experimental technologies. In this article we propose to adopt and adapt the concepts of influence and investment from the world of social network analysis to biological problems, and in particular to apply this approach to infer causality in the tumor microenvironment. We showed that constructing a bidirectional network of influence between cell and cell communication molecules allowed us to determine the direction of inferred regulations at the expression level and correctly recapitulate cause-effect relationships described in literature. This work constitutes an example of a transfer of knowledge and concepts from the world of social network analysis to biomedical research, in particular to infer network causality in biological networks. This causality elucidation is essential to model the homeostatic response of biological systems to internal and external factors, such as environmental conditions, pathogens or treatments.

Clustering Genes of Common Evolutionary History

PubMed Central

Gori, Kevin; Suchan, Tomasz; Alvarez, Nadir; Goldman, Nick; Dessimoz, Christophe

2016-01-01

Phylogenetic inference can potentially result in a more accurate tree using data from multiple loci. However, if the loci are incongruent—due to events such as incomplete lineage sorting or horizontal gene transfer—it can be misleading to infer a single tree. To address this, many previous contributions have taken a mechanistic approach, by modeling specific processes. Alternatively, one can cluster loci without assuming how these incongruencies might arise. Such “process-agnostic” approaches typically infer a tree for each locus and cluster these. There are, however, many possible combinations of tree distance and clustering methods; their comparative performance in the context of tree incongruence is largely unknown. Furthermore, because standard model selection criteria such as AIC cannot be applied to problems with a variable number of topologies, the issue of inferring the optimal number of clusters is poorly understood. Here, we perform a large-scale simulation study of phylogenetic distances and clustering methods to infer loci of common evolutionary history. We observe that the best-performing combinations are distances accounting for branch lengths followed by spectral clustering or Ward’s method. We also introduce two statistical tests to infer the optimal number of clusters and show that they strongly outperform the silhouette criterion, a general-purpose heuristic. We illustrate the usefulness of the approach by 1) identifying errors in a previous phylogenetic analysis of yeast species and 2) identifying topological incongruence among newly sequenced loci of the globeflower fly genus Chiastocheta. We release treeCl, a new program to cluster genes of common evolutionary history (http://git.io/treeCl). PMID:26893301

Asymptotic inference in system identification for the atom maser.

PubMed

Catana, Catalin; van Horssen, Merlijn; Guta, Madalin

2012-11-28

System identification is closely related to control theory and plays an increasing role in quantum engineering. In the quantum set-up, system identification is usually equated to process tomography, i.e. estimating a channel by probing it repeatedly with different input states. However, for quantum dynamical systems such as quantum Markov processes, it is more natural to consider the estimation based on continuous measurements of the output, with a given input that may be stationary. We address this problem using asymptotic statistics tools, for the specific example of estimating the Rabi frequency of an atom maser. We compute the Fisher information of different measurement processes as well as the quantum Fisher information of the atom maser, and establish the local asymptotic normality of these statistical models. The statistical notions can be expressed in terms of spectral properties of certain deformed Markov generators, and the connection to large deviations is briefly discussed.

Exercise Sensing and Pose Recovery Inference Tool (ESPRIT) - A Compact Stereo-based Motion Capture Solution For Exercise Monitoring

NASA Technical Reports Server (NTRS)

Lee, Mun Wai

2015-01-01

Crew exercise is important during long-duration space flight not only for maintaining health and fitness but also for preventing adverse health problems, such as losses in muscle strength and bone density. Monitoring crew exercise via motion capture and kinematic analysis aids understanding of the effects of microgravity on exercise and helps ensure that exercise prescriptions are effective. Intelligent Automation, Inc., has developed ESPRIT to monitor exercise activities, detect body markers, extract image features, and recover three-dimensional (3D) kinematic body poses. The system relies on prior knowledge and modeling of the human body and on advanced statistical inference techniques to achieve robust and accurate motion capture. In Phase I, the company demonstrated motion capture of several exercises, including walking, curling, and dead lifting. Phase II efforts focused on enhancing algorithms and delivering an ESPRIT prototype for testing and demonstration.

Reconstruction of stochastic temporal networks through diffusive arrival times

NASA Astrophysics Data System (ADS)

Li, Xun; Li, Xiang

2017-06-01

Temporal networks have opened a new dimension in defining and quantification of complex interacting systems. Our ability to identify and reproduce time-resolved interaction patterns is, however, limited by the restricted access to empirical individual-level data. Here we propose an inverse modelling method based on first-arrival observations of the diffusion process taking place on temporal networks. We describe an efficient coordinate-ascent implementation for inferring stochastic temporal networks that builds in particular but not exclusively on the null model assumption of mutually independent interaction sequences at the dyadic level. The results of benchmark tests applied on both synthesized and empirical network data sets confirm the validity of our algorithm, showing the feasibility of statistically accurate inference of temporal networks only from moderate-sized samples of diffusion cascades. Our approach provides an effective and flexible scheme for the temporally augmented inverse problems of network reconstruction and has potential in a broad variety of applications.

Improved Doubly Robust Estimation when Data are Monotonely Coarsened, with Application to Longitudinal Studies with Dropout

PubMed Central

Tsiatis, Anastasios A.; Davidian, Marie; Cao, Weihua

2010-01-01

Summary A routine challenge is that of making inference on parameters in a statistical model of interest from longitudinal data subject to drop out, which are a special case of the more general setting of monotonely coarsened data. Considerable recent attention has focused on doubly robust estimators, which in this context involve positing models for both the missingness (more generally, coarsening) mechanism and aspects of the distribution of the full data, that have the appealing property of yielding consistent inferences if only one of these models is correctly specified. Doubly robust estimators have been criticized for potentially disastrous performance when both of these models are even only mildly misspecified. We propose a doubly robust estimator applicable in general monotone coarsening problems that achieves comparable or improved performance relative to existing doubly robust methods, which we demonstrate via simulation studies and by application to data from an AIDS clinical trial. PMID:20731640

Gaussian process inference for estimating pharmacokinetic parameters of dynamic contrast-enhanced MR images.

PubMed

Wang, Shijun; Liu, Peter; Turkbey, Baris; Choyke, Peter; Pinto, Peter; Summers, Ronald M

2012-01-01

In this paper, we propose a new pharmacokinetic model for parameter estimation of dynamic contrast-enhanced (DCE) MRI by using Gaussian process inference. Our model is based on the Tofts dual-compartment model for the description of tracer kinetics and the observed time series from DCE-MRI is treated as a Gaussian stochastic process. The parameter estimation is done through a maximum likelihood approach and we propose a variant of the coordinate descent method to solve this likelihood maximization problem. The new model was shown to outperform a baseline method on simulated data. Parametric maps generated on prostate DCE data with the new model also provided better enhancement of tumors, lower intensity on false positives, and better boundary delineation when compared with the baseline method. New statistical parameter maps from the process model were also found to be informative, particularly when paired with the PK parameter maps.

Reconstruction of stochastic temporal networks through diffusive arrival times

PubMed Central

Li, Xun; Li, Xiang

2017-01-01

Temporal networks have opened a new dimension in defining and quantification of complex interacting systems. Our ability to identify and reproduce time-resolved interaction patterns is, however, limited by the restricted access to empirical individual-level data. Here we propose an inverse modelling method based on first-arrival observations of the diffusion process taking place on temporal networks. We describe an efficient coordinate-ascent implementation for inferring stochastic temporal networks that builds in particular but not exclusively on the null model assumption of mutually independent interaction sequences at the dyadic level. The results of benchmark tests applied on both synthesized and empirical network data sets confirm the validity of our algorithm, showing the feasibility of statistically accurate inference of temporal networks only from moderate-sized samples of diffusion cascades. Our approach provides an effective and flexible scheme for the temporally augmented inverse problems of network reconstruction and has potential in a broad variety of applications. PMID:28604687

Deconvolution of mixing time series on a graph

PubMed Central

Blocker, Alexander W.; Airoldi, Edoardo M.

2013-01-01

In many applications we are interested in making inference on latent time series from indirect measurements, which are often low-dimensional projections resulting from mixing or aggregation. Positron emission tomography, super-resolution, and network traffic monitoring are some examples. Inference in such settings requires solving a sequence of ill-posed inverse problems, yt = Axt, where the projection mechanism provides information on A. We consider problems in which A specifies mixing on a graph of times series that are bursty and sparse. We develop a multilevel state-space model for mixing times series and an efficient approach to inference. A simple model is used to calibrate regularization parameters that lead to efficient inference in the multilevel state-space model. We apply this method to the problem of estimating point-to-point traffic flows on a network from aggregate measurements. Our solution outperforms existing methods for this problem, and our two-stage approach suggests an efficient inference strategy for multilevel models of multivariate time series. PMID:25309135

Inferring causal relationships between phenotypes using summary statistics from genome-wide association studies.

PubMed

Meng, Xiang-He; Shen, Hui; Chen, Xiang-Ding; Xiao, Hong-Mei; Deng, Hong-Wen

2018-03-01

Genome-wide association studies (GWAS) have successfully identified numerous genetic variants associated with diverse complex phenotypes and diseases, and provided tremendous opportunities for further analyses using summary association statistics. Recently, Pickrell et al. developed a robust method for causal inference using independent putative causal SNPs. However, this method may fail to infer the causal relationship between two phenotypes when only a limited number of independent putative causal SNPs identified. Here, we extended Pickrell's method to make it more applicable for the general situations. We extended the causal inference method by replacing the putative causal SNPs with the lead SNPs (the set of the most significant SNPs in each independent locus) and tested the performance of our extended method using both simulation and empirical data. Simulations suggested that when the same number of genetic variants is used, our extended method had similar distribution of test statistic under the null model as well as comparable power under the causal model compared with the original method by Pickrell et al. But in practice, our extended method would generally be more powerful because the number of independent lead SNPs was often larger than the number of independent putative causal SNPs. And including more SNPs, on the other hand, would not cause more false positives. By applying our extended method to summary statistics from GWAS for blood metabolites and femoral neck bone mineral density (FN-BMD), we successfully identified ten blood metabolites that may causally influence FN-BMD. We extended a causal inference method for inferring putative causal relationship between two phenotypes using summary statistics from GWAS, and identified a number of potential causal metabolites for FN-BMD, which may provide novel insights into the pathophysiological mechanisms underlying osteoporosis.

In defence of model-based inference in phylogeography

PubMed Central

Beaumont, Mark A.; Nielsen, Rasmus; Robert, Christian; Hey, Jody; Gaggiotti, Oscar; Knowles, Lacey; Estoup, Arnaud; Panchal, Mahesh; Corander, Jukka; Hickerson, Mike; Sisson, Scott A.; Fagundes, Nelson; Chikhi, Lounès; Beerli, Peter; Vitalis, Renaud; Cornuet, Jean-Marie; Huelsenbeck, John; Foll, Matthieu; Yang, Ziheng; Rousset, Francois; Balding, David; Excoffier, Laurent

2017-01-01

Recent papers have promoted the view that model-based methods in general, and those based on Approximate Bayesian Computation (ABC) in particular, are flawed in a number of ways, and are therefore inappropriate for the analysis of phylogeographic data. These papers further argue that Nested Clade Phylogeographic Analysis (NCPA) offers the best approach in statistical phylogeography. In order to remove the confusion and misconceptions introduced by these papers, we justify and explain the reasoning behind model-based inference. We argue that ABC is a statistically valid approach, alongside other computational statistical techniques that have been successfully used to infer parameters and compare models in population genetics. We also examine the NCPA method and highlight numerous deficiencies, either when used with single or multiple loci. We further show that the ages of clades are carelessly used to infer ages of demographic events, that these ages are estimated under a simple model of panmixia and population stationarity but are then used under different and unspecified models to test hypotheses, a usage the invalidates these testing procedures. We conclude by encouraging researchers to study and use model-based inference in population genetics. PMID:29284924

Statistical inference for remote sensing-based estimates of net deforestation

Treesearch

Ronald E. McRoberts; Brian F. Walters

2012-01-01

Statistical inference requires expression of an estimate in probabilistic terms, usually in the form of a confidence interval. An approach to constructing confidence intervals for remote sensing-based estimates of net deforestation is illustrated. The approach is based on post-classification methods using two independent forest/non-forest classifications because...

The epistemological status of general circulation models

NASA Astrophysics Data System (ADS)

Loehle, Craig

2018-03-01

Forecasts of both likely anthropogenic effects on climate and consequent effects on nature and society are based on large, complex software tools called general circulation models (GCMs). Forecasts generated by GCMs have been used extensively in policy decisions related to climate change. However, the relation between underlying physical theories and results produced by GCMs is unclear. In the case of GCMs, many discretizations and approximations are made, and simulating Earth system processes is far from simple and currently leads to some results with unknown energy balance implications. Statistical testing of GCM forecasts for degree of agreement with data would facilitate assessment of fitness for use. If model results need to be put on an anomaly basis due to model bias, then both visual and quantitative measures of model fit depend strongly on the reference period used for normalization, making testing problematic. Epistemology is here applied to problems of statistical inference during testing, the relationship between the underlying physics and the models, the epistemic meaning of ensemble statistics, problems of spatial and temporal scale, the existence or not of an unforced null for climate fluctuations, the meaning of existing uncertainty estimates, and other issues. Rigorous reasoning entails carefully quantifying levels of uncertainty.

Considerations in the statistical analysis of clinical trials in periodontitis.

PubMed

Imrey, P B

1986-05-01

Adult periodontitis has been described as a chronic infectious process exhibiting sporadic, acute exacerbations which cause quantal, localized losses of dental attachment. Many analytic problems of periodontal trials are similar to those of other chronic diseases. However, the episodic, localized, infrequent, and relatively unpredictable behavior of exacerbations, coupled with measurement error difficulties, cause some specific problems. Considerable controversy exists as to the proper selection and treatment of multiple site data from the same patient for group comparisons for epidemiologic or therapeutic evaluative purposes. This paper comments, with varying degrees of emphasis, on several issues pertinent to the analysis of periodontal trials. Considerable attention is given to the ways in which measurement variability may distort analytic results. Statistical treatments of multiple site data for descriptive summaries are distinguished from treatments for formal statistical inference to validate therapeutic effects. Evidence suggesting that sites behave independently is contested. For inferential analyses directed at therapeutic or preventive effects, analytic models based on site independence are deemed unsatisfactory. Methods of summarization that may yield more powerful analyses than all-site mean scores, while retaining appropriate treatment of inter-site associations, are suggested. Brief comments and opinions on an assortment of other issues in clinical trial analysis are preferred.

Influence of valproate on language functions in children with epilepsy.

PubMed

Doo, Jin Woong; Kim, Soon Chul; Kim, Sun Jun

2018-01-01

The aim of the current study was to assess the influences of valproate (VPA) on the language functions in newly diagnosed pediatric patients with epilepsy. We reviewed medical records of 53 newly diagnosed patients with epilepsy, who were being treated with VPA monotherapy (n=53; 22 male patients and 31 female patients). The subjects underwent standardized language tests, at least twice, before and after the initiation of VPA. The standardized language tests used were The Test of Language Problem Solving Abilities, a Korean version of The Expressive/Receptive Language Function Test, and the Urimal Test of Articulation and Phonology. Since all the patients analyzed spoke Korean as their first language, we used Korean language tests to reduce the bias within the data. All the language parameters of the Test of Language Problem Solving Abilities slightly improved after the initiation of VPA in the 53 pediatric patients with epilepsy (mean age: 11.6±3.2years), but only "prediction" was statistically significant (determining cause, 14.9±5.1 to 15.5±4.3; making inference, 16.1±5.8 to 16.9±5.6; prediction, 11.1±4.9 to 11.9±4.2; total score of TOPS, 42.0±14.4 to 44.2±12.5). The patients treated with VPA also exhibited a small extension in mean length of utterance in words (MLU-w) when responding, but this was not statistically significant (determining cause, 5.4±2.0 to 5.7±1.6; making inference, 5.8±2.2 to 6.0±1.8; prediction, 5.9±2.5 to 5.9±2.1; total, 5.7±2.1 to 5.9±1.7). The administration of VPA led to a slight, but not statistically significant, improvement in the receptive language function (range: 144.7±41.1 to 148.2±39.7). Finally, there were no statistically significant changes in the percentage of articulation performance after taking VPA. Therefore, our data suggested that VPA did not have negative impact on the language function, but rather slightly improved problem-solving abilities. Copyright © 2017 Elsevier Inc. All rights reserved.

Progressive statistics for studies in sports medicine and exercise science.

PubMed

Hopkins, William G; Marshall, Stephen W; Batterham, Alan M; Hanin, Juri

2009-01-01

Statistical guidelines and expert statements are now available to assist in the analysis and reporting of studies in some biomedical disciplines. We present here a more progressive resource for sample-based studies, meta-analyses, and case studies in sports medicine and exercise science. We offer forthright advice on the following controversial or novel issues: using precision of estimation for inferences about population effects in preference to null-hypothesis testing, which is inadequate for assessing clinical or practical importance; justifying sample size via acceptable precision or confidence for clinical decisions rather than via adequate power for statistical significance; showing SD rather than SEM, to better communicate the magnitude of differences in means and nonuniformity of error; avoiding purely nonparametric analyses, which cannot provide inferences about magnitude and are unnecessary; using regression statistics in validity studies, in preference to the impractical and biased limits of agreement; making greater use of qualitative methods to enrich sample-based quantitative projects; and seeking ethics approval for public access to the depersonalized raw data of a study, to address the need for more scrutiny of research and better meta-analyses. Advice on less contentious issues includes the following: using covariates in linear models to adjust for confounders, to account for individual differences, and to identify potential mechanisms of an effect; using log transformation to deal with nonuniformity of effects and error; identifying and deleting outliers; presenting descriptive, effect, and inferential statistics in appropriate formats; and contending with bias arising from problems with sampling, assignment, blinding, measurement error, and researchers' prejudices. This article should advance the field by stimulating debate, promoting innovative approaches, and serving as a useful checklist for authors, reviewers, and editors.

MIDER: Network Inference with Mutual Information Distance and Entropy Reduction

PubMed Central

Villaverde, Alejandro F.; Ross, John; Morán, Federico; Banga, Julio R.

2014-01-01

The prediction of links among variables from a given dataset is a task referred to as network inference or reverse engineering. It is an open problem in bioinformatics and systems biology, as well as in other areas of science. Information theory, which uses concepts such as mutual information, provides a rigorous framework for addressing it. While a number of information-theoretic methods are already available, most of them focus on a particular type of problem, introducing assumptions that limit their generality. Furthermore, many of these methods lack a publicly available implementation. Here we present MIDER, a method for inferring network structures with information theoretic concepts. It consists of two steps: first, it provides a representation of the network in which the distance among nodes indicates their statistical closeness. Second, it refines the prediction of the existing links to distinguish between direct and indirect interactions and to assign directionality. The method accepts as input time-series data related to some quantitative features of the network nodes (such as e.g. concentrations, if the nodes are chemical species). It takes into account time delays between variables, and allows choosing among several definitions and normalizations of mutual information. It is general purpose: it may be applied to any type of network, cellular or otherwise. A Matlab implementation including source code and data is freely available (http://www.iim.csic.es/~gingproc/mider.html). The performance of MIDER has been evaluated on seven different benchmark problems that cover the main types of cellular networks, including metabolic, gene regulatory, and signaling. Comparisons with state of the art information–theoretic methods have demonstrated the competitive performance of MIDER, as well as its versatility. Its use does not demand any a priori knowledge from the user; the default settings and the adaptive nature of the method provide good results for a wide range of problems without requiring tuning. PMID:24806471

A Self-Organizing State-Space-Model Approach for Parameter Estimation in Hodgkin-Huxley-Type Models of Single Neurons

PubMed Central

Vavoulis, Dimitrios V.; Straub, Volko A.; Aston, John A. D.; Feng, Jianfeng

2012-01-01

Traditional approaches to the problem of parameter estimation in biophysical models of neurons and neural networks usually adopt a global search algorithm (for example, an evolutionary algorithm), often in combination with a local search method (such as gradient descent) in order to minimize the value of a cost function, which measures the discrepancy between various features of the available experimental data and model output. In this study, we approach the problem of parameter estimation in conductance-based models of single neurons from a different perspective. By adopting a hidden-dynamical-systems formalism, we expressed parameter estimation as an inference problem in these systems, which can then be tackled using a range of well-established statistical inference methods. The particular method we used was Kitagawa's self-organizing state-space model, which was applied on a number of Hodgkin-Huxley-type models using simulated or actual electrophysiological data. We showed that the algorithm can be used to estimate a large number of parameters, including maximal conductances, reversal potentials, kinetics of ionic currents, measurement and intrinsic noise, based on low-dimensional experimental data and sufficiently informative priors in the form of pre-defined constraints imposed on model parameters. The algorithm remained operational even when very noisy experimental data were used. Importantly, by combining the self-organizing state-space model with an adaptive sampling algorithm akin to the Covariance Matrix Adaptation Evolution Strategy, we achieved a significant reduction in the variance of parameter estimates. The algorithm did not require the explicit formulation of a cost function and it was straightforward to apply on compartmental models and multiple data sets. Overall, the proposed methodology is particularly suitable for resolving high-dimensional inference problems based on noisy electrophysiological data and, therefore, a potentially useful tool in the construction of biophysical neuron models. PMID:22396632

MIDER: network inference with mutual information distance and entropy reduction.

PubMed

Villaverde, Alejandro F; Ross, John; Morán, Federico; Banga, Julio R

2014-01-01

The prediction of links among variables from a given dataset is a task referred to as network inference or reverse engineering. It is an open problem in bioinformatics and systems biology, as well as in other areas of science. Information theory, which uses concepts such as mutual information, provides a rigorous framework for addressing it. While a number of information-theoretic methods are already available, most of them focus on a particular type of problem, introducing assumptions that limit their generality. Furthermore, many of these methods lack a publicly available implementation. Here we present MIDER, a method for inferring network structures with information theoretic concepts. It consists of two steps: first, it provides a representation of the network in which the distance among nodes indicates their statistical closeness. Second, it refines the prediction of the existing links to distinguish between direct and indirect interactions and to assign directionality. The method accepts as input time-series data related to some quantitative features of the network nodes (such as e.g. concentrations, if the nodes are chemical species). It takes into account time delays between variables, and allows choosing among several definitions and normalizations of mutual information. It is general purpose: it may be applied to any type of network, cellular or otherwise. A Matlab implementation including source code and data is freely available (http://www.iim.csic.es/~gingproc/mider.html). The performance of MIDER has been evaluated on seven different benchmark problems that cover the main types of cellular networks, including metabolic, gene regulatory, and signaling. Comparisons with state of the art information-theoretic methods have demonstrated the competitive performance of MIDER, as well as its versatility. Its use does not demand any a priori knowledge from the user; the default settings and the adaptive nature of the method provide good results for a wide range of problems without requiring tuning.

Approximation and inference methods for stochastic biochemical kinetics—a tutorial review

NASA Astrophysics Data System (ADS)

Schnoerr, David; Sanguinetti, Guido; Grima, Ramon

2017-03-01

Stochastic fluctuations of molecule numbers are ubiquitous in biological systems. Important examples include gene expression and enzymatic processes in living cells. Such systems are typically modelled as chemical reaction networks whose dynamics are governed by the chemical master equation. Despite its simple structure, no analytic solutions to the chemical master equation are known for most systems. Moreover, stochastic simulations are computationally expensive, making systematic analysis and statistical inference a challenging task. Consequently, significant effort has been spent in recent decades on the development of efficient approximation and inference methods. This article gives an introduction to basic modelling concepts as well as an overview of state of the art methods. First, we motivate and introduce deterministic and stochastic methods for modelling chemical networks, and give an overview of simulation and exact solution methods. Next, we discuss several approximation methods, including the chemical Langevin equation, the system size expansion, moment closure approximations, time-scale separation approximations and hybrid methods. We discuss their various properties and review recent advances and remaining challenges for these methods. We present a comparison of several of these methods by means of a numerical case study and highlight some of their respective advantages and disadvantages. Finally, we discuss the problem of inference from experimental data in the Bayesian framework and review recent methods developed the literature. In summary, this review gives a self-contained introduction to modelling, approximations and inference methods for stochastic chemical kinetics.

Multiple hot-deck imputation for network inference from RNA sequencing data.

PubMed

Imbert, Alyssa; Valsesia, Armand; Le Gall, Caroline; Armenise, Claudia; Lefebvre, Gregory; Gourraud, Pierre-Antoine; Viguerie, Nathalie; Villa-Vialaneix, Nathalie

2018-05-15

Network inference provides a global view of the relations existing between gene expression in a given transcriptomic experiment (often only for a restricted list of chosen genes). However, it is still a challenging problem: even if the cost of sequencing techniques has decreased over the last years, the number of samples in a given experiment is still (very) small compared to the number of genes. We propose a method to increase the reliability of the inference when RNA-seq expression data have been measured together with an auxiliary dataset that can provide external information on gene expression similarity between samples. Our statistical approach, hd-MI, is based on imputation for samples without available RNA-seq data that are considered as missing data but are observed on the secondary dataset. hd-MI can improve the reliability of the inference for missing rates up to 30% and provides more stable networks with a smaller number of false positive edges. On a biological point of view, hd-MI was also found relevant to infer networks from RNA-seq data acquired in adipose tissue during a nutritional intervention in obese individuals. In these networks, novel links between genes were highlighted, as well as an improved comparability between the two steps of the nutritional intervention. Software and sample data are available as an R package, RNAseqNet, that can be downloaded from the Comprehensive R Archive Network (CRAN). alyssa.imbert@inra.fr or nathalie.villa-vialaneix@inra.fr. Supplementary data are available at Bioinformatics online.

A Bayesian state-space approach for damage detection and classification

NASA Astrophysics Data System (ADS)

Dzunic, Zoran; Chen, Justin G.; Mobahi, Hossein; Büyüköztürk, Oral; Fisher, John W.

2017-11-01

The problem of automatic damage detection in civil structures is complex and requires a system that can interpret collected sensor data into meaningful information. We apply our recently developed switching Bayesian model for dependency analysis to the problems of damage detection and classification. The model relies on a state-space approach that accounts for noisy measurement processes and missing data, which also infers the statistical temporal dependency between measurement locations signifying the potential flow of information within the structure. A Gibbs sampling algorithm is used to simultaneously infer the latent states, parameters of the state dynamics, the dependence graph, and any changes in behavior. By employing a fully Bayesian approach, we are able to characterize uncertainty in these variables via their posterior distribution and provide probabilistic estimates of the occurrence of damage or a specific damage scenario. We also implement a single class classification method which is more realistic for most real world situations where training data for a damaged structure is not available. We demonstrate the methodology with experimental test data from a laboratory model structure and accelerometer data from a real world structure during different environmental and excitation conditions.

A Fiducial Approach to Extremes and Multiple Comparisons

ERIC Educational Resources Information Center

Wandler, Damian V.

2010-01-01

Generalized fiducial inference is a powerful tool for many difficult problems. Based on an extension of R. A. Fisher's work, we used generalized fiducial inference for two extreme value problems and a multiple comparison procedure. The first extreme value problem is dealing with the generalized Pareto distribution. The generalized Pareto…

A critical issue in model-based inference for studying trait-based community assembly and a solution.

PubMed

Ter Braak, Cajo J F; Peres-Neto, Pedro; Dray, Stéphane

2017-01-01

Statistical testing of trait-environment association from data is a challenge as there is no common unit of observation: the trait is observed on species, the environment on sites and the mediating abundance on species-site combinations. A number of correlation-based methods, such as the community weighted trait means method (CWM), the fourth-corner correlation method and the multivariate method RLQ, have been proposed to estimate such trait-environment associations. In these methods, valid statistical testing proceeds by performing two separate resampling tests, one site-based and the other species-based and by assessing significance by the largest of the two p -values (the p max test). Recently, regression-based methods using generalized linear models (GLM) have been proposed as a promising alternative with statistical inference via site-based resampling. We investigated the performance of this new approach along with approaches that mimicked the p max test using GLM instead of fourth-corner. By simulation using models with additional random variation in the species response to the environment, the site-based resampling tests using GLM are shown to have severely inflated type I error, of up to 90%, when the nominal level is set as 5%. In addition, predictive modelling of such data using site-based cross-validation very often identified trait-environment interactions that had no predictive value. The problem that we identify is not an "omitted variable bias" problem as it occurs even when the additional random variation is independent of the observed trait and environment data. Instead, it is a problem of ignoring a random effect. In the same simulations, the GLM-based p max test controlled the type I error in all models proposed so far in this context, but still gave slightly inflated error in more complex models that included both missing (but important) traits and missing (but important) environmental variables. For screening the importance of single trait-environment combinations, the fourth-corner test is shown to give almost the same results as the GLM-based tests in far less computing time.

Thermodynamics of statistical inference by cells.

PubMed

Lang, Alex H; Fisher, Charles K; Mora, Thierry; Mehta, Pankaj

2014-10-03

The deep connection between thermodynamics, computation, and information is now well established both theoretically and experimentally. Here, we extend these ideas to show that thermodynamics also places fundamental constraints on statistical estimation and learning. To do so, we investigate the constraints placed by (nonequilibrium) thermodynamics on the ability of biochemical signaling networks to estimate the concentration of an external signal. We show that accuracy is limited by energy consumption, suggesting that there are fundamental thermodynamic constraints on statistical inference.

Proper and Paradigmatic Metonymy as a Lens for Characterizing Student Conceptions of Distributions and Sampling

ERIC Educational Resources Information Center

Noll, Jennifer; Hancock, Stacey

2015-01-01

This research investigates what students' use of statistical language can tell us about their conceptions of distribution and sampling in relation to informal inference. Prior research documents students' challenges in understanding ideas of distribution and sampling as tools for making informal statistical inferences. We know that these…

Powerful Inference with the D-Statistic on Low-Coverage Whole-Genome Data

PubMed Central

Soraggi, Samuele; Wiuf, Carsten; Albrechtsen, Anders

2017-01-01

The detection of ancient gene flow between human populations is an important issue in population genetics. A common tool for detecting ancient admixture events is the D-statistic. The D-statistic is based on the hypothesis of a genetic relationship that involves four populations, whose correctness is assessed by evaluating specific coincidences of alleles between the groups. When working with high-throughput sequencing data, calling genotypes accurately is not always possible; therefore, the D-statistic currently samples a single base from the reads of one individual per population. This implies ignoring much of the information in the data, an issue especially striking in the case of ancient genomes. We provide a significant improvement to overcome the problems of the D-statistic by considering all reads from multiple individuals in each population. We also apply type-specific error correction to combat the problems of sequencing errors, and show a way to correct for introgression from an external population that is not part of the supposed genetic relationship, and how this leads to an estimate of the admixture rate. We prove that the D-statistic is approximated by a standard normal distribution. Furthermore, we show that our method outperforms the traditional D-statistic in detecting admixtures. The power gain is most pronounced for low and medium sequencing depth (1–10×), and performances are as good as with perfectly called genotypes at a sequencing depth of 2×. We show the reliability of error correction in scenarios with simulated errors and ancient data, and correct for introgression in known scenarios to estimate the admixture rates. PMID:29196497

New methods in iris recognition.

PubMed

Daugman, John

2007-10-01

This paper presents the following four advances in iris recognition: 1) more disciplined methods for detecting and faithfully modeling the iris inner and outer boundaries with active contours, leading to more flexible embedded coordinate systems; 2) Fourier-based methods for solving problems in iris trigonometry and projective geometry, allowing off-axis gaze to be handled by detecting it and "rotating" the eye into orthographic perspective; 3) statistical inference methods for detecting and excluding eyelashes; and 4) exploration of score normalizations, depending on the amount of iris data that is available in images and the required scale of database search. Statistical results are presented based on 200 billion iris cross-comparisons that were generated from 632500 irises in the United Arab Emirates database to analyze the normalization issues raised in different regions of receiver operating characteristic curves.

Robust inference from multiple test statistics via permutations: a better alternative to the single test statistic approach for randomized trials.

PubMed

Ganju, Jitendra; Yu, Xinxin; Ma, Guoguang Julie

2013-01-01

Formal inference in randomized clinical trials is based on controlling the type I error rate associated with a single pre-specified statistic. The deficiency of using just one method of analysis is that it depends on assumptions that may not be met. For robust inference, we propose pre-specifying multiple test statistics and relying on the minimum p-value for testing the null hypothesis of no treatment effect. The null hypothesis associated with the various test statistics is that the treatment groups are indistinguishable. The critical value for hypothesis testing comes from permutation distributions. Rejection of the null hypothesis when the smallest p-value is less than the critical value controls the type I error rate at its designated value. Even if one of the candidate test statistics has low power, the adverse effect on the power of the minimum p-value statistic is not much. Its use is illustrated with examples. We conclude that it is better to rely on the minimum p-value rather than a single statistic particularly when that single statistic is the logrank test, because of the cost and complexity of many survival trials. Copyright © 2013 John Wiley & Sons, Ltd.

Ensemble stacking mitigates biases in inference of synaptic connectivity.

PubMed

Chambers, Brendan; Levy, Maayan; Dechery, Joseph B; MacLean, Jason N

2018-01-01

A promising alternative to directly measuring the anatomical connections in a neuronal population is inferring the connections from the activity. We employ simulated spiking neuronal networks to compare and contrast commonly used inference methods that identify likely excitatory synaptic connections using statistical regularities in spike timing. We find that simple adjustments to standard algorithms improve inference accuracy: A signing procedure improves the power of unsigned mutual-information-based approaches and a correction that accounts for differences in mean and variance of background timing relationships, such as those expected to be induced by heterogeneous firing rates, increases the sensitivity of frequency-based methods. We also find that different inference methods reveal distinct subsets of the synaptic network and each method exhibits different biases in the accurate detection of reciprocity and local clustering. To correct for errors and biases specific to single inference algorithms, we combine methods into an ensemble. Ensemble predictions, generated as a linear combination of multiple inference algorithms, are more sensitive than the best individual measures alone, and are more faithful to ground-truth statistics of connectivity, mitigating biases specific to single inference methods. These weightings generalize across simulated datasets, emphasizing the potential for the broad utility of ensemble-based approaches.

Is it possible to identify a trend in problem/failure data

NASA Technical Reports Server (NTRS)

Church, Curtis K.

1990-01-01

One of the major obstacles in identifying and interpreting a trend is the small number of data points. Future trending reports will begin with 1983 data. As the problem/failure data are aggregated by year, there are just seven observations (1983 to 1989) for the 1990 reports. Any statistical inferences with a small amount of data will have a large degree of uncertainty. Consequently, a regression technique approach to identify a trend is limited. Though trend determination by failure mode may be unrealistic, the data may be explored for consistency or stability and the failure rate investigated. Various alternative data analysis procedures are briefly discussed. Techniques that could be used to explore problem/failure data by failure mode are addressed. The data used are taken from Section One, Space Shuttle Main Engine, of the Calspan Quarterly Report dated April 2, 1990.

Bayesian inference of physiologically meaningful parameters from body sway measurements.

PubMed

Tietäväinen, A; Gutmann, M U; Keski-Vakkuri, E; Corander, J; Hæggström, E

2017-06-19

The control of the human body sway by the central nervous system, muscles, and conscious brain is of interest since body sway carries information about the physiological status of a person. Several models have been proposed to describe body sway in an upright standing position, however, due to the statistical intractability of the more realistic models, no formal parameter inference has previously been conducted and the expressive power of such models for real human subjects remains unknown. Using the latest advances in Bayesian statistical inference for intractable models, we fitted a nonlinear control model to posturographic measurements, and we showed that it can accurately predict the sway characteristics of both simulated and real subjects. Our method provides a full statistical characterization of the uncertainty related to all model parameters as quantified by posterior probability density functions, which is useful for comparisons across subjects and test settings. The ability to infer intractable control models from sensor data opens new possibilities for monitoring and predicting body status in health applications.

A brief introduction to mixed effects modelling and multi-model inference in ecology

PubMed Central

Donaldson, Lynda; Correa-Cano, Maria Eugenia; Goodwin, Cecily E.D.

2018-01-01

The use of linear mixed effects models (LMMs) is increasingly common in the analysis of biological data. Whilst LMMs offer a flexible approach to modelling a broad range of data types, ecological data are often complex and require complex model structures, and the fitting and interpretation of such models is not always straightforward. The ability to achieve robust biological inference requires that practitioners know how and when to apply these tools. Here, we provide a general overview of current methods for the application of LMMs to biological data, and highlight the typical pitfalls that can be encountered in the statistical modelling process. We tackle several issues regarding methods of model selection, with particular reference to the use of information theory and multi-model inference in ecology. We offer practical solutions and direct the reader to key references that provide further technical detail for those seeking a deeper understanding. This overview should serve as a widely accessible code of best practice for applying LMMs to complex biological problems and model structures, and in doing so improve the robustness of conclusions drawn from studies investigating ecological and evolutionary questions. PMID:29844961

A brief introduction to mixed effects modelling and multi-model inference in ecology.

PubMed

Harrison, Xavier A; Donaldson, Lynda; Correa-Cano, Maria Eugenia; Evans, Julian; Fisher, David N; Goodwin, Cecily E D; Robinson, Beth S; Hodgson, David J; Inger, Richard

2018-01-01

The use of linear mixed effects models (LMMs) is increasingly common in the analysis of biological data. Whilst LMMs offer a flexible approach to modelling a broad range of data types, ecological data are often complex and require complex model structures, and the fitting and interpretation of such models is not always straightforward. The ability to achieve robust biological inference requires that practitioners know how and when to apply these tools. Here, we provide a general overview of current methods for the application of LMMs to biological data, and highlight the typical pitfalls that can be encountered in the statistical modelling process. We tackle several issues regarding methods of model selection, with particular reference to the use of information theory and multi-model inference in ecology. We offer practical solutions and direct the reader to key references that provide further technical detail for those seeking a deeper understanding. This overview should serve as a widely accessible code of best practice for applying LMMs to complex biological problems and model structures, and in doing so improve the robustness of conclusions drawn from studies investigating ecological and evolutionary questions.

Research participant compensation: A matter of statistical inference as well as ethics.

PubMed

Swanson, David M; Betensky, Rebecca A

2015-11-01

The ethics of compensation of research subjects for participation in clinical trials has been debated for years. One ethical issue of concern is variation among subjects in the level of compensation for identical treatments. Surprisingly, the impact of variation on the statistical inferences made from trial results has not been examined. We seek to identify how variation in compensation may influence any existing dependent censoring in clinical trials, thereby also influencing inference about the survival curve, hazard ratio, or other measures of treatment efficacy. In simulation studies, we consider a model for how compensation structure may influence the censoring model. Under existing dependent censoring, we estimate survival curves under different compensation structures and observe how these structures induce variability in the estimates. We show through this model that if the compensation structure affects the censoring model and dependent censoring is present, then variation in that structure induces variation in the estimates and affects the accuracy of estimation and inference on treatment efficacy. From the perspectives of both ethics and statistical inference, standardization and transparency in the compensation of participants in clinical trials are warranted. Copyright © 2015 Elsevier Inc. All rights reserved.

Hierarchical spatial models of abundance and occurrence from imperfect survey data

USGS Publications Warehouse

Royle, J. Andrew; Kery, M.; Gautier, R.; Schmid, Hans

2007-01-01

Many estimation and inference problems arising from large-scale animal surveys are focused on developing an understanding of patterns in abundance or occurrence of a species based on spatially referenced count data. One fundamental challenge, then, is that it is generally not feasible to completely enumerate ('census') all individuals present in each sample unit. This observation bias may consist of several components, including spatial coverage bias (not all individuals in the Population are exposed to sampling) and detection bias (exposed individuals may go undetected). Thus, observations are biased for the state variable (abundance, occupancy) that is the object of inference. Moreover, data are often sparse for most observation locations, requiring consideration of methods for spatially aggregating or otherwise combining sparse data among sample units. The development of methods that unify spatial statistical models with models accommodating non-detection is necessary to resolve important spatial inference problems based on animal survey data. In this paper, we develop a novel hierarchical spatial model for estimation of abundance and occurrence from survey data wherein detection is imperfect. Our application is focused on spatial inference problems in the Swiss Survey of Common Breeding Birds. The observation model for the survey data is specified conditional on the unknown quadrat population size, N(s). We augment the observation model with a spatial process model for N(s), describing the spatial variation in abundance of the species. The model includes explicit sources of variation in habitat structure (forest, elevation) and latent variation in the form of a correlated spatial process. This provides a model-based framework for combining the spatially referenced samples while at the same time yielding a unified treatment of estimation problems involving both abundance and occurrence. We provide a Bayesian framework for analysis and prediction based on the integrated likelihood, and we use the model to obtain estimates of abundance and occurrence maps for the European Jay (Garrulus glandarius), a widespread, elusive, forest bird. The naive national abundance estimate ignoring imperfect detection and incomplete quadrat coverage was 77 766 territories. Accounting for imperfect detection added approximately 18 000 territories, and adjusting for coverage bias added another 131 000 territories to yield a fully corrected estimate of the national total of about 227 000 territories. This is approximately three times as high as previous estimates that assume every territory is detected in each quadrat.

Pre-Service Mathematics Teachers' Use of Probability Models in Making Informal Inferences about a Chance Game

ERIC Educational Resources Information Center

Kazak, Sibel; Pratt, Dave

2017-01-01

This study considers probability models as tools for both making informal statistical inferences and building stronger conceptual connections between data and chance topics in teaching statistics. In this paper, we aim to explore pre-service mathematics teachers' use of probability models for a chance game, where the sum of two dice matters in…

Phylogeography Takes a Relaxed Random Walk in Continuous Space and Time

PubMed Central

Lemey, Philippe; Rambaut, Andrew; Welch, John J.; Suchard, Marc A.

2010-01-01

Research aimed at understanding the geographic context of evolutionary histories is burgeoning across biological disciplines. Recent endeavors attempt to interpret contemporaneous genetic variation in the light of increasingly detailed geographical and environmental observations. Such interest has promoted the development of phylogeographic inference techniques that explicitly aim to integrate such heterogeneous data. One promising development involves reconstructing phylogeographic history on a continuous landscape. Here, we present a Bayesian statistical approach to infer continuous phylogeographic diffusion using random walk models while simultaneously reconstructing the evolutionary history in time from molecular sequence data. Moreover, by accommodating branch-specific variation in dispersal rates, we relax the most restrictive assumption of the standard Brownian diffusion process and demonstrate increased statistical efficiency in spatial reconstructions of overdispersed random walks by analyzing both simulated and real viral genetic data. We further illustrate how drawing inference about summary statistics from a fully specified stochastic process over both sequence evolution and spatial movement reveals important characteristics of a rabies epidemic. Together with recent advances in discrete phylogeographic inference, the continuous model developments furnish a flexible statistical framework for biogeographical reconstructions that is easily expanded upon to accommodate various landscape genetic features. PMID:20203288

Variation in reaction norms: Statistical considerations and biological interpretation.

PubMed

Morrissey, Michael B; Liefting, Maartje

2016-09-01

Analysis of reaction norms, the functions by which the phenotype produced by a given genotype depends on the environment, is critical to studying many aspects of phenotypic evolution. Different techniques are available for quantifying different aspects of reaction norm variation. We examine what biological inferences can be drawn from some of the more readily applicable analyses for studying reaction norms. We adopt a strongly biologically motivated view, but draw on statistical theory to highlight strengths and drawbacks of different techniques. In particular, consideration of some formal statistical theory leads to revision of some recently, and forcefully, advocated opinions on reaction norm analysis. We clarify what simple analysis of the slope between mean phenotype in two environments can tell us about reaction norms, explore the conditions under which polynomial regression can provide robust inferences about reaction norm shape, and explore how different existing approaches may be used to draw inferences about variation in reaction norm shape. We show how mixed model-based approaches can provide more robust inferences than more commonly used multistep statistical approaches, and derive new metrics of the relative importance of variation in reaction norm intercepts, slopes, and curvatures. © 2016 The Author(s). Evolution © 2016 The Society for the Study of Evolution.

Affective cognition: Exploring lay theories of emotion.

PubMed

Ong, Desmond C; Zaki, Jamil; Goodman, Noah D

2015-10-01

Humans skillfully reason about others' emotions, a phenomenon we term affective cognition. Despite its importance, few formal, quantitative theories have described the mechanisms supporting this phenomenon. We propose that affective cognition involves applying domain-general reasoning processes to domain-specific content knowledge. Observers' knowledge about emotions is represented in rich and coherent lay theories, which comprise consistent relationships between situations, emotions, and behaviors. Observers utilize this knowledge in deciphering social agents' behavior and signals (e.g., facial expressions), in a manner similar to rational inference in other domains. We construct a computational model of a lay theory of emotion, drawing on tools from Bayesian statistics, and test this model across four experiments in which observers drew inferences about others' emotions in a simple gambling paradigm. This work makes two main contributions. First, the model accurately captures observers' flexible but consistent reasoning about the ways that events and others' emotional responses to those events relate to each other. Second, our work models the problem of emotional cue integration-reasoning about others' emotion from multiple emotional cues-as rational inference via Bayes' rule, and we show that this model tightly tracks human observers' empirical judgments. Our results reveal a deep structural relationship between affective cognition and other forms of inference, and suggest wide-ranging applications to basic psychological theory and psychiatry. Copyright © 2015 The Authors. Published by Elsevier B.V. All rights reserved.

Concerns regarding a call for pluralism of information theory and hypothesis testing

USGS Publications Warehouse

Lukacs, P.M.; Thompson, W.L.; Kendall, W.L.; Gould, W.R.; Doherty, P.F.; Burnham, K.P.; Anderson, D.R.

2007-01-01

1. Stephens et al . (2005) argue for `pluralism? in statistical analysis, combining null hypothesis testing and information-theoretic (I-T) methods. We show that I-T methods are more informative even in single variable problems and we provide an ecological example. 2. I-T methods allow inferences to be made from multiple models simultaneously. We believe multimodel inference is the future of data analysis, which cannot be achieved with null hypothesis-testing approaches. 3. We argue for a stronger emphasis on critical thinking in science in general and less reliance on exploratory data analysis and data dredging. Deriving alternative hypotheses is central to science; deriving a single interesting science hypothesis and then comparing it to a default null hypothesis (e.g. `no difference?) is not an efficient strategy for gaining knowledge. We think this single-hypothesis strategy has been relied upon too often in the past. 4. We clarify misconceptions presented by Stephens et al . (2005). 5. We think inference should be made about models, directly linked to scientific hypotheses, and their parameters conditioned on data, Prob(Hj| data). I-T methods provide a basis for this inference. Null hypothesis testing merely provides a probability statement about the data conditioned on a null model, Prob(data |H0). 6. Synthesis and applications. I-T methods provide a more informative approach to inference. I-T methods provide a direct measure of evidence for or against hypotheses and a means to consider simultaneously multiple hypotheses as a basis for rigorous inference. Progress in our science can be accelerated if modern methods can be used intelligently; this includes various I-T and Bayesian methods.

Identifying Keystone Species in the Human Gut Microbiome from Metagenomic Timeseries Using Sparse Linear Regression

PubMed Central

Fisher, Charles K.; Mehta, Pankaj

2014-01-01

Human associated microbial communities exert tremendous influence over human health and disease. With modern metagenomic sequencing methods it is now possible to follow the relative abundance of microbes in a community over time. These microbial communities exhibit rich ecological dynamics and an important goal of microbial ecology is to infer the ecological interactions between species directly from sequence data. Any algorithm for inferring ecological interactions must overcome three major obstacles: 1) a correlation between the abundances of two species does not imply that those species are interacting, 2) the sum constraint on the relative abundances obtained from metagenomic studies makes it difficult to infer the parameters in timeseries models, and 3) errors due to experimental uncertainty, or mis-assignment of sequencing reads into operational taxonomic units, bias inferences of species interactions due to a statistical problem called “errors-in-variables”. Here we introduce an approach, Learning Interactions from MIcrobial Time Series (LIMITS), that overcomes these obstacles. LIMITS uses sparse linear regression with boostrap aggregation to infer a discrete-time Lotka-Volterra model for microbial dynamics. We tested LIMITS on synthetic data and showed that it could reliably infer the topology of the inter-species ecological interactions. We then used LIMITS to characterize the species interactions in the gut microbiomes of two individuals and found that the interaction networks varied significantly between individuals. Furthermore, we found that the interaction networks of the two individuals are dominated by distinct “keystone species”, Bacteroides fragilis and Bacteroided stercosis, that have a disproportionate influence on the structure of the gut microbiome even though they are only found in moderate abundance. Based on our results, we hypothesize that the abundances of certain keystone species may be responsible for individuality in the human gut microbiome. PMID:25054627

The Role of Probability-Based Inference in an Intelligent Tutoring System.

ERIC Educational Resources Information Center

Mislevy, Robert J.; Gitomer, Drew H.

Probability-based inference in complex networks of interdependent variables is an active topic in statistical research, spurred by such diverse applications as forecasting, pedigree analysis, troubleshooting, and medical diagnosis. This paper concerns the role of Bayesian inference networks for updating student models in intelligent tutoring…

Identification of Patient Zero in Static and Temporal Networks: Robustness and Limitations

NASA Astrophysics Data System (ADS)

Antulov-Fantulin, Nino; Lančić, Alen; Šmuc, Tomislav; Štefančić, Hrvoje; Šikić, Mile

2015-06-01

Detection of patient zero can give new insights to epidemiologists about the nature of first transmissions into a population. In this Letter, we study the statistical inference problem of detecting the source of epidemics from a snapshot of spreading on an arbitrary network structure. By using exact analytic calculations and Monte Carlo estimators, we demonstrate the detectability limits for the susceptible-infected-recovered model, which primarily depend on the spreading process characteristics. Finally, we demonstrate the applicability of the approach in a case of a simulated sexually transmitted infection spreading over an empirical temporal network of sexual interactions.

An inferentialist perspective on the coordination of actions and reasons involved in making a statistical inference

NASA Astrophysics Data System (ADS)

Bakker, Arthur; Ben-Zvi, Dani; Makar, Katie

2017-12-01

To understand how statistical and other types of reasoning are coordinated with actions to reduce uncertainty, we conducted a case study in vocational education that involved statistical hypothesis testing. We analyzed an intern's research project in a hospital laboratory in which reducing uncertainties was crucial to make a valid statistical inference. In his project, the intern, Sam, investigated whether patients' blood could be sent through pneumatic post without influencing the measurement of particular blood components. We asked, in the process of making a statistical inference, how are reasons and actions coordinated to reduce uncertainty? For the analysis, we used the semantic theory of inferentialism, specifically, the concept of webs of reasons and actions—complexes of interconnected reasons for facts and actions; these reasons include premises and conclusions, inferential relations, implications, motives for action, and utility of tools for specific purposes in a particular context. Analysis of interviews with Sam, his supervisor and teacher as well as video data of Sam in the classroom showed that many of Sam's actions aimed to reduce variability, rule out errors, and thus reduce uncertainties so as to arrive at a valid inference. Interestingly, the decisive factor was not the outcome of a t test but of the reference change value, a clinical chemical measure of analytic and biological variability. With insights from this case study, we expect that students can be better supported in connecting statistics with context and in dealing with uncertainty.

Challenges in Species Tree Estimation Under the Multispecies Coalescent Model

PubMed Central

Xu, Bo; Yang, Ziheng

2016-01-01

The multispecies coalescent (MSC) model has emerged as a powerful framework for inferring species phylogenies while accounting for ancestral polymorphism and gene tree-species tree conflict. A number of methods have been developed in the past few years to estimate the species tree under the MSC. The full likelihood methods (including maximum likelihood and Bayesian inference) average over the unknown gene trees and accommodate their uncertainties properly but involve intensive computation. The approximate or summary coalescent methods are computationally fast and are applicable to genomic datasets with thousands of loci, but do not make an efficient use of information in the multilocus data. Most of them take the two-step approach of reconstructing the gene trees for multiple loci by phylogenetic methods and then treating the estimated gene trees as observed data, without accounting for their uncertainties appropriately. In this article we review the statistical nature of the species tree estimation problem under the MSC, and explore the conceptual issues and challenges of species tree estimation by focusing mainly on simple cases of three or four closely related species. We use mathematical analysis and computer simulation to demonstrate that large differences in statistical performance may exist between the two classes of methods. We illustrate that several counterintuitive behaviors may occur with the summary methods but they are due to inefficient use of information in the data by summary methods and vanish when the data are analyzed using full-likelihood methods. These include (i) unidentifiability of parameters in the model, (ii) inconsistency in the so-called anomaly zone, (iii) singularity on the likelihood surface, and (iv) deterioration of performance upon addition of more data. We discuss the challenges and strategies of species tree inference for distantly related species when the molecular clock is violated, and highlight the need for improving the computational efficiency and model realism of the likelihood methods as well as the statistical efficiency of the summary methods. PMID:27927902

Astrocytic tracer dynamics estimated from [1-¹¹C]-acetate PET measurements.

PubMed

Arnold, Andrea; Calvetti, Daniela; Gjedde, Albert; Iversen, Peter; Somersalo, Erkki

2015-12-01

We address the problem of estimating the unknown parameters of a model of tracer kinetics from sequences of positron emission tomography (PET) scan data using a statistical sequential algorithm for the inference of magnitudes of dynamic parameters. The method, based on Bayesian statistical inference, is a modification of a recently proposed particle filtering and sequential Monte Carlo algorithm, where instead of preassigning the accuracy in the propagation of each particle, we fix the time step and account for the numerical errors in the innovation term. We apply the algorithm to PET images of [1-¹¹C]-acetate-derived tracer accumulation, estimating the transport rates in a three-compartment model of astrocytic uptake and metabolism of the tracer for a cohort of 18 volunteers from 3 groups, corresponding to healthy control individuals, cirrhotic liver and hepatic encephalopathy patients. The distribution of the parameters for the individuals and for the groups presented within the Bayesian framework support the hypothesis that the parameters for the hepatic encephalopathy group follow a significantly different distribution than the other two groups. The biological implications of the findings are also discussed. © The Authors 2014. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved.

Quantum-Like Bayesian Networks for Modeling Decision Making

PubMed Central

Moreira, Catarina; Wichert, Andreas

2016-01-01

In this work, we explore an alternative quantum structure to perform quantum probabilistic inferences to accommodate the paradoxical findings of the Sure Thing Principle. We propose a Quantum-Like Bayesian Network, which consists in replacing classical probabilities by quantum probability amplitudes. However, since this approach suffers from the problem of exponential growth of quantum parameters, we also propose a similarity heuristic that automatically fits quantum parameters through vector similarities. This makes the proposed model general and predictive in contrast to the current state of the art models, which cannot be generalized for more complex decision scenarios and that only provide an explanatory nature for the observed paradoxes. In the end, the model that we propose consists in a nonparametric method for estimating inference effects from a statistical point of view. It is a statistical model that is simpler than the previous quantum dynamic and quantum-like models proposed in the literature. We tested the proposed network with several empirical data from the literature, mainly from the Prisoner's Dilemma game and the Two Stage Gambling game. The results obtained show that the proposed quantum Bayesian Network is a general method that can accommodate violations of the laws of classical probability theory and make accurate predictions regarding human decision-making in these scenarios. PMID:26858669

Foundational Principles for Large-Scale Inference: Illustrations Through Correlation Mining

DOE Office of Scientific and Technical Information (OSTI.GOV)

Hero, Alfred O.; Rajaratnam, Bala

When can reliable inference be drawn in the ‘‘Big Data’’ context? This article presents a framework for answering this fundamental question in the context of correlation mining, with implications for general large-scale inference. In large-scale data applications like genomics, connectomics, and eco-informatics, the data set is often variable rich but sample starved: a regime where the number n of acquired samples (statistical replicates) is far fewer than the number p of observed variables (genes, neurons, voxels, or chemical constituents). Much of recent work has focused on understanding the computational complexity of proposed methods for ‘‘Big Data.’’ Sample complexity, however, hasmore » received relatively less attention, especially in the setting when the sample size n is fixed, and the dimension p grows without bound. To address this gap, we develop a unified statistical framework that explicitly quantifies the sample complexity of various inferential tasks. Sampling regimes can be divided into several categories: 1) the classical asymptotic regime where the variable dimension is fixed and the sample size goes to infinity; 2) the mixed asymptotic regime where both variable dimension and sample size go to infinity at comparable rates; and 3) the purely high-dimensional asymptotic regime where the variable dimension goes to infinity and the sample size is fixed. Each regime has its niche but only the latter regime applies to exa-scale data dimension. We illustrate this high-dimensional framework for the problem of correlation mining, where it is the matrix of pairwise and partial correlations among the variables that are of interest. Correlation mining arises in numerous applications and subsumes the regression context as a special case. We demonstrate various regimes of correlation mining based on the unifying perspective of high-dimensional learning rates and sample complexity for different structured covariance models and different inference tasks.« less

Foundational Principles for Large-Scale Inference: Illustrations Through Correlation Mining

PubMed Central

Hero, Alfred O.; Rajaratnam, Bala

2015-01-01

When can reliable inference be drawn in fue “Big Data” context? This paper presents a framework for answering this fundamental question in the context of correlation mining, wifu implications for general large scale inference. In large scale data applications like genomics, connectomics, and eco-informatics fue dataset is often variable-rich but sample-starved: a regime where the number n of acquired samples (statistical replicates) is far fewer than fue number p of observed variables (genes, neurons, voxels, or chemical constituents). Much of recent work has focused on understanding the computational complexity of proposed methods for “Big Data”. Sample complexity however has received relatively less attention, especially in the setting when the sample size n is fixed, and the dimension p grows without bound. To address fuis gap, we develop a unified statistical framework that explicitly quantifies the sample complexity of various inferential tasks. Sampling regimes can be divided into several categories: 1) the classical asymptotic regime where fue variable dimension is fixed and fue sample size goes to infinity; 2) the mixed asymptotic regime where both variable dimension and sample size go to infinity at comparable rates; 3) the purely high dimensional asymptotic regime where the variable dimension goes to infinity and the sample size is fixed. Each regime has its niche but only the latter regime applies to exa cale data dimension. We illustrate this high dimensional framework for the problem of correlation mining, where it is the matrix of pairwise and partial correlations among the variables fua t are of interest. Correlation mining arises in numerous applications and subsumes the regression context as a special case. we demonstrate various regimes of correlation mining based on the unifying perspective of high dimensional learning rates and sample complexity for different structured covariance models and different inference tasks. PMID:27087700

Foundational Principles for Large-Scale Inference: Illustrations Through Correlation Mining

DOE PAGES

Hero, Alfred O.; Rajaratnam, Bala

2015-12-09

When can reliable inference be drawn in the ‘‘Big Data’’ context? This article presents a framework for answering this fundamental question in the context of correlation mining, with implications for general large-scale inference. In large-scale data applications like genomics, connectomics, and eco-informatics, the data set is often variable rich but sample starved: a regime where the number n of acquired samples (statistical replicates) is far fewer than the number p of observed variables (genes, neurons, voxels, or chemical constituents). Much of recent work has focused on understanding the computational complexity of proposed methods for ‘‘Big Data.’’ Sample complexity, however, hasmore » received relatively less attention, especially in the setting when the sample size n is fixed, and the dimension p grows without bound. To address this gap, we develop a unified statistical framework that explicitly quantifies the sample complexity of various inferential tasks. Sampling regimes can be divided into several categories: 1) the classical asymptotic regime where the variable dimension is fixed and the sample size goes to infinity; 2) the mixed asymptotic regime where both variable dimension and sample size go to infinity at comparable rates; and 3) the purely high-dimensional asymptotic regime where the variable dimension goes to infinity and the sample size is fixed. Each regime has its niche but only the latter regime applies to exa-scale data dimension. We illustrate this high-dimensional framework for the problem of correlation mining, where it is the matrix of pairwise and partial correlations among the variables that are of interest. Correlation mining arises in numerous applications and subsumes the regression context as a special case. We demonstrate various regimes of correlation mining based on the unifying perspective of high-dimensional learning rates and sample complexity for different structured covariance models and different inference tasks.« less

Bayesian inference for psychology. Part II: Example applications with JASP.

PubMed

Wagenmakers, Eric-Jan; Love, Jonathon; Marsman, Maarten; Jamil, Tahira; Ly, Alexander; Verhagen, Josine; Selker, Ravi; Gronau, Quentin F; Dropmann, Damian; Boutin, Bruno; Meerhoff, Frans; Knight, Patrick; Raj, Akash; van Kesteren, Erik-Jan; van Doorn, Johnny; Šmíra, Martin; Epskamp, Sacha; Etz, Alexander; Matzke, Dora; de Jong, Tim; van den Bergh, Don; Sarafoglou, Alexandra; Steingroever, Helen; Derks, Koen; Rouder, Jeffrey N; Morey, Richard D

2018-02-01

Bayesian hypothesis testing presents an attractive alternative to p value hypothesis testing. Part I of this series outlined several advantages of Bayesian hypothesis testing, including the ability to quantify evidence and the ability to monitor and update this evidence as data come in, without the need to know the intention with which the data were collected. Despite these and other practical advantages, Bayesian hypothesis tests are still reported relatively rarely. An important impediment to the widespread adoption of Bayesian tests is arguably the lack of user-friendly software for the run-of-the-mill statistical problems that confront psychologists for the analysis of almost every experiment: the t-test, ANOVA, correlation, regression, and contingency tables. In Part II of this series we introduce JASP ( http://www.jasp-stats.org ), an open-source, cross-platform, user-friendly graphical software package that allows users to carry out Bayesian hypothesis tests for standard statistical problems. JASP is based in part on the Bayesian analyses implemented in Morey and Rouder's BayesFactor package for R. Armed with JASP, the practical advantages of Bayesian hypothesis testing are only a mouse click away.

PyClone: statistical inference of clonal population structure in cancer.

PubMed

Roth, Andrew; Khattra, Jaswinder; Yap, Damian; Wan, Adrian; Laks, Emma; Biele, Justina; Ha, Gavin; Aparicio, Samuel; Bouchard-Côté, Alexandre; Shah, Sohrab P

2014-04-01

We introduce PyClone, a statistical model for inference of clonal population structures in cancers. PyClone is a Bayesian clustering method for grouping sets of deeply sequenced somatic mutations into putative clonal clusters while estimating their cellular prevalences and accounting for allelic imbalances introduced by segmental copy-number changes and normal-cell contamination. Single-cell sequencing validation demonstrates PyClone's accuracy.

Statistical Signal Models and Algorithms for Image Analysis

DTIC Science & Technology

1984-10-25

In this report, two-dimensional stochastic linear models are used in developing algorithms for image analysis such as classification, segmentation, and object detection in images characterized by textured backgrounds. These models generate two-dimensional random processes as outputs to which statistical inference procedures can naturally be applied. A common thread throughout our algorithms is the interpretation of the inference procedures in terms of linear prediction

Statistical inference of the generation probability of T-cell receptors from sequence repertoires.

PubMed

Murugan, Anand; Mora, Thierry; Walczak, Aleksandra M; Callan, Curtis G

2012-10-02

Stochastic rearrangement of germline V-, D-, and J-genes to create variable coding sequence for certain cell surface receptors is at the origin of immune system diversity. This process, known as "VDJ recombination", is implemented via a series of stochastic molecular events involving gene choices and random nucleotide insertions between, and deletions from, genes. We use large sequence repertoires of the variable CDR3 region of human CD4+ T-cell receptor beta chains to infer the statistical properties of these basic biochemical events. Because any given CDR3 sequence can be produced in multiple ways, the probability distribution of hidden recombination events cannot be inferred directly from the observed sequences; we therefore develop a maximum likelihood inference method to achieve this end. To separate the properties of the molecular rearrangement mechanism from the effects of selection, we focus on nonproductive CDR3 sequences in T-cell DNA. We infer the joint distribution of the various generative events that occur when a new T-cell receptor gene is created. We find a rich picture of correlation (and absence thereof), providing insight into the molecular mechanisms involved. The generative event statistics are consistent between individuals, suggesting a universal biochemical process. Our probabilistic model predicts the generation probability of any specific CDR3 sequence by the primitive recombination process, allowing us to quantify the potential diversity of the T-cell repertoire and to understand why some sequences are shared between individuals. We argue that the use of formal statistical inference methods, of the kind presented in this paper, will be essential for quantitative understanding of the generation and evolution of diversity in the adaptive immune system.

Statistical Inference and Reverse Engineering of Gene Regulatory Networks from Observational Expression Data

PubMed Central

Emmert-Streib, Frank; Glazko, Galina V.; Altay, Gökmen; de Matos Simoes, Ricardo

2012-01-01

In this paper, we present a systematic and conceptual overview of methods for inferring gene regulatory networks from observational gene expression data. Further, we discuss two classic approaches to infer causal structures and compare them with contemporary methods by providing a conceptual categorization thereof. We complement the above by surveying global and local evaluation measures for assessing the performance of inference algorithms. PMID:22408642

Information Entropy Production of Maximum Entropy Markov Chains from Spike Trains

NASA Astrophysics Data System (ADS)

Cofré, Rodrigo; Maldonado, Cesar

2018-01-01

We consider the maximum entropy Markov chain inference approach to characterize the collective statistics of neuronal spike trains, focusing on the statistical properties of the inferred model. We review large deviations techniques useful in this context to describe properties of accuracy and convergence in terms of sampling size. We use these results to study the statistical fluctuation of correlations, distinguishability and irreversibility of maximum entropy Markov chains. We illustrate these applications using simple examples where the large deviation rate function is explicitly obtained for maximum entropy models of relevance in this field.

Bayesian Orbit Computation Tools for Objects on Geocentric Orbits

NASA Astrophysics Data System (ADS)

Virtanen, J.; Granvik, M.; Muinonen, K.; Oszkiewicz, D.

2013-08-01

We consider the space-debris orbital inversion problem via the concept of Bayesian inference. The methodology has been put forward for the orbital analysis of solar system small bodies in early 1990's [7] and results in a full solution of the statistical inverse problem given in terms of a posteriori probability density function (PDF) for the orbital parameters. We demonstrate the applicability of our statistical orbital analysis software to Earth orbiting objects, both using well-established Monte Carlo (MC) techniques (for a review, see e.g. [13] as well as recently developed Markov-chain MC (MCMC) techniques (e.g., [9]). In particular, we exploit the novel virtual observation MCMC method [8], which is based on the characterization of the phase-space volume of orbital solutions before the actual MCMC sampling. Our statistical methods and the resulting PDFs immediately enable probabilistic impact predictions to be carried out. Furthermore, this can be readily done also for very sparse data sets and data sets of poor quality - providing that some a priori information on the observational uncertainty is available. For asteroids, impact probabilities with the Earth from the discovery night onwards have been provided, e.g., by [11] and [10], the latter study includes the sampling of the observational-error standard deviation as a random variable.

Powerful Inference with the D-Statistic on Low-Coverage Whole-Genome Data.

PubMed

Soraggi, Samuele; Wiuf, Carsten; Albrechtsen, Anders

2018-02-02

The detection of ancient gene flow between human populations is an important issue in population genetics. A common tool for detecting ancient admixture events is the D-statistic. The D-statistic is based on the hypothesis of a genetic relationship that involves four populations, whose correctness is assessed by evaluating specific coincidences of alleles between the groups. When working with high-throughput sequencing data, calling genotypes accurately is not always possible; therefore, the D-statistic currently samples a single base from the reads of one individual per population. This implies ignoring much of the information in the data, an issue especially striking in the case of ancient genomes. We provide a significant improvement to overcome the problems of the D-statistic by considering all reads from multiple individuals in each population. We also apply type-specific error correction to combat the problems of sequencing errors, and show a way to correct for introgression from an external population that is not part of the supposed genetic relationship, and how this leads to an estimate of the admixture rate. We prove that the D-statistic is approximated by a standard normal distribution. Furthermore, we show that our method outperforms the traditional D-statistic in detecting admixtures. The power gain is most pronounced for low and medium sequencing depth (1-10×), and performances are as good as with perfectly called genotypes at a sequencing depth of 2×. We show the reliability of error correction in scenarios with simulated errors and ancient data, and correct for introgression in known scenarios to estimate the admixture rates. Copyright © 2018 Soraggi et al.

Statistical inference based on the nonparametric maximum likelihood estimator under double-truncation.

PubMed

Emura, Takeshi; Konno, Yoshihiko; Michimae, Hirofumi

2015-07-01

Doubly truncated data consist of samples whose observed values fall between the right- and left- truncation limits. With such samples, the distribution function of interest is estimated using the nonparametric maximum likelihood estimator (NPMLE) that is obtained through a self-consistency algorithm. Owing to the complicated asymptotic distribution of the NPMLE, the bootstrap method has been suggested for statistical inference. This paper proposes a closed-form estimator for the asymptotic covariance function of the NPMLE, which is computationally attractive alternative to bootstrapping. Furthermore, we develop various statistical inference procedures, such as confidence interval, goodness-of-fit tests, and confidence bands to demonstrate the usefulness of the proposed covariance estimator. Simulations are performed to compare the proposed method with both the bootstrap and jackknife methods. The methods are illustrated using the childhood cancer dataset.

Structured statistical models of inductive reasoning.

PubMed

Kemp, Charles; Tenenbaum, Joshua B

2009-01-01

Everyday inductive inferences are often guided by rich background knowledge. Formal models of induction should aim to incorporate this knowledge and should explain how different kinds of knowledge lead to the distinctive patterns of reasoning found in different inductive contexts. This article presents a Bayesian framework that attempts to meet both goals and describes [corrected] 4 applications of the framework: a taxonomic model, a spatial model, a threshold model, and a causal model. Each model makes probabilistic inferences about the extensions of novel properties, but the priors for the 4 models are defined over different kinds of structures that capture different relationships between the categories in a domain. The framework therefore shows how statistical inference can operate over structured background knowledge, and the authors argue that this interaction between structure and statistics is critical for explaining the power and flexibility of human reasoning.

Inference on network statistics by restricting to the network space: applications to sexual history data.

PubMed

Goyal, Ravi; De Gruttola, Victor

2018-01-30

Analysis of sexual history data intended to describe sexual networks presents many challenges arising from the fact that most surveys collect information on only a very small fraction of the population of interest. In addition, partners are rarely identified and responses are subject to reporting biases. Typically, each network statistic of interest, such as mean number of sexual partners for men or women, is estimated independently of other network statistics. There is, however, a complex relationship among networks statistics; and knowledge of these relationships can aid in addressing concerns mentioned earlier. We develop a novel method that constrains a posterior predictive distribution of a collection of network statistics in order to leverage the relationships among network statistics in making inference about network properties of interest. The method ensures that inference on network properties is compatible with an actual network. Through extensive simulation studies, we also demonstrate that use of this method can improve estimates in settings where there is uncertainty that arises both from sampling and from systematic reporting bias compared with currently available approaches to estimation. To illustrate the method, we apply it to estimate network statistics using data from the Chicago Health and Social Life Survey. Copyright © 2017 John Wiley & Sons, Ltd. Copyright © 2017 John Wiley & Sons, Ltd.

Statistical comparison of a hybrid approach with approximate and exact inference models for Fusion 2+

NASA Astrophysics Data System (ADS)

Lee, K. David; Wiesenfeld, Eric; Gelfand, Andrew

2007-04-01

One of the greatest challenges in modern combat is maintaining a high level of timely Situational Awareness (SA). In many situations, computational complexity and accuracy considerations make the development and deployment of real-time, high-level inference tools very difficult. An innovative hybrid framework that combines Bayesian inference, in the form of Bayesian Networks, and Possibility Theory, in the form of Fuzzy Logic systems, has recently been introduced to provide a rigorous framework for high-level inference. In previous research, the theoretical basis and benefits of the hybrid approach have been developed. However, lacking is a concrete experimental comparison of the hybrid framework with traditional fusion methods, to demonstrate and quantify this benefit. The goal of this research, therefore, is to provide a statistical analysis on the comparison of the accuracy and performance of hybrid network theory, with pure Bayesian and Fuzzy systems and an inexact Bayesian system approximated using Particle Filtering. To accomplish this task, domain specific models will be developed under these different theoretical approaches and then evaluated, via Monte Carlo Simulation, in comparison to situational ground truth to measure accuracy and fidelity. Following this, a rigorous statistical analysis of the performance results will be performed, to quantify the benefit of hybrid inference to other fusion tools.

Statistical detection of EEG synchrony using empirical bayesian inference.

PubMed

Singh, Archana K; Asoh, Hideki; Takeda, Yuji; Phillips, Steven

2015-01-01

There is growing interest in understanding how the brain utilizes synchronized oscillatory activity to integrate information across functionally connected regions. Computing phase-locking values (PLV) between EEG signals is a popular method for quantifying such synchronizations and elucidating their role in cognitive tasks. However, high-dimensionality in PLV data incurs a serious multiple testing problem. Standard multiple testing methods in neuroimaging research (e.g., false discovery rate, FDR) suffer severe loss of power, because they fail to exploit complex dependence structure between hypotheses that vary in spectral, temporal and spatial dimension. Previously, we showed that a hierarchical FDR and optimal discovery procedures could be effectively applied for PLV analysis to provide better power than FDR. In this article, we revisit the multiple comparison problem from a new Empirical Bayes perspective and propose the application of the local FDR method (locFDR; Efron, 2001) for PLV synchrony analysis to compute FDR as a posterior probability that an observed statistic belongs to a null hypothesis. We demonstrate the application of Efron's Empirical Bayes approach for PLV synchrony analysis for the first time. We use simulations to validate the specificity and sensitivity of locFDR and a real EEG dataset from a visual search study for experimental validation. We also compare locFDR with hierarchical FDR and optimal discovery procedures in both simulation and experimental analyses. Our simulation results showed that the locFDR can effectively control false positives without compromising on the power of PLV synchrony inference. Our results from the application locFDR on experiment data detected more significant discoveries than our previously proposed methods whereas the standard FDR method failed to detect any significant discoveries.

Data analytics for simplifying thermal efficiency planning in cities

PubMed Central

Abdolhosseini Qomi, Mohammad Javad; Noshadravan, Arash; Sobstyl, Jake M.; Toole, Jameson; Ferreira, Joseph; Pellenq, Roland J.-M.; Ulm, Franz-Josef; Gonzalez, Marta C.

2016-01-01

More than 44% of building energy consumption in the USA is used for space heating and cooling, and this accounts for 20% of national CO2 emissions. This prompts the need to identify among the 130 million households in the USA those with the greatest energy-saving potential and the associated costs of the path to reach that goal. Whereas current solutions address this problem by analysing each building in detail, we herein reduce the dimensionality of the problem by simplifying the calculations of energy losses in buildings. We present a novel inference method that can be used via a ranking algorithm that allows us to estimate the potential energy saving for heating purposes. To that end, we only need consumption from records of gas bills integrated with a building's footprint. The method entails a statistical screening of the intricate interplay between weather, infrastructural and residents' choice variables to determine building gas consumption and potential savings at a city scale. We derive a general statistical pattern of consumption in an urban settlement, reducing it to a set of the most influential buildings' parameters that operate locally. By way of example, the implications are explored using records of a set of (N = 6200) buildings in Cambridge, MA, USA, which indicate that retrofitting only 16% of buildings entails a 40% reduction in gas consumption of the whole building stock. We find that the inferred heat loss rate of buildings exhibits a power-law data distribution akin to Zipf's law, which provides a means to map an optimum path for gas savings per retrofit at a city scale. These findings have implications for improving the thermal efficiency of cities' building stock, as outlined by current policy efforts seeking to reduce home heating and cooling energy consumption and lower associated greenhouse gas emissions. PMID:27097652

Bias in logistic regression due to imperfect diagnostic test results and practical correction approaches.

PubMed

Valle, Denis; Lima, Joanna M Tucker; Millar, Justin; Amratia, Punam; Haque, Ubydul

2015-11-04

Logistic regression is a statistical model widely used in cross-sectional and cohort studies to identify and quantify the effects of potential disease risk factors. However, the impact of imperfect tests on adjusted odds ratios (and thus on the identification of risk factors) is under-appreciated. The purpose of this article is to draw attention to the problem associated with modelling imperfect diagnostic tests, and propose simple Bayesian models to adequately address this issue. A systematic literature review was conducted to determine the proportion of malaria studies that appropriately accounted for false-negatives/false-positives in a logistic regression setting. Inference from the standard logistic regression was also compared with that from three proposed Bayesian models using simulations and malaria data from the western Brazilian Amazon. A systematic literature review suggests that malaria epidemiologists are largely unaware of the problem of using logistic regression to model imperfect diagnostic test results. Simulation results reveal that statistical inference can be substantially improved when using the proposed Bayesian models versus the standard logistic regression. Finally, analysis of original malaria data with one of the proposed Bayesian models reveals that microscopy sensitivity is strongly influenced by how long people have lived in the study region, and an important risk factor (i.e., participation in forest extractivism) is identified that would have been missed by standard logistic regression. Given the numerous diagnostic methods employed by malaria researchers and the ubiquitous use of logistic regression to model the results of these diagnostic tests, this paper provides critical guidelines to improve data analysis practice in the presence of misclassification error. Easy-to-use code that can be readily adapted to WinBUGS is provided, enabling straightforward implementation of the proposed Bayesian models.

Statistically optimal perception and learning: from behavior to neural representations

PubMed Central

Fiser, József; Berkes, Pietro; Orbán, Gergő; Lengyel, Máté

2010-01-01

Human perception has recently been characterized as statistical inference based on noisy and ambiguous sensory inputs. Moreover, suitable neural representations of uncertainty have been identified that could underlie such probabilistic computations. In this review, we argue that learning an internal model of the sensory environment is another key aspect of the same statistical inference procedure and thus perception and learning need to be treated jointly. We review evidence for statistically optimal learning in humans and animals, and reevaluate possible neural representations of uncertainty based on their potential to support statistically optimal learning. We propose that spontaneous activity can have a functional role in such representations leading to a new, sampling-based, framework of how the cortex represents information and uncertainty. PMID:20153683

On the analysis of very small samples of Gaussian repeated measurements: an alternative approach.

PubMed

Westgate, Philip M; Burchett, Woodrow W

2017-03-15

The analysis of very small samples of Gaussian repeated measurements can be challenging. First, due to a very small number of independent subjects contributing outcomes over time, statistical power can be quite small. Second, nuisance covariance parameters must be appropriately accounted for in the analysis in order to maintain the nominal test size. However, available statistical strategies that ensure valid statistical inference may lack power, whereas more powerful methods may have the potential for inflated test sizes. Therefore, we explore an alternative approach to the analysis of very small samples of Gaussian repeated measurements, with the goal of maintaining valid inference while also improving statistical power relative to other valid methods. This approach uses generalized estimating equations with a bias-corrected empirical covariance matrix that accounts for all small-sample aspects of nuisance correlation parameter estimation in order to maintain valid inference. Furthermore, the approach utilizes correlation selection strategies with the goal of choosing the working structure that will result in the greatest power. In our study, we show that when accurate modeling of the nuisance correlation structure impacts the efficiency of regression parameter estimation, this method can improve power relative to existing methods that yield valid inference. Copyright © 2017 John Wiley & Sons, Ltd. Copyright © 2017 John Wiley & Sons, Ltd.

Statistical inference for noisy nonlinear ecological dynamic systems.

PubMed

Wood, Simon N

2010-08-26

Chaotic ecological dynamic systems defy conventional statistical analysis. Systems with near-chaotic dynamics are little better. Such systems are almost invariably driven by endogenous dynamic processes plus demographic and environmental process noise, and are only observable with error. Their sensitivity to history means that minute changes in the driving noise realization, or the system parameters, will cause drastic changes in the system trajectory. This sensitivity is inherited and amplified by the joint probability density of the observable data and the process noise, rendering it useless as the basis for obtaining measures of statistical fit. Because the joint density is the basis for the fit measures used by all conventional statistical methods, this is a major theoretical shortcoming. The inability to make well-founded statistical inferences about biological dynamic models in the chaotic and near-chaotic regimes, other than on an ad hoc basis, leaves dynamic theory without the methods of quantitative validation that are essential tools in the rest of biological science. Here I show that this impasse can be resolved in a simple and general manner, using a method that requires only the ability to simulate the observed data on a system from the dynamic model about which inferences are required. The raw data series are reduced to phase-insensitive summary statistics, quantifying local dynamic structure and the distribution of observations. Simulation is used to obtain the mean and the covariance matrix of the statistics, given model parameters, allowing the construction of a 'synthetic likelihood' that assesses model fit. This likelihood can be explored using a straightforward Markov chain Monte Carlo sampler, but one further post-processing step returns pure likelihood-based inference. I apply the method to establish the dynamic nature of the fluctuations in Nicholson's classic blowfly experiments.

Empirical intrinsic geometry for nonlinear modeling and time series filtering.

PubMed

Talmon, Ronen; Coifman, Ronald R

2013-07-30

In this paper, we present a method for time series analysis based on empirical intrinsic geometry (EIG). EIG enables one to reveal the low-dimensional parametric manifold as well as to infer the underlying dynamics of high-dimensional time series. By incorporating concepts of information geometry, this method extends existing geometric analysis tools to support stochastic settings and parametrizes the geometry of empirical distributions. However, the statistical models are not required as priors; hence, EIG may be applied to a wide range of real signals without existing definitive models. We show that the inferred model is noise-resilient and invariant under different observation and instrumental modalities. In addition, we show that it can be extended efficiently to newly acquired measurements in a sequential manner. These two advantages enable us to revisit the Bayesian approach and incorporate empirical dynamics and intrinsic geometry into a nonlinear filtering framework. We show applications to nonlinear and non-Gaussian tracking problems as well as to acoustic signal localization.

A Conceptual Framework for Pharmacodynamic Genome-wide Association Studies in Pharmacogenomics

PubMed Central

Wu, Rongling; Tong, Chunfa; Wang, Zhong; Mauger, David; Tantisira, Kelan; Szefler, Stanley J.; Chinchilli, Vernon M.; Israel, Elliot

2013-01-01

Summary Genome-wide association studies (GWAS) have emerged as a powerful tool to identify loci that affect drug response or susceptibility to adverse drug reactions. However, current GWAS based on a simple analysis of associations between genotype and phenotype ignores the biochemical reactions of drug response, thus limiting the scope of inference about its genetic architecture. To facilitate the inference of GWAS in pharmacogenomics, we sought to undertake the mathematical integration of the pharmacodynamic process of drug reactions through computational models. By estimating and testing the genetic control of pharmacodynamic and pharmacokinetic parameters, this mechanistic approach does not only enhance the biological and clinical relevance of significant genetic associations, but also improve the statistical power and robustness of gene detection. This report discusses the general principle and development of pharmacodynamics-based GWAS, highlights the practical use of this approach in addressing various pharmacogenomic problems, and suggests that this approach will be an important method to study the genetic architecture of drug responses or reactions. PMID:21920452

Inference for dynamics of continuous variables: the extended Plefka expansion with hidden nodes

NASA Astrophysics Data System (ADS)

Bravi, B.; Sollich, P.

2017-06-01

We consider the problem of a subnetwork of observed nodes embedded into a larger bulk of unknown (i.e. hidden) nodes, where the aim is to infer these hidden states given information about the subnetwork dynamics. The biochemical networks underlying many cellular and metabolic processes are important realizations of such a scenario as typically one is interested in reconstructing the time evolution of unobserved chemical concentrations starting from the experimentally more accessible ones. We present an application to this problem of a novel dynamical mean field approximation, the extended Plefka expansion, which is based on a path integral description of the stochastic dynamics. As a paradigmatic model we study the stochastic linear dynamics of continuous degrees of freedom interacting via random Gaussian couplings. The resulting joint distribution is known to be Gaussian and this allows us to fully characterize the posterior statistics of the hidden nodes. In particular the equal-time hidden-to-hidden variance—conditioned on observations—gives the expected error at each node when the hidden time courses are predicted based on the observations. We assess the accuracy of the extended Plefka expansion in predicting these single node variances as well as error correlations over time, focussing on the role of the system size and the number of observed nodes.

Weibull mixture regression for marginal inference in zero-heavy continuous outcomes.

PubMed

Gebregziabher, Mulugeta; Voronca, Delia; Teklehaimanot, Abeba; Santa Ana, Elizabeth J

2017-06-01

Continuous outcomes with preponderance of zero values are ubiquitous in data that arise from biomedical studies, for example studies of addictive disorders. This is known to lead to violation of standard assumptions in parametric inference and enhances the risk of misleading conclusions unless managed properly. Two-part models are commonly used to deal with this problem. However, standard two-part models have limitations with respect to obtaining parameter estimates that have marginal interpretation of covariate effects which are important in many biomedical applications. Recently marginalized two-part models are proposed but their development is limited to log-normal and log-skew-normal distributions. Thus, in this paper, we propose a finite mixture approach, with Weibull mixture regression as a special case, to deal with the problem. We use extensive simulation study to assess the performance of the proposed model in finite samples and to make comparisons with other family of models via statistical information and mean squared error criteria. We demonstrate its application on real data from a randomized controlled trial of addictive disorders. Our results show that a two-component Weibull mixture model is preferred for modeling zero-heavy continuous data when the non-zero part are simulated from Weibull or similar distributions such as Gamma or truncated Gauss.

Longitudinal data analysis with non-ignorable missing data.

PubMed

Tseng, Chi-hong; Elashoff, Robert; Li, Ning; Li, Gang

2016-02-01

A common problem in the longitudinal data analysis is the missing data problem. Two types of missing patterns are generally considered in statistical literature: monotone and non-monotone missing data. Nonmonotone missing data occur when study participants intermittently miss scheduled visits, while monotone missing data can be from discontinued participation, loss to follow-up, and mortality. Although many novel statistical approaches have been developed to handle missing data in recent years, few methods are available to provide inferences to handle both types of missing data simultaneously. In this article, a latent random effects model is proposed to analyze longitudinal outcomes with both monotone and non-monotone missingness in the context of missing not at random. Another significant contribution of this article is to propose a new computational algorithm for latent random effects models. To reduce the computational burden of high-dimensional integration problem in latent random effects models, we develop a new computational algorithm that uses a new adaptive quadrature approach in conjunction with the Taylor series approximation for the likelihood function to simplify the E-step computation in the expectation-maximization algorithm. Simulation study is performed and the data from the scleroderma lung study are used to demonstrate the effectiveness of this method. © The Author(s) 2012.

Probabilistic Graphical Model Representation in Phylogenetics

PubMed Central

Höhna, Sebastian; Heath, Tracy A.; Boussau, Bastien; Landis, Michael J.; Ronquist, Fredrik; Huelsenbeck, John P.

2014-01-01

Recent years have seen a rapid expansion of the model space explored in statistical phylogenetics, emphasizing the need for new approaches to statistical model representation and software development. Clear communication and representation of the chosen model is crucial for: (i) reproducibility of an analysis, (ii) model development, and (iii) software design. Moreover, a unified, clear and understandable framework for model representation lowers the barrier for beginners and nonspecialists to grasp complex phylogenetic models, including their assumptions and parameter/variable dependencies. Graphical modeling is a unifying framework that has gained in popularity in the statistical literature in recent years. The core idea is to break complex models into conditionally independent distributions. The strength lies in the comprehensibility, flexibility, and adaptability of this formalism, and the large body of computational work based on it. Graphical models are well-suited to teach statistical models, to facilitate communication among phylogeneticists and in the development of generic software for simulation and statistical inference. Here, we provide an introduction to graphical models for phylogeneticists and extend the standard graphical model representation to the realm of phylogenetics. We introduce a new graphical model component, tree plates, to capture the changing structure of the subgraph corresponding to a phylogenetic tree. We describe a range of phylogenetic models using the graphical model framework and introduce modules to simplify the representation of standard components in large and complex models. Phylogenetic model graphs can be readily used in simulation, maximum likelihood inference, and Bayesian inference using, for example, Metropolis–Hastings or Gibbs sampling of the posterior distribution. [Computation; graphical models; inference; modularization; statistical phylogenetics; tree plate.] PMID:24951559

minet: A R/Bioconductor package for inferring large transcriptional networks using mutual information.

PubMed

Meyer, Patrick E; Lafitte, Frédéric; Bontempi, Gianluca

2008-10-29

This paper presents the R/Bioconductor package minet (version 1.1.6) which provides a set of functions to infer mutual information networks from a dataset. Once fed with a microarray dataset, the package returns a network where nodes denote genes, edges model statistical dependencies between genes and the weight of an edge quantifies the statistical evidence of a specific (e.g transcriptional) gene-to-gene interaction. Four different entropy estimators are made available in the package minet (empirical, Miller-Madow, Schurmann-Grassberger and shrink) as well as four different inference methods, namely relevance networks, ARACNE, CLR and MRNET. Also, the package integrates accuracy assessment tools, like F-scores, PR-curves and ROC-curves in order to compare the inferred network with a reference one. The package minet provides a series of tools for inferring transcriptional networks from microarray data. It is freely available from the Comprehensive R Archive Network (CRAN) as well as from the Bioconductor website.

Inferring the mesoscale structure of layered, edge-valued, and time-varying networks

NASA Astrophysics Data System (ADS)

Peixoto, Tiago P.

2015-10-01

Many network systems are composed of interdependent but distinct types of interactions, which cannot be fully understood in isolation. These different types of interactions are often represented as layers, attributes on the edges, or as a time dependence of the network structure. Although they are crucial for a more comprehensive scientific understanding, these representations offer substantial challenges. Namely, it is an open problem how to precisely characterize the large or mesoscale structure of network systems in relation to these additional aspects. Furthermore, the direct incorporation of these features invariably increases the effective dimension of the network description, and hence aggravates the problem of overfitting, i.e., the use of overly complex characterizations that mistake purely random fluctuations for actual structure. In this work, we propose a robust and principled method to tackle these problems, by constructing generative models of modular network structure, incorporating layered, attributed and time-varying properties, as well as a nonparametric Bayesian methodology to infer the parameters from data and select the most appropriate model according to statistical evidence. We show that the method is capable of revealing hidden structure in layered, edge-valued, and time-varying networks, and that the most appropriate level of granularity with respect to the additional dimensions can be reliably identified. We illustrate our approach on a variety of empirical systems, including a social network of physicians, the voting correlations of deputies in the Brazilian national congress, the global airport network, and a proximity network of high-school students.

Application of temporal LNC logic in artificial intelligence

NASA Astrophysics Data System (ADS)

Adamek, Marek; Mulawka, Jan

2016-09-01

This paper presents the temporal logic inference engine developed in our university. It is an attempt to demonstrate implementation and practical application of temporal logic LNC developed in Cardinal Stefan Wyszynski University in Warsaw.1 The paper describes the fundamentals of LNC logic, architecture and implementation of inference engine. The practical application is shown by providing the solution for popular in Artificial Intelligence problem of Missionaries and Cannibals in terms of LNC logic. Both problem formulation and inference engine are described in details.

Teach a Confidence Interval for the Median in the First Statistics Course

ERIC Educational Resources Information Center

Howington, Eric B.

2017-01-01

Few introductory statistics courses consider statistical inference for the median. This article argues in favour of adding a confidence interval for the median to the first statistics course. Several methods suitable for introductory statistics students are identified and briefly reviewed.

Constraining Mass Anomalies Using Trans-dimensional Gravity Inversions

NASA Astrophysics Data System (ADS)

Izquierdo, K.; Montesi, L.; Lekic, V.

2016-12-01

The density structure of planetary interiors constitutes a key constraint on their composition, temperature, and dynamics. This has motivated the development of non-invasive methods to infer 3D distribution of density anomalies within a planet's interior using gravity observations made from the surface or orbit. On Earth, this information can be supplemented by seismic and electromagnetic observations, but such data are generally not available on other planets and inferences must be made from gravity observations alone. Unfortunately, inferences of density anomalies from gravity are non-unique and even the dimensionality of the problem - i.e., the number of density anomalies detectable in the planetary interior - is unknown. In this project, we use the Reversible Jump Markov chain Monte Carlo (RJMCMC) algorithm to approach gravity inversions in a trans-dimensional way, that is, considering the magnitude of the mass, the latitude, longitude, depth and number of anomalies itself as unknowns to be constrained by the observed gravity field at the surface of a planet. Our approach builds upon previous work using trans-dimensional gravity inversions in which the density contrast between the anomaly and the surrounding material is known. We validate the algorithm by analyzing a synthetic gravity field produced by a known density structure and comparing the retrieved and input density structures. We find excellent agreement between the input and retrieved structure when working in 1D and 2D domains. However, in 3D domains, comprehensive exploration of the much larger space of possible models makes search efficiency a key ingredient in successful gravity inversion. We find that upon a sufficiently long RJMCMC run, it is possible to use statistical information to recover a predicted model that matches the real model. We argue that even more complex problems, such as those involving real gravity acceleration data of a planet as the constraint, our trans-dimensional gravity inversion algorithm provides a good option to overcome the problem of non-uniqueness while achieving parsimony in gravity inversions.

RevBayes: Bayesian Phylogenetic Inference Using Graphical Models and an Interactive Model-Specification Language

PubMed Central

Höhna, Sebastian; Landis, Michael J.

2016-01-01

Programs for Bayesian inference of phylogeny currently implement a unique and fixed suite of models. Consequently, users of these software packages are simultaneously forced to use a number of programs for a given study, while also lacking the freedom to explore models that have not been implemented by the developers of those programs. We developed a new open-source software package, RevBayes, to address these problems. RevBayes is entirely based on probabilistic graphical models, a powerful generic framework for specifying and analyzing statistical models. Phylogenetic-graphical models can be specified interactively in RevBayes, piece by piece, using a new succinct and intuitive language called Rev. Rev is similar to the R language and the BUGS model-specification language, and should be easy to learn for most users. The strength of RevBayes is the simplicity with which one can design, specify, and implement new and complex models. Fortunately, this tremendous flexibility does not come at the cost of slower computation; as we demonstrate, RevBayes outperforms competing software for several standard analyses. Compared with other programs, RevBayes has fewer black-box elements. Users need to explicitly specify each part of the model and analysis. Although this explicitness may initially be unfamiliar, we are convinced that this transparency will improve understanding of phylogenetic models in our field. Moreover, it will motivate the search for improvements to existing methods by brazenly exposing the model choices that we make to critical scrutiny. RevBayes is freely available at http://www.RevBayes.com. [Bayesian inference; Graphical models; MCMC; statistical phylogenetics.] PMID:27235697

DESCARTES' RULE OF SIGNS AND THE IDENTIFIABILITY OF POPULATION DEMOGRAPHIC MODELS FROM GENOMIC VARIATION DATA.

PubMed

Bhaskar, Anand; Song, Yun S

2014-01-01

The sample frequency spectrum (SFS) is a widely-used summary statistic of genomic variation in a sample of homologous DNA sequences. It provides a highly efficient dimensional reduction of large-scale population genomic data and its mathematical dependence on the underlying population demography is well understood, thus enabling the development of efficient inference algorithms. However, it has been recently shown that very different population demographies can actually generate the same SFS for arbitrarily large sample sizes. Although in principle this nonidentifiability issue poses a thorny challenge to statistical inference, the population size functions involved in the counterexamples are arguably not so biologically realistic. Here, we revisit this problem and examine the identifiability of demographic models under the restriction that the population sizes are piecewise-defined where each piece belongs to some family of biologically-motivated functions. Under this assumption, we prove that the expected SFS of a sample uniquely determines the underlying demographic model, provided that the sample is sufficiently large. We obtain a general bound on the sample size sufficient for identifiability; the bound depends on the number of pieces in the demographic model and also on the type of population size function in each piece. In the cases of piecewise-constant, piecewise-exponential and piecewise-generalized-exponential models, which are often assumed in population genomic inferences, we provide explicit formulas for the bounds as simple functions of the number of pieces. Lastly, we obtain analogous results for the "folded" SFS, which is often used when there is ambiguity as to which allelic type is ancestral. Our results are proved using a generalization of Descartes' rule of signs for polynomials to the Laplace transform of piecewise continuous functions.

DESCARTES’ RULE OF SIGNS AND THE IDENTIFIABILITY OF POPULATION DEMOGRAPHIC MODELS FROM GENOMIC VARIATION DATA1

PubMed Central

Bhaskar, Anand; Song, Yun S.

2016-01-01

The sample frequency spectrum (SFS) is a widely-used summary statistic of genomic variation in a sample of homologous DNA sequences. It provides a highly efficient dimensional reduction of large-scale population genomic data and its mathematical dependence on the underlying population demography is well understood, thus enabling the development of efficient inference algorithms. However, it has been recently shown that very different population demographies can actually generate the same SFS for arbitrarily large sample sizes. Although in principle this nonidentifiability issue poses a thorny challenge to statistical inference, the population size functions involved in the counterexamples are arguably not so biologically realistic. Here, we revisit this problem and examine the identifiability of demographic models under the restriction that the population sizes are piecewise-defined where each piece belongs to some family of biologically-motivated functions. Under this assumption, we prove that the expected SFS of a sample uniquely determines the underlying demographic model, provided that the sample is sufficiently large. We obtain a general bound on the sample size sufficient for identifiability; the bound depends on the number of pieces in the demographic model and also on the type of population size function in each piece. In the cases of piecewise-constant, piecewise-exponential and piecewise-generalized-exponential models, which are often assumed in population genomic inferences, we provide explicit formulas for the bounds as simple functions of the number of pieces. Lastly, we obtain analogous results for the “folded” SFS, which is often used when there is ambiguity as to which allelic type is ancestral. Our results are proved using a generalization of Descartes’ rule of signs for polynomials to the Laplace transform of piecewise continuous functions. PMID:28018011

RevBayes: Bayesian Phylogenetic Inference Using Graphical Models and an Interactive Model-Specification Language.

PubMed

Höhna, Sebastian; Landis, Michael J; Heath, Tracy A; Boussau, Bastien; Lartillot, Nicolas; Moore, Brian R; Huelsenbeck, John P; Ronquist, Fredrik

2016-07-01

Programs for Bayesian inference of phylogeny currently implement a unique and fixed suite of models. Consequently, users of these software packages are simultaneously forced to use a number of programs for a given study, while also lacking the freedom to explore models that have not been implemented by the developers of those programs. We developed a new open-source software package, RevBayes, to address these problems. RevBayes is entirely based on probabilistic graphical models, a powerful generic framework for specifying and analyzing statistical models. Phylogenetic-graphical models can be specified interactively in RevBayes, piece by piece, using a new succinct and intuitive language called Rev. Rev is similar to the R language and the BUGS model-specification language, and should be easy to learn for most users. The strength of RevBayes is the simplicity with which one can design, specify, and implement new and complex models. Fortunately, this tremendous flexibility does not come at the cost of slower computation; as we demonstrate, RevBayes outperforms competing software for several standard analyses. Compared with other programs, RevBayes has fewer black-box elements. Users need to explicitly specify each part of the model and analysis. Although this explicitness may initially be unfamiliar, we are convinced that this transparency will improve understanding of phylogenetic models in our field. Moreover, it will motivate the search for improvements to existing methods by brazenly exposing the model choices that we make to critical scrutiny. RevBayes is freely available at http://www.RevBayes.com [Bayesian inference; Graphical models; MCMC; statistical phylogenetics.]. © The Author(s) 2016. Published by Oxford University Press, on behalf of the Society of Systematic Biologists.

Demographics of the gay and lesbian population in the United States: evidence from available systematic data sources.

PubMed

Black, D; Gates, G; Sanders, S; Taylor, L

2000-05-01

This work provides an overview of standard social science data sources that now allow some systematic study of the gay and lesbian population in the United States. For each data source, we consider how sexual orientation can be defined, and we note the potential sample sizes. We give special attention to the important problem of measurement error, especially the extent to which individuals recorded as gay and lesbian are indeed recorded correctly. Our concern is that because gays and lesbians constitute a relatively small fraction of the population, modest measurement problems could lead to serious errors in inference. In examining gays and lesbians in multiple data sets we also achieve a second objective: We provide a set of statistics about this population that is relevant to several current policy debates.

The two-sample problem with induced dependent censorship.

PubMed

Huang, Y

1999-12-01

Induced dependent censorship is a general phenomenon in health service evaluation studies in which a measure such as quality-adjusted survival time or lifetime medical cost is of interest. We investigate the two-sample problem and propose two classes of nonparametric tests. Based on consistent estimation of the survival function for each sample, the two classes of test statistics examine the cumulative weighted difference in hazard functions and in survival functions. We derive a unified asymptotic null distribution theory and inference procedure. The tests are applied to trial V of the International Breast Cancer Study Group and show that long duration chemotherapy significantly improves time without symptoms of disease and toxicity of treatment as compared with the short duration treatment. Simulation studies demonstrate that the proposed tests, with a wide range of weight choices, perform well under moderate sample sizes.

A generative inference framework for analysing patterns of cultural change in sparse population data with evidence for fashion trends in LBK culture.

PubMed

Kandler, Anne; Shennan, Stephen

2015-12-06

Cultural change can be quantified by temporal changes in frequency of different cultural artefacts and it is a central question to identify what underlying cultural transmission processes could have caused the observed frequency changes. Observed changes, however, often describe the dynamics in samples of the population of artefacts, whereas transmission processes act on the whole population. Here we develop a modelling framework aimed at addressing this inference problem. To do so, we firstly generate population structures from which the observed sample could have been drawn randomly and then determine theoretical samples at a later time t2 produced under the assumption that changes in frequencies are caused by a specific transmission process. Thereby we also account for the potential effect of time-averaging processes in the generation of the observed sample. Subsequent statistical comparisons (e.g. using Bayesian inference) of the theoretical and observed samples at t2 can establish which processes could have produced the observed frequency data. In this way, we infer underlying transmission processes directly from available data without any equilibrium assumption. We apply this framework to a dataset describing pottery from settlements of some of the first farmers in Europe (the LBK culture) and conclude that the observed frequency dynamic of different types of decorated pottery is consistent with age-dependent selection, a preference for 'young' pottery types which is potentially indicative of fashion trends. © 2015 The Author(s).

Pointwise probability reinforcements for robust statistical inference.

PubMed

Frénay, Benoît; Verleysen, Michel

2014-02-01

Statistical inference using machine learning techniques may be difficult with small datasets because of abnormally frequent data (AFDs). AFDs are observations that are much more frequent in the training sample that they should be, with respect to their theoretical probability, and include e.g. outliers. Estimates of parameters tend to be biased towards models which support such data. This paper proposes to introduce pointwise probability reinforcements (PPRs): the probability of each observation is reinforced by a PPR and a regularisation allows controlling the amount of reinforcement which compensates for AFDs. The proposed solution is very generic, since it can be used to robustify any statistical inference method which can be formulated as a likelihood maximisation. Experiments show that PPRs can be easily used to tackle regression, classification and projection: models are freed from the influence of outliers. Moreover, outliers can be filtered manually since an abnormality degree is obtained for each observation. Copyright © 2013 Elsevier Ltd. All rights reserved.

Probability, statistics, and computational science.

PubMed

Beerenwinkel, Niko; Siebourg, Juliane

2012-01-01

In this chapter, we review basic concepts from probability theory and computational statistics that are fundamental to evolutionary genomics. We provide a very basic introduction to statistical modeling and discuss general principles, including maximum likelihood and Bayesian inference. Markov chains, hidden Markov models, and Bayesian network models are introduced in more detail as they occur frequently and in many variations in genomics applications. In particular, we discuss efficient inference algorithms and methods for learning these models from partially observed data. Several simple examples are given throughout the text, some of which point to models that are discussed in more detail in subsequent chapters.

A Not-So-Fundamental Limitation on Studying Complex Systems with Statistics: Comment on Rabin (2011)

NASA Astrophysics Data System (ADS)

Thomas, Drew M.

2012-12-01

Although living organisms are affected by many interrelated and unidentified variables, this complexity does not automatically impose a fundamental limitation on statistical inference. Nor need one invoke such complexity as an explanation of the "Truth Wears Off" or "decline" effect; similar "decline" effects occur with far simpler systems studied in physics. Selective reporting and publication bias, and scientists' biases in favor of reporting eye-catching results (in general) or conforming to others' results (in physics) better explain this feature of the "Truth Wears Off" effect than Rabin's suggested limitation on statistical inference.

Inference Processing in Adolescents with Asperger Syndrome: Relationship with Theory of Mind Abilities

ERIC Educational Resources Information Center

Le Sourn-Bissaoui, Sandrine; Caillies, Stephanie; Gierski, Fabien; Motte, Jacques

2009-01-01

The aim of this study was to investigate the role of theory of mind competence in inference processing in adolescents with Asperger syndrome (AS). We sought to pinpoint the level at which AS individuals experience difficulty drawing inferences and identify the factors that account for their inference-drawing problems. We hypothesized that this…

Adaptation in pronoun resolution: Evidence from Brazilian and European Portuguese.

PubMed

Fernandes, Eunice G; Luegi, Paula; Correa Soares, Eduardo; de la Fuente, Israel; Hemforth, Barbara

2018-04-26

Previous research accounting for pronoun resolution as a problem of probabilistic inference has not explored the phenomenon of adaptation, whereby the processor constantly tracks and adapts, rationally, to changes in a statistical environment. We investigate whether Brazilian (BP) and European Portuguese (EP) speakers adapt to variations in the probability of occurrence of ambiguous overt and null pronouns, in two experiments assessing resolution toward subject and object referents. For each variety (BP, EP), participants were faced with either the same number of null and overt pronouns (equal distribution), or with an environment with fewer overt (than null) pronouns (unequal distribution). We find that the preference for interpreting overt pronouns as referring back to an object referent (object-biased interpretation) is higher when there are fewer overt pronouns (i.e., in the unequal, relative to the equal distribution condition). This is especially the case for BP, a variety with higher prior frequency and smaller object-biased interpretation of overt pronouns, suggesting that participants adapted incrementally and integrated prior statistical knowledge with the knowledge obtained in the experiment. We hypothesize that comprehenders adapted rationally, with the goal of maintaining, across variations in pronoun probability, the likelihood of subject and object referents. Our findings unify insights from research in pronoun resolution and in adaptation, and add to previous studies in both topics: They provide evidence for the influence of pronoun probability in pronoun resolution, and for an adaptation process whereby the language processor not only tracks statistical information, but uses it to make interpretational inferences. (PsycINFO Database Record (c) 2018 APA, all rights reserved).

Much ado about two: reconsidering retransformation and the two-part model in health econometrics.

PubMed

Mullahy, J

1998-06-01

In health economics applications involving outcomes (y) and covariates (x), it is often the case that the central inferential problems of interest involve E[y/x] and its associated partial effects or elasticities. Many such outcomes have two fundamental statistical properties: y > or = 0; and the outcome y = 0 is observed with sufficient frequency that the zeros cannot be ignored econometrically. This paper (1) describes circumstances where the standard two-part model with homoskedastic retransformation will fail to provide consistent inferences about important policy parameters; and (2) demonstrates some alternative approaches that are likely to prove helpful in applications.

Motor control is decision-making.

PubMed

Wolpert, Daniel M; Landy, Michael S

2012-12-01

Motor behavior may be viewed as a problem of maximizing the utility of movement outcome in the face of sensory, motor and task uncertainty. Viewed in this way, and allowing for the availability of prior knowledge in the form of a probability distribution over possible states of the world, the choice of a movement plan and strategy for motor control becomes an application of statistical decision theory. This point of view has proven successful in recent years in accounting for movement under risk, inferring the loss function used in motor tasks, and explaining motor behavior in a wide variety of circumstances. Copyright © 2012 Elsevier Ltd. All rights reserved.

Divide et impera: subgoaling reduces the complexity of probabilistic inference and problem solving

PubMed Central

Maisto, Domenico; Donnarumma, Francesco; Pezzulo, Giovanni

2015-01-01

It has long been recognized that humans (and possibly other animals) usually break problems down into smaller and more manageable problems using subgoals. Despite a general consensus that subgoaling helps problem solving, it is still unclear what the mechanisms guiding online subgoal selection are during the solution of novel problems for which predefined solutions are not available. Under which conditions does subgoaling lead to optimal behaviour? When is subgoaling better than solving a problem from start to finish? Which is the best number and sequence of subgoals to solve a given problem? How are these subgoals selected during online inference? Here, we present a computational account of subgoaling in problem solving. Following Occam's razor, we propose that good subgoals are those that permit planning solutions and controlling behaviour using less information resources, thus yielding parsimony in inference and control. We implement this principle using approximate probabilistic inference: subgoals are selected using a sampling method that considers the descriptive complexity of the resulting sub-problems. We validate the proposed method using a standard reinforcement learning benchmark (four-rooms scenario) and show that the proposed method requires less inferential steps and permits selecting more compact control programs compared to an equivalent procedure without subgoaling. Furthermore, we show that the proposed method offers a mechanistic explanation of the neuronal dynamics found in the prefrontal cortex of monkeys that solve planning problems. Our computational framework provides a novel integrative perspective on subgoaling and its adaptive advantages for planning, control and learning, such as for example lowering cognitive effort and working memory load. PMID:25652466

Bayesian Inference: with ecological applications

USGS Publications Warehouse

Link, William A.; Barker, Richard J.

2010-01-01

This text provides a mathematically rigorous yet accessible and engaging introduction to Bayesian inference with relevant examples that will be of interest to biologists working in the fields of ecology, wildlife management and environmental studies as well as students in advanced undergraduate statistics.. This text opens the door to Bayesian inference, taking advantage of modern computational efficiencies and easily accessible software to evaluate complex hierarchical models.

Theory-based Bayesian Models of Inductive Inference

DTIC Science & Technology

2010-07-19

Subjective randomness and natural scene statistics. Psychonomic Bulletin & Review . http://cocosci.berkeley.edu/tom/papers/randscenes.pdf Page 1...in press). Exemplar models as a mechanism for performing Bayesian inference. Psychonomic Bulletin & Review . http://cocosci.berkeley.edu/tom

Separate and Simultaneous Adjustment of Light Qualities in a Real Scene

PubMed Central

Pont, Sylvia C.; Heynderick, Ingrid

2017-01-01

Humans are able to estimate light field properties in a scene in that they have expectations of the objects’ appearance inside it. Previously, we probed such expectations in a real scene by asking whether a “probe object” fitted a real scene with regard to its lighting. But how well are observers able to interactively adjust the light properties on a “probe object” to its surrounding real scene? Image ambiguities can result in perceptual interactions between light properties. Such interactions formed a major problem for the “readability” of the illumination direction and diffuseness on a matte smooth spherical probe. We found that light direction and diffuseness judgments using a rough sphere as probe were slightly more accurate than when using a smooth sphere, due to the three-dimensional (3D) texture. We here extended the previous work by testing independent and simultaneous (i.e., the light field properties separated one by one or blended together) adjustments of light intensity, direction, and diffuseness using a rough probe. Independently inferred light intensities were close to the veridical values, and the simultaneously inferred light intensity interacted somewhat with the light direction and diffuseness. The independently inferred light directions showed no statistical difference with the simultaneously inferred directions. The light diffuseness inferences correlated with but contracted around medium veridical values. In summary, observers were able to adjust the basic light properties through both independent and simultaneous adjustments. The light intensity, direction, and diffuseness are well “readable” from our rough probe. Our method allows “tuning the light” (adjustment of its spatial distribution) in interfaces for lighting design or perception research. PMID:28203350

Differences in Performance Among Test Statistics for Assessing Phylogenomic Model Adequacy.

PubMed

Duchêne, David A; Duchêne, Sebastian; Ho, Simon Y W

2018-05-18

Statistical phylogenetic analyses of genomic data depend on models of nucleotide or amino acid substitution. The adequacy of these substitution models can be assessed using a number of test statistics, allowing the model to be rejected when it is found to provide a poor description of the evolutionary process. A potentially valuable use of model-adequacy test statistics is to identify when data sets are likely to produce unreliable phylogenetic estimates, but their differences in performance are rarely explored. We performed a comprehensive simulation study to identify test statistics that are sensitive to some of the most commonly cited sources of phylogenetic estimation error. Our results show that, for many test statistics, traditional thresholds for assessing model adequacy can fail to reject the model when the phylogenetic inferences are inaccurate and imprecise. This is particularly problematic when analysing loci that have few variable informative sites. We propose new thresholds for assessing substitution model adequacy and demonstrate their effectiveness in analyses of three phylogenomic data sets. These thresholds lead to frequent rejection of the model for loci that yield topological inferences that are imprecise and are likely to be inaccurate. We also propose the use of a summary statistic that provides a practical assessment of overall model adequacy. Our approach offers a promising means of enhancing model choice in genome-scale data sets, potentially leading to improvements in the reliability of phylogenomic inference.

Powerful Statistical Inference for Nested Data Using Sufficient Summary Statistics

PubMed Central

Dowding, Irene; Haufe, Stefan

2018-01-01

Hierarchically-organized data arise naturally in many psychology and neuroscience studies. As the standard assumption of independent and identically distributed samples does not hold for such data, two important problems are to accurately estimate group-level effect sizes, and to obtain powerful statistical tests against group-level null hypotheses. A common approach is to summarize subject-level data by a single quantity per subject, which is often the mean or the difference between class means, and treat these as samples in a group-level t-test. This “naive” approach is, however, suboptimal in terms of statistical power, as it ignores information about the intra-subject variance. To address this issue, we review several approaches to deal with nested data, with a focus on methods that are easy to implement. With what we call the sufficient-summary-statistic approach, we highlight a computationally efficient technique that can improve statistical power by taking into account within-subject variances, and we provide step-by-step instructions on how to apply this approach to a number of frequently-used measures of effect size. The properties of the reviewed approaches and the potential benefits over a group-level t-test are quantitatively assessed on simulated data and demonstrated on EEG data from a simulated-driving experiment. PMID:29615885

Applications of statistics to medical science (1) Fundamental concepts.

PubMed

Watanabe, Hiroshi

2011-01-01

The conceptual framework of statistical tests and statistical inferences are discussed, and the epidemiological background of statistics is briefly reviewed. This study is one of a series in which we survey the basics of statistics and practical methods used in medical statistics. Arguments related to actual statistical analysis procedures will be made in subsequent papers.

Two Approaches to Calibration in Metrology

DOE Office of Scientific and Technical Information (OSTI.GOV)

Campanelli, Mark

2014-04-01

Inferring mathematical relationships with quantified uncertainty from measurement data is common to computational science and metrology. Sufficient knowledge of measurement process noise enables Bayesian inference. Otherwise, an alternative approach is required, here termed compartmentalized inference, because collection of uncertain data and model inference occur independently. Bayesian parameterized model inference is compared to a Bayesian-compatible compartmentalized approach for ISO-GUM compliant calibration problems in renewable energy metrology. In either approach, model evidence can help reduce model discrepancy.

Benchmarking Inverse Statistical Approaches for Protein Structure and Design with Exactly Solvable Models.

PubMed

Jacquin, Hugo; Gilson, Amy; Shakhnovich, Eugene; Cocco, Simona; Monasson, Rémi

2016-05-01

Inverse statistical approaches to determine protein structure and function from Multiple Sequence Alignments (MSA) are emerging as powerful tools in computational biology. However the underlying assumptions of the relationship between the inferred effective Potts Hamiltonian and real protein structure and energetics remain untested so far. Here we use lattice protein model (LP) to benchmark those inverse statistical approaches. We build MSA of highly stable sequences in target LP structures, and infer the effective pairwise Potts Hamiltonians from those MSA. We find that inferred Potts Hamiltonians reproduce many important aspects of 'true' LP structures and energetics. Careful analysis reveals that effective pairwise couplings in inferred Potts Hamiltonians depend not only on the energetics of the native structure but also on competing folds; in particular, the coupling values reflect both positive design (stabilization of native conformation) and negative design (destabilization of competing folds). In addition to providing detailed structural information, the inferred Potts models used as protein Hamiltonian for design of new sequences are able to generate with high probability completely new sequences with the desired folds, which is not possible using independent-site models. Those are remarkable results as the effective LP Hamiltonians used to generate MSA are not simple pairwise models due to the competition between the folds. Our findings elucidate the reasons for the success of inverse approaches to the modelling of proteins from sequence data, and their limitations.

Constructing networks with correlation maximization methods.

PubMed

Mellor, Joseph C; Wu, Jie; Delisi, Charles

2004-01-01

Problems of inference in systems biology are ideally reduced to formulations which can efficiently represent the features of interest. In the case of predicting gene regulation and pathway networks, an important feature which describes connected genes and proteins is the relationship between active and inactive forms, i.e. between the "on" and "off" states of the components. While not optimal at the limits of resolution, these logical relationships between discrete states can often yield good approximations of the behavior in larger complex systems, where exact representation of measurement relationships may be intractable. We explore techniques for extracting binary state variables from measurement of gene expression, and go on to describe robust measures for statistical significance and information that can be applied to many such types of data. We show how statistical strength and information are equivalent criteria in limiting cases, and demonstrate the application of these measures to simple systems of gene regulation.

Stationarity: Wanted dead or alive?

USGS Publications Warehouse

Lins, H.F.; Cohn, T.A.

2011-01-01

Aligning engineering practice with natural process behavior would appear, on its face, to be a prudent and reasonable course of action. However, if we do not understand the long-term characteristics of hydroclimatic processes, how does one find the prudent and reasonable course needed for water management? We consider this question in light of three aspects of existing and unresolved issues affecting hydroclimatic variability and statistical inference: Hurst-Kolmogorov phenomena; the complications long-term persistence introduces with respect to statistical understanding; and the dependence of process understanding on arbitrary sampling choices. These problems are not easily addressed. In such circumstances, humility may be more important than physics; a simple model with well-understood flaws may be preferable to a sophisticated model whose correspondence to reality is uncertain. ?? 2011 American Water Resources Association. This article is a U.S. Government work and is in the public domain in the USA.

Logical reasoning versus information processing in the dual-strategy model of reasoning.

PubMed

Markovits, Henry; Brisson, Janie; de Chantal, Pier-Luc

2017-01-01

One of the major debates concerning the nature of inferential reasoning is between counterexample-based strategies such as mental model theory and statistical strategies underlying probabilistic models. The dual-strategy model, proposed by Verschueren, Schaeken, & d'Ydewalle (2005a, 2005b), which suggests that people might have access to both kinds of strategy has been supported by several recent studies. These have shown that statistical reasoners make inferences based on using information about premises in order to generate a likelihood estimate of conclusion probability. However, while results concerning counterexample reasoners are consistent with a counterexample detection model, these results could equally be interpreted as indicating a greater sensitivity to logical form. In order to distinguish these 2 interpretations, in Studies 1 and 2, we presented reasoners with Modus ponens (MP) inferences with statistical information about premise strength and in Studies 3 and 4, naturalistic MP inferences with premises having many disabling conditions. Statistical reasoners accepted the MP inference more often than counterexample reasoners in Studies 1 and 2, while the opposite pattern was observed in Studies 3 and 4. Results show that these strategies must be defined in terms of information processing, with no clear relations to "logical" reasoning. These results have additional implications for the underlying debate about the nature of human reasoning. (PsycINFO Database Record (c) 2017 APA, all rights reserved).

Statistical inference for Hardy-Weinberg proportions in the presence of missing genotype information.

PubMed

Graffelman, Jan; Sánchez, Milagros; Cook, Samantha; Moreno, Victor

2013-01-01

In genetic association studies, tests for Hardy-Weinberg proportions are often employed as a quality control checking procedure. Missing genotypes are typically discarded prior to testing. In this paper we show that inference for Hardy-Weinberg proportions can be biased when missing values are discarded. We propose to use multiple imputation of missing values in order to improve inference for Hardy-Weinberg proportions. For imputation we employ a multinomial logit model that uses information from allele intensities and/or neighbouring markers. Analysis of an empirical data set of single nucleotide polymorphisms possibly related to colon cancer reveals that missing genotypes are not missing completely at random. Deviation from Hardy-Weinberg proportions is mostly due to a lack of heterozygotes. Inbreeding coefficients estimated by multiple imputation of the missings are typically lowered with respect to inbreeding coefficients estimated by discarding the missings. Accounting for missings by multiple imputation qualitatively changed the results of 10 to 17% of the statistical tests performed. Estimates of inbreeding coefficients obtained by multiple imputation showed high correlation with estimates obtained by single imputation using an external reference panel. Our conclusion is that imputation of missing data leads to improved statistical inference for Hardy-Weinberg proportions.

[Application of statistics on chronic-diseases-relating observational research papers].

PubMed

Hong, Zhi-heng; Wang, Ping; Cao, Wei-hua

2012-09-01

To study the application of statistics on Chronic-diseases-relating observational research papers which were recently published in the Chinese Medical Association Magazines, with influential index above 0.5. Using a self-developed criterion, two investigators individually participated in assessing the application of statistics on Chinese Medical Association Magazines, with influential index above 0.5. Different opinions reached an agreement through discussion. A total number of 352 papers from 6 magazines, including the Chinese Journal of Epidemiology, Chinese Journal of Oncology, Chinese Journal of Preventive Medicine, Chinese Journal of Cardiology, Chinese Journal of Internal Medicine and Chinese Journal of Endocrinology and Metabolism, were reviewed. The rate of clear statement on the following contents as: research objectives, t target audience, sample issues, objective inclusion criteria and variable definitions were 99.43%, 98.57%, 95.43%, 92.86% and 96.87%. The correct rates of description on quantitative and qualitative data were 90.94% and 91.46%, respectively. The rates on correctly expressing the results, on statistical inference methods related to quantitative, qualitative data and modeling were 100%, 95.32% and 87.19%, respectively. 89.49% of the conclusions could directly response to the research objectives. However, 69.60% of the papers did not mention the exact names of the study design, statistically, that the papers were using. 11.14% of the papers were in lack of further statement on the exclusion criteria. Percentage of the papers that could clearly explain the sample size estimation only taking up as 5.16%. Only 24.21% of the papers clearly described the variable value assignment. Regarding the introduction on statistical conduction and on database methods, the rate was only 24.15%. 18.75% of the papers did not express the statistical inference methods sufficiently. A quarter of the papers did not use 'standardization' appropriately. As for the aspect of statistical inference, the rate of description on statistical testing prerequisite was only 24.12% while 9.94% papers did not even employ the statistical inferential method that should be used. The main deficiencies on the application of Statistics used in papers related to Chronic-diseases-related observational research were as follows: lack of sample-size determination, variable value assignment description not sufficient, methods on statistics were not introduced clearly or properly, lack of consideration for pre-requisition regarding the use of statistical inferences.

[Bayesian approach for the cost-effectiveness evaluation of healthcare technologies].

PubMed

Berchialla, Paola; Gregori, Dario; Brunello, Franco; Veltri, Andrea; Petrinco, Michele; Pagano, Eva

2009-01-01

The development of Bayesian statistical methods for the assessment of the cost-effectiveness of health care technologies is reviewed. Although many studies adopt a frequentist approach, several authors have advocated the use of Bayesian methods in health economics. Emphasis has been placed on the advantages of the Bayesian approach, which include: (i) the ability to make more intuitive and meaningful inferences; (ii) the ability to tackle complex problems, such as allowing for the inclusion of patients who generate no cost, thanks to the availability of powerful computational algorithms; (iii) the importance of a full use of quantitative and structural prior information to produce realistic inferences. Much literature comparing the cost-effectiveness of two treatments is based on the incremental cost-effectiveness ratio. However, new methods are arising with the purpose of decision making. These methods are based on a net benefits approach. In the present context, the cost-effectiveness acceptability curves have been pointed out to be intrinsically Bayesian in their formulation. They plot the probability of a positive net benefit against the threshold cost of a unit increase in efficacy.A case study is presented in order to illustrate the Bayesian statistics in the cost-effectiveness analysis. Emphasis is placed on the cost-effectiveness acceptability curves. Advantages and disadvantages of the method described in this paper have been compared to frequentist methods and discussed.

Basics of Bayesian methods.

PubMed

Ghosh, Sujit K

2010-01-01

Bayesian methods are rapidly becoming popular tools for making statistical inference in various fields of science including biology, engineering, finance, and genetics. One of the key aspects of Bayesian inferential method is its logical foundation that provides a coherent framework to utilize not only empirical but also scientific information available to a researcher. Prior knowledge arising from scientific background, expert judgment, or previously collected data is used to build a prior distribution which is then combined with current data via the likelihood function to characterize the current state of knowledge using the so-called posterior distribution. Bayesian methods allow the use of models of complex physical phenomena that were previously too difficult to estimate (e.g., using asymptotic approximations). Bayesian methods offer a means of more fully understanding issues that are central to many practical problems by allowing researchers to build integrated models based on hierarchical conditional distributions that can be estimated even with limited amounts of data. Furthermore, advances in numerical integration methods, particularly those based on Monte Carlo methods, have made it possible to compute the optimal Bayes estimators. However, there is a reasonably wide gap between the background of the empirically trained scientists and the full weight of Bayesian statistical inference. Hence, one of the goals of this chapter is to bridge the gap by offering elementary to advanced concepts that emphasize linkages between standard approaches and full probability modeling via Bayesian methods.

A linear programming model for protein inference problem in shotgun proteomics.

PubMed

Huang, Ting; He, Zengyou

2012-11-15

Assembling peptides identified from tandem mass spectra into a list of proteins, referred to as protein inference, is an important issue in shotgun proteomics. The objective of protein inference is to find a subset of proteins that are truly present in the sample. Although many methods have been proposed for protein inference, several issues such as peptide degeneracy still remain unsolved. In this article, we present a linear programming model for protein inference. In this model, we use a transformation of the joint probability that each peptide/protein pair is present in the sample as the variable. Then, both the peptide probability and protein probability can be expressed as a formula in terms of the linear combination of these variables. Based on this simple fact, the protein inference problem is formulated as an optimization problem: minimize the number of proteins with non-zero probabilities under the constraint that the difference between the calculated peptide probability and the peptide probability generated from peptide identification algorithms should be less than some threshold. This model addresses the peptide degeneracy issue by forcing some joint probability variables involving degenerate peptides to be zero in a rigorous manner. The corresponding inference algorithm is named as ProteinLP. We test the performance of ProteinLP on six datasets. Experimental results show that our method is competitive with the state-of-the-art protein inference algorithms. The source code of our algorithm is available at: https://sourceforge.net/projects/prolp/. zyhe@dlut.edu.cn. Supplementary data are available at Bioinformatics Online.

Causal Inference in Retrospective Studies.

ERIC Educational Resources Information Center

Holland, Paul W.; Rubin, Donald B.

1988-01-01

The problem of drawing causal inferences from retrospective case-controlled studies is considered. A model for causal inference in prospective studies is applied to retrospective studies. Limitations of case-controlled studies are formulated concerning relevant parameters that can be estimated in such studies. A coffee-drinking/myocardial…

Using speakers' referential intentions to model early cross-situational word learning.

PubMed

Frank, Michael C; Goodman, Noah D; Tenenbaum, Joshua B

2009-05-01

Word learning is a "chicken and egg" problem. If a child could understand speakers' utterances, it would be easy to learn the meanings of individual words, and once a child knows what many words mean, it is easy to infer speakers' intended meanings. To the beginning learner, however, both individual word meanings and speakers' intentions are unknown. We describe a computational model of word learning that solves these two inference problems in parallel, rather than relying exclusively on either the inferred meanings of utterances or cross-situational word-meaning associations. We tested our model using annotated corpus data and found that it inferred pairings between words and object concepts with higher precision than comparison models. Moreover, as the result of making probabilistic inferences about speakers' intentions, our model explains a variety of behavioral phenomena described in the word-learning literature. These phenomena include mutual exclusivity, one-trial learning, cross-situational learning, the role of words in object individuation, and the use of inferred intentions to disambiguate reference.

Truth, models, model sets, AIC, and multimodel inference: a Bayesian perspective

USGS Publications Warehouse

Barker, Richard J.; Link, William A.

2015-01-01

Statistical inference begins with viewing data as realizations of stochastic processes. Mathematical models provide partial descriptions of these processes; inference is the process of using the data to obtain a more complete description of the stochastic processes. Wildlife and ecological scientists have become increasingly concerned with the conditional nature of model-based inference: what if the model is wrong? Over the last 2 decades, Akaike's Information Criterion (AIC) has been widely and increasingly used in wildlife statistics for 2 related purposes, first for model choice and second to quantify model uncertainty. We argue that for the second of these purposes, the Bayesian paradigm provides the natural framework for describing uncertainty associated with model choice and provides the most easily communicated basis for model weighting. Moreover, Bayesian arguments provide the sole justification for interpreting model weights (including AIC weights) as coherent (mathematically self consistent) model probabilities. This interpretation requires treating the model as an exact description of the data-generating mechanism. We discuss the implications of this assumption, and conclude that more emphasis is needed on model checking to provide confidence in the quality of inference.

Analysis of Statistical Methods and Errors in the Articles Published in the Korean Journal of Pain

PubMed Central

Yim, Kyoung Hoon; Han, Kyoung Ah; Park, Soo Young

2010-01-01

Background Statistical analysis is essential in regard to obtaining objective reliability for medical research. However, medical researchers do not have enough statistical knowledge to properly analyze their study data. To help understand and potentially alleviate this problem, we have analyzed the statistical methods and errors of articles published in the Korean Journal of Pain (KJP), with the intention to improve the statistical quality of the journal. Methods All the articles, except case reports and editorials, published from 2004 to 2008 in the KJP were reviewed. The types of applied statistical methods and errors in the articles were evaluated. Results One hundred and thirty-nine original articles were reviewed. Inferential statistics and descriptive statistics were used in 119 papers and 20 papers, respectively. Only 20.9% of the papers were free from statistical errors. The most commonly adopted statistical method was the t-test (21.0%) followed by the chi-square test (15.9%). Errors of omission were encountered 101 times in 70 papers. Among the errors of omission, "no statistics used even though statistical methods were required" was the most common (40.6%). The errors of commission were encountered 165 times in 86 papers, among which "parametric inference for nonparametric data" was the most common (33.9%). Conclusions We found various types of statistical errors in the articles published in the KJP. This suggests that meticulous attention should be given not only in the applying statistical procedures but also in the reviewing process to improve the value of the article. PMID:20552071

Selecting the right statistical model for analysis of insect count data by using information theoretic measures.

PubMed

Sileshi, G

2006-10-01

Researchers and regulatory agencies often make statistical inferences from insect count data using modelling approaches that assume homogeneous variance. Such models do not allow for formal appraisal of variability which in its different forms is the subject of interest in ecology. Therefore, the objectives of this paper were to (i) compare models suitable for handling variance heterogeneity and (ii) select optimal models to ensure valid statistical inferences from insect count data. The log-normal, standard Poisson, Poisson corrected for overdispersion, zero-inflated Poisson, the negative binomial distribution and zero-inflated negative binomial models were compared using six count datasets on foliage-dwelling insects and five families of soil-dwelling insects. Akaike's and Schwarz Bayesian information criteria were used for comparing the various models. Over 50% of the counts were zeros even in locally abundant species such as Ootheca bennigseni Weise, Mesoplatys ochroptera Stål and Diaecoderus spp. The Poisson model after correction for overdispersion and the standard negative binomial distribution model provided better description of the probability distribution of seven out of the 11 insects than the log-normal, standard Poisson, zero-inflated Poisson or zero-inflated negative binomial models. It is concluded that excess zeros and variance heterogeneity are common data phenomena in insect counts. If not properly modelled, these properties can invalidate the normal distribution assumptions resulting in biased estimation of ecological effects and jeopardizing the integrity of the scientific inferences. Therefore, it is recommended that statistical models appropriate for handling these data properties be selected using objective criteria to ensure efficient statistical inference.

Comparison of a non-stationary voxelation-corrected cluster-size test with TFCE for group-Level MRI inference.

PubMed

Li, Huanjie; Nickerson, Lisa D; Nichols, Thomas E; Gao, Jia-Hong

2017-03-01

Two powerful methods for statistical inference on MRI brain images have been proposed recently, a non-stationary voxelation-corrected cluster-size test (CST) based on random field theory and threshold-free cluster enhancement (TFCE) based on calculating the level of local support for a cluster, then using permutation testing for inference. Unlike other statistical approaches, these two methods do not rest on the assumptions of a uniform and high degree of spatial smoothness of the statistic image. Thus, they are strongly recommended for group-level fMRI analysis compared to other statistical methods. In this work, the non-stationary voxelation-corrected CST and TFCE methods for group-level analysis were evaluated for both stationary and non-stationary images under varying smoothness levels, degrees of freedom and signal to noise ratios. Our results suggest that, both methods provide adequate control for the number of voxel-wise statistical tests being performed during inference on fMRI data and they are both superior to current CSTs implemented in popular MRI data analysis software packages. However, TFCE is more sensitive and stable for group-level analysis of VBM data. Thus, the voxelation-corrected CST approach may confer some advantages by being computationally less demanding for fMRI data analysis than TFCE with permutation testing and by also being applicable for single-subject fMRI analyses, while the TFCE approach is advantageous for VBM data. Hum Brain Mapp 38:1269-1280, 2017. © 2016 Wiley Periodicals, Inc. © 2016 Wiley Periodicals, Inc.

Unbiased split variable selection for random survival forests using maximally selected rank statistics.

PubMed

Wright, Marvin N; Dankowski, Theresa; Ziegler, Andreas

2017-04-15

The most popular approach for analyzing survival data is the Cox regression model. The Cox model may, however, be misspecified, and its proportionality assumption may not always be fulfilled. An alternative approach for survival prediction is random forests for survival outcomes. The standard split criterion for random survival forests is the log-rank test statistic, which favors splitting variables with many possible split points. Conditional inference forests avoid this split variable selection bias. However, linear rank statistics are utilized by default in conditional inference forests to select the optimal splitting variable, which cannot detect non-linear effects in the independent variables. An alternative is to use maximally selected rank statistics for the split point selection. As in conditional inference forests, splitting variables are compared on the p-value scale. However, instead of the conditional Monte-Carlo approach used in conditional inference forests, p-value approximations are employed. We describe several p-value approximations and the implementation of the proposed random forest approach. A simulation study demonstrates that unbiased split variable selection is possible. However, there is a trade-off between unbiased split variable selection and runtime. In benchmark studies of prediction performance on simulated and real datasets, the new method performs better than random survival forests if informative dichotomous variables are combined with uninformative variables with more categories and better than conditional inference forests if non-linear covariate effects are included. In a runtime comparison, the method proves to be computationally faster than both alternatives, if a simple p-value approximation is used. Copyright © 2017 John Wiley & Sons, Ltd. Copyright © 2017 John Wiley & Sons, Ltd.

FuncPatch: a web server for the fast Bayesian inference of conserved functional patches in protein 3D structures.

PubMed

Huang, Yi-Fei; Golding, G Brian

2015-02-15

A number of statistical phylogenetic methods have been developed to infer conserved functional sites or regions in proteins. Many methods, e.g. Rate4Site, apply the standard phylogenetic models to infer site-specific substitution rates and totally ignore the spatial correlation of substitution rates in protein tertiary structures, which may reduce their power to identify conserved functional patches in protein tertiary structures when the sequences used in the analysis are highly similar. The 3D sliding window method has been proposed to infer conserved functional patches in protein tertiary structures, but the window size, which reflects the strength of the spatial correlation, must be predefined and is not inferred from data. We recently developed GP4Rate to solve these problems under the Bayesian framework. Unfortunately, GP4Rate is computationally slow. Here, we present an intuitive web server, FuncPatch, to perform a fast approximate Bayesian inference of conserved functional patches in protein tertiary structures. Both simulations and four case studies based on empirical data suggest that FuncPatch is a good approximation to GP4Rate. However, FuncPatch is orders of magnitudes faster than GP4Rate. In addition, simulations suggest that FuncPatch is potentially a useful tool complementary to Rate4Site, but the 3D sliding window method is less powerful than FuncPatch and Rate4Site. The functional patches predicted by FuncPatch in the four case studies are supported by experimental evidence, which corroborates the usefulness of FuncPatch. The software FuncPatch is freely available at the web site, http://info.mcmaster.ca/yifei/FuncPatch golding@mcmaster.ca Supplementary data are available at Bioinformatics online. © The Author 2014. Published by Oxford University Press. All rights reserved. For Permissions, please e-mail: journals.permissions@oup.com.

Divide et impera: subgoaling reduces the complexity of probabilistic inference and problem solving.

PubMed

Maisto, Domenico; Donnarumma, Francesco; Pezzulo, Giovanni

2015-03-06

It has long been recognized that humans (and possibly other animals) usually break problems down into smaller and more manageable problems using subgoals. Despite a general consensus that subgoaling helps problem solving, it is still unclear what the mechanisms guiding online subgoal selection are during the solution of novel problems for which predefined solutions are not available. Under which conditions does subgoaling lead to optimal behaviour? When is subgoaling better than solving a problem from start to finish? Which is the best number and sequence of subgoals to solve a given problem? How are these subgoals selected during online inference? Here, we present a computational account of subgoaling in problem solving. Following Occam's razor, we propose that good subgoals are those that permit planning solutions and controlling behaviour using less information resources, thus yielding parsimony in inference and control. We implement this principle using approximate probabilistic inference: subgoals are selected using a sampling method that considers the descriptive complexity of the resulting sub-problems. We validate the proposed method using a standard reinforcement learning benchmark (four-rooms scenario) and show that the proposed method requires less inferential steps and permits selecting more compact control programs compared to an equivalent procedure without subgoaling. Furthermore, we show that the proposed method offers a mechanistic explanation of the neuronal dynamics found in the prefrontal cortex of monkeys that solve planning problems. Our computational framework provides a novel integrative perspective on subgoaling and its adaptive advantages for planning, control and learning, such as for example lowering cognitive effort and working memory load. © 2015 The Author(s) Published by the Royal Society. All rights reserved.

Incorporating Biological Knowledge into Evaluation of Casual Regulatory Hypothesis

NASA Technical Reports Server (NTRS)

Chrisman, Lonnie; Langley, Pat; Bay, Stephen; Pohorille, Andrew; DeVincenzi, D. (Technical Monitor)

2002-01-01

Biological data can be scarce and costly to obtain. The small number of samples available typically limits statistical power and makes reliable inference of causal relations extremely difficult. However, we argue that statistical power can be increased substantially by incorporating prior knowledge and data from diverse sources. We present a Bayesian framework that combines information from different sources and we show empirically that this lets one make correct causal inferences with small sample sizes that otherwise would be impossible.

A Review of Some Aspects of Robust Inference for Time Series.

DTIC Science & Technology

1984-09-01

REVIEW OF SOME ASPECTSOF ROBUST INFERNCE FOR TIME SERIES by Ad . Dougla Main TE "iAL REPOW No. 63 Septermber 1984 Department of Statistics University of ...clear. One cannot hope to have a good method for dealing with outliers in time series by using only an instantaneous nonlinear transformation of the data...AI.49 716 A REVIEWd OF SOME ASPECTS OF ROBUST INFERENCE FOR TIME 1/1 SERIES(U) WASHINGTON UNIV SEATTLE DEPT OF STATISTICS R D MARTIN SEP 84 TR-53

The researcher and the consultant: from testing to probability statements.

PubMed

Hamra, Ghassan B; Stang, Andreas; Poole, Charles

2015-09-01

In the first instalment of this series, Stang and Poole provided an overview of Fisher significance testing (ST), Neyman-Pearson null hypothesis testing (NHT), and their unfortunate and unintended offspring, null hypothesis significance testing. In addition to elucidating the distinction between the first two and the evolution of the third, the authors alluded to alternative models of statistical inference; namely, Bayesian statistics. Bayesian inference has experienced a revival in recent decades, with many researchers advocating for its use as both a complement and an alternative to NHT and ST. This article will continue in the direction of the first instalment, providing practicing researchers with an introduction to Bayesian inference. Our work will draw on the examples and discussion of the previous dialogue.

Spectral likelihood expansions for Bayesian inference

NASA Astrophysics Data System (ADS)

Nagel, Joseph B.; Sudret, Bruno

2016-03-01

A spectral approach to Bayesian inference is presented. It pursues the emulation of the posterior probability density. The starting point is a series expansion of the likelihood function in terms of orthogonal polynomials. From this spectral likelihood expansion all statistical quantities of interest can be calculated semi-analytically. The posterior is formally represented as the product of a reference density and a linear combination of polynomial basis functions. Both the model evidence and the posterior moments are related to the expansion coefficients. This formulation avoids Markov chain Monte Carlo simulation and allows one to make use of linear least squares instead. The pros and cons of spectral Bayesian inference are discussed and demonstrated on the basis of simple applications from classical statistics and inverse modeling.

What You Learn is What You See: Using Eye Movements to Study Infant Cross-Situational Word Learning

PubMed Central

Smith, Linda

2016-01-01

Recent studies show that both adults and young children possess powerful statistical learning capabilities to solve the word-to-world mapping problem. However, the underlying mechanisms that make statistical learning possible and powerful are not yet known. With the goal of providing new insights into this issue, the research reported in this paper used an eye tracker to record the moment-by-moment eye movement data of 14-month-old babies in statistical learning tasks. Various measures are applied to such fine-grained temporal data, such as looking duration and shift rate (the number of shifts in gaze from one visual object to the other) trial by trial, showing different eye movement patterns between strong and weak statistical learners. Moreover, an information-theoretic measure is developed and applied to gaze data to quantify the degree of learning uncertainty trial by trial. Next, a simple associative statistical learning model is applied to eye movement data and these simulation results are compared with empirical results from young children, showing strong correlations between these two. This suggests that an associative learning mechanism with selective attention can provide a cognitively plausible model of cross-situational statistical learning. The work represents the first steps to use eye movement data to infer underlying real-time processes in statistical word learning. PMID:22213894

DOE Office of Scientific and Technical Information (OSTI.GOV)

Deka, Deepjyoti; Backhaus, Scott N.; Chertkov, Michael

Limited placement of real-time monitoring devices in the distribution grid, recent trends notwithstanding, has prevented the easy implementation of demand-response and other smart grid applications. Part I of this paper discusses the problem of learning the operational structure of the grid from nodal voltage measurements. In this work (Part II), the learning of the operational radial structure is coupled with the problem of estimating nodal consumption statistics and inferring the line parameters in the grid. Based on a Linear-Coupled(LC) approximation of AC power flows equations, polynomial time algorithms are designed to identify the structure and estimate nodal load characteristics and/ormore » line parameters in the grid using the available nodal voltage measurements. Then the structure learning algorithm is extended to cases with missing data, where available observations are limited to a fraction of the grid nodes. The efficacy of the presented algorithms are demonstrated through simulations on several distribution test cases.« less

Evolution, Energy Landscapes and the Paradoxes of Protein Folding

PubMed Central

Wolynes, Peter G.

2014-01-01

Protein folding has been viewed as a difficult problem of molecular self-organization. The search problem involved in folding however has been simplified through the evolution of folding energy landscapes that are funneled. The funnel hypothesis can be quantified using energy landscape theory based on the minimal frustration principle. Strong quantitative predictions that follow from energy landscape theory have been widely confirmed both through laboratory folding experiments and from detailed simulations. Energy landscape ideas also have allowed successful protein structure prediction algorithms to be developed. The selection constraint of having funneled folding landscapes has left its imprint on the sequences of existing protein structural families. Quantitative analysis of co-evolution patterns allows us to infer the statistical characteristics of the folding landscape. These turn out to be consistent with what has been obtained from laboratory physicochemical folding experiments signalling a beautiful confluence of genomics and chemical physics. PMID:25530262

Augmented switching linear dynamical system model for gas concentration estimation with MOX sensors in an open sampling system.

PubMed

Di Lello, Enrico; Trincavelli, Marco; Bruyninckx, Herman; De Laet, Tinne

2014-07-11

In this paper, we introduce a Bayesian time series model approach for gas concentration estimation using Metal Oxide (MOX) sensors in Open Sampling System (OSS). Our approach focuses on the compensation of the slow response of MOX sensors, while concurrently solving the problem of estimating the gas concentration in OSS. The proposed Augmented Switching Linear System model allows to include all the sources of uncertainty arising at each step of the problem in a single coherent probabilistic formulation. In particular, the problem of detecting on-line the current sensor dynamical regime and estimating the underlying gas concentration under environmental disturbances and noisy measurements is formulated and solved as a statistical inference problem. Our model improves, with respect to the state of the art, where system modeling approaches have been already introduced, but only provided an indirect relative measures proportional to the gas concentration and the problem of modeling uncertainty was ignored. Our approach is validated experimentally and the performances in terms of speed of and quality of the gas concentration estimation are compared with the ones obtained using a photo-ionization detector.

Augmented Switching Linear Dynamical System Model for Gas Concentration Estimation with MOX Sensors in an Open Sampling System

PubMed Central

Di Lello, Enrico; Trincavelli, Marco; Bruyninckx, Herman; De Laet, Tinne

2014-01-01

In this paper, we introduce a Bayesian time series model approach for gas concentration estimation using Metal Oxide (MOX) sensors in Open Sampling System (OSS). Our approach focuses on the compensation of the slow response of MOX sensors, while concurrently solving the problem of estimating the gas concentration in OSS. The proposed Augmented Switching Linear System model allows to include all the sources of uncertainty arising at each step of the problem in a single coherent probabilistic formulation. In particular, the problem of detecting on-line the current sensor dynamical regime and estimating the underlying gas concentration under environmental disturbances and noisy measurements is formulated and solved as a statistical inference problem. Our model improves, with respect to the state of the art, where system modeling approaches have been already introduced, but only provided an indirect relative measures proportional to the gas concentration and the problem of modeling uncertainty was ignored. Our approach is validated experimentally and the performances in terms of speed of and quality of the gas concentration estimation are compared with the ones obtained using a photo-ionization detector. PMID:25019637

PhySIC_IST: cleaning source trees to infer more informative supertrees

PubMed Central

Scornavacca, Celine; Berry, Vincent; Lefort, Vincent; Douzery, Emmanuel JP; Ranwez, Vincent

2008-01-01

Background Supertree methods combine phylogenies with overlapping sets of taxa into a larger one. Topological conflicts frequently arise among source trees for methodological or biological reasons, such as long branch attraction, lateral gene transfers, gene duplication/loss or deep gene coalescence. When topological conflicts occur among source trees, liberal methods infer supertrees containing the most frequent alternative, while veto methods infer supertrees not contradicting any source tree, i.e. discard all conflicting resolutions. When the source trees host a significant number of topological conflicts or have a small taxon overlap, supertree methods of both kinds can propose poorly resolved, hence uninformative, supertrees. Results To overcome this problem, we propose to infer non-plenary supertrees, i.e. supertrees that do not necessarily contain all the taxa present in the source trees, discarding those whose position greatly differs among source trees or for which insufficient information is provided. We detail a variant of the PhySIC veto method called PhySIC_IST that can infer non-plenary supertrees. PhySIC_IST aims at inferring supertrees that satisfy the same appealing theoretical properties as with PhySIC, while being as informative as possible under this constraint. The informativeness of a supertree is estimated using a variation of the CIC (Cladistic Information Content) criterion, that takes into account both the presence of multifurcations and the absence of some taxa. Additionally, we propose a statistical preprocessing step called STC (Source Trees Correction) to correct the source trees prior to the supertree inference. STC is a liberal step that removes the parts of each source tree that significantly conflict with other source trees. Combining STC with a veto method allows an explicit trade-off between veto and liberal approaches, tuned by a single parameter. Performing large-scale simulations, we observe that STC+PhySIC_IST infers much more informative supertrees than PhySIC, while preserving low type I error compared to the well-known MRP method. Two biological case studies on animals confirm that the STC preprocess successfully detects anomalies in the source trees while STC+PhySIC_IST provides well-resolved supertrees agreeing with current knowledge in systematics. Conclusion The paper introduces and tests two new methodologies, PhySIC_IST and STC, that demonstrate the interest in inferring non-plenary supertrees as well as preprocessing the source trees. An implementation of the methods is available at: . PMID:18834542

PhySIC_IST: cleaning source trees to infer more informative supertrees.

PubMed

Scornavacca, Celine; Berry, Vincent; Lefort, Vincent; Douzery, Emmanuel J P; Ranwez, Vincent

2008-10-04

Supertree methods combine phylogenies with overlapping sets of taxa into a larger one. Topological conflicts frequently arise among source trees for methodological or biological reasons, such as long branch attraction, lateral gene transfers, gene duplication/loss or deep gene coalescence. When topological conflicts occur among source trees, liberal methods infer supertrees containing the most frequent alternative, while veto methods infer supertrees not contradicting any source tree, i.e. discard all conflicting resolutions. When the source trees host a significant number of topological conflicts or have a small taxon overlap, supertree methods of both kinds can propose poorly resolved, hence uninformative, supertrees. To overcome this problem, we propose to infer non-plenary supertrees, i.e. supertrees that do not necessarily contain all the taxa present in the source trees, discarding those whose position greatly differs among source trees or for which insufficient information is provided. We detail a variant of the PhySIC veto method called PhySIC_IST that can infer non-plenary supertrees. PhySIC_IST aims at inferring supertrees that satisfy the same appealing theoretical properties as with PhySIC, while being as informative as possible under this constraint. The informativeness of a supertree is estimated using a variation of the CIC (Cladistic Information Content) criterion, that takes into account both the presence of multifurcations and the absence of some taxa. Additionally, we propose a statistical preprocessing step called STC (Source Trees Correction) to correct the source trees prior to the supertree inference. STC is a liberal step that removes the parts of each source tree that significantly conflict with other source trees. Combining STC with a veto method allows an explicit trade-off between veto and liberal approaches, tuned by a single parameter.Performing large-scale simulations, we observe that STC+PhySIC_IST infers much more informative supertrees than PhySIC, while preserving low type I error compared to the well-known MRP method. Two biological case studies on animals confirm that the STC preprocess successfully detects anomalies in the source trees while STC+PhySIC_IST provides well-resolved supertrees agreeing with current knowledge in systematics. The paper introduces and tests two new methodologies, PhySIC_IST and STC, that demonstrate the interest in inferring non-plenary supertrees as well as preprocessing the source trees. An implementation of the methods is available at: http://www.atgc-montpellier.fr/physic_ist/.

MultiNest: Efficient and Robust Bayesian Inference

NASA Astrophysics Data System (ADS)

Feroz, F.; Hobson, M. P.; Bridges, M.

2011-09-01

We present further development and the first public release of our multimodal nested sampling algorithm, called MultiNest. This Bayesian inference tool calculates the evidence, with an associated error estimate, and produces posterior samples from distributions that may contain multiple modes and pronounced (curving) degeneracies in high dimensions. The developments presented here lead to further substantial improvements in sampling efficiency and robustness, as compared to the original algorithm presented in Feroz & Hobson (2008), which itself significantly outperformed existing MCMC techniques in a wide range of astrophysical inference problems. The accuracy and economy of the MultiNest algorithm is demonstrated by application to two toy problems and to a cosmological inference problem focusing on the extension of the vanilla LambdaCDM model to include spatial curvature and a varying equation of state for dark energy. The MultiNest software is fully parallelized using MPI and includes an interface to CosmoMC. It will also be released as part of the SuperBayeS package, for the analysis of supersymmetric theories of particle physics, at this http URL.

Activation of Background Knowledge for Inference Making: Effects on Reading Comprehension

ERIC Educational Resources Information Center

Elbro, Carsten; Buch-Iversen, Ida

2013-01-01

Failure to "activate" relevant, existing background knowledge may be a cause of poor reading comprehension. This failure may cause particular problems with inferences that depend heavily on prior knowledge. Conversely, teaching how to use background knowledge in the context of gap-filling inferences could improve reading comprehension in…

Interpreting support vector machine models for multivariate group wise analysis in neuroimaging

PubMed Central

Gaonkar, Bilwaj; Shinohara, Russell T; Davatzikos, Christos

2015-01-01

Machine learning based classification algorithms like support vector machines (SVMs) have shown great promise for turning a high dimensional neuroimaging data into clinically useful decision criteria. However, tracing imaging based patterns that contribute significantly to classifier decisions remains an open problem. This is an issue of critical importance in imaging studies seeking to determine which anatomical or physiological imaging features contribute to the classifier’s decision, thereby allowing users to critically evaluate the findings of such machine learning methods and to understand disease mechanisms. The majority of published work addresses the question of statistical inference for support vector classification using permutation tests based on SVM weight vectors. Such permutation testing ignores the SVM margin, which is critical in SVM theory. In this work we emphasize the use of a statistic that explicitly accounts for the SVM margin and show that the null distributions associated with this statistic are asymptotically normal. Further, our experiments show that this statistic is a lot less conservative as compared to weight based permutation tests and yet specific enough to tease out multivariate patterns in the data. Thus, we can better understand the multivariate patterns that the SVM uses for neuroimaging based classification. PMID:26210913

The Information Content of Discrete Functions and Their Application in Genetic Data Analysis

DOE PAGES

Sakhanenko, Nikita A.; Kunert-Graf, James; Galas, David J.

2017-10-13

The complex of central problems in data analysis consists of three components: (1) detecting the dependence of variables using quantitative measures, (2) defining the significance of these dependence measures, and (3) inferring the functional relationships among dependent variables. We have argued previously that an information theory approach allows separation of the detection problem from the inference of functional form problem. We approach here the third component of inferring functional forms based on information encoded in the functions. Here, we present here a direct method for classifying the functional forms of discrete functions of three variables represented in data sets. Discretemore » variables are frequently encountered in data analysis, both as the result of inherently categorical variables and from the binning of continuous numerical variables into discrete alphabets of values. The fundamental question of how much information is contained in a given function is answered for these discrete functions, and their surprisingly complex relationships are illustrated. The all-important effect of noise on the inference of function classes is found to be highly heterogeneous and reveals some unexpected patterns. We apply this classification approach to an important area of biological data analysis—that of inference of genetic interactions. Genetic analysis provides a rich source of real and complex biological data analysis problems, and our general methods provide an analytical basis and tools for characterizing genetic problems and for analyzing genetic data. Finally, we illustrate the functional description and the classes of a number of common genetic interaction modes and also show how different modes vary widely in their sensitivity to noise.« less

The Information Content of Discrete Functions and Their Application in Genetic Data Analysis

DOE Office of Scientific and Technical Information (OSTI.GOV)

Sakhanenko, Nikita A.; Kunert-Graf, James; Galas, David J.

The complex of central problems in data analysis consists of three components: (1) detecting the dependence of variables using quantitative measures, (2) defining the significance of these dependence measures, and (3) inferring the functional relationships among dependent variables. We have argued previously that an information theory approach allows separation of the detection problem from the inference of functional form problem. We approach here the third component of inferring functional forms based on information encoded in the functions. Here, we present here a direct method for classifying the functional forms of discrete functions of three variables represented in data sets. Discretemore » variables are frequently encountered in data analysis, both as the result of inherently categorical variables and from the binning of continuous numerical variables into discrete alphabets of values. The fundamental question of how much information is contained in a given function is answered for these discrete functions, and their surprisingly complex relationships are illustrated. The all-important effect of noise on the inference of function classes is found to be highly heterogeneous and reveals some unexpected patterns. We apply this classification approach to an important area of biological data analysis—that of inference of genetic interactions. Genetic analysis provides a rich source of real and complex biological data analysis problems, and our general methods provide an analytical basis and tools for characterizing genetic problems and for analyzing genetic data. Finally, we illustrate the functional description and the classes of a number of common genetic interaction modes and also show how different modes vary widely in their sensitivity to noise.« less

The Information Content of Discrete Functions and Their Application in Genetic Data Analysis.

PubMed

Sakhanenko, Nikita A; Kunert-Graf, James; Galas, David J

2017-12-01

The complex of central problems in data analysis consists of three components: (1) detecting the dependence of variables using quantitative measures, (2) defining the significance of these dependence measures, and (3) inferring the functional relationships among dependent variables. We have argued previously that an information theory approach allows separation of the detection problem from the inference of functional form problem. We approach here the third component of inferring functional forms based on information encoded in the functions. We present here a direct method for classifying the functional forms of discrete functions of three variables represented in data sets. Discrete variables are frequently encountered in data analysis, both as the result of inherently categorical variables and from the binning of continuous numerical variables into discrete alphabets of values. The fundamental question of how much information is contained in a given function is answered for these discrete functions, and their surprisingly complex relationships are illustrated. The all-important effect of noise on the inference of function classes is found to be highly heterogeneous and reveals some unexpected patterns. We apply this classification approach to an important area of biological data analysis-that of inference of genetic interactions. Genetic analysis provides a rich source of real and complex biological data analysis problems, and our general methods provide an analytical basis and tools for characterizing genetic problems and for analyzing genetic data. We illustrate the functional description and the classes of a number of common genetic interaction modes and also show how different modes vary widely in their sensitivity to noise.

Experiments with a decision-theoretic scheduler

NASA Technical Reports Server (NTRS)

Hansson, Othar; Holt, Gerhard; Mayer, Andrew

1992-01-01

This paper describes DTS, a decision-theoretic scheduler designed to employ state-of-the-art probabilistic inference technology to speed the search for efficient solutions to constraint-satisfaction problems. Our approach involves assessing the performance of heuristic control strategies that are normally hard-coded into scheduling systems, and using probabilistic inference to aggregate this information in light of features of a given problem. BPS, the Bayesian Problem-Solver, introduced a similar approach to solving single-agent and adversarial graph search problems, yielding orders-of-magnitude improvement over traditional techniques. Initial efforts suggest that similar improvements will be realizable when applied to typical constraint-satisfaction scheduling problems.

Bayesian Inference in Satellite Gravity Inversion

NASA Technical Reports Server (NTRS)

Kis, K. I.; Taylor, Patrick T.; Wittmann, G.; Kim, Hyung Rae; Torony, B.; Mayer-Guerr, T.

2005-01-01

To solve a geophysical inverse problem means applying measurements to determine the parameters of the selected model. The inverse problem is formulated as the Bayesian inference. The Gaussian probability density functions are applied in the Bayes's equation. The CHAMP satellite gravity data are determined at the altitude of 400 kilometer altitude over the South part of the Pannonian basin. The model of interpretation is the right vertical cylinder. The parameters of the model are obtained from the minimum problem solved by the Simplex method.

Reading biological processes from nucleotide sequences

NASA Astrophysics Data System (ADS)

Murugan, Anand

Cellular processes have traditionally been investigated by techniques of imaging and biochemical analysis of the molecules involved. The recent rapid progress in our ability to manipulate and read nucleic acid sequences gives us direct access to the genetic information that directs and constrains biological processes. While sequence data is being used widely to investigate genotype-phenotype relationships and population structure, here we use sequencing to understand biophysical mechanisms. We present work on two different systems. First, in chapter 2, we characterize the stochastic genetic editing mechanism that produces diverse T-cell receptors in the human immune system. We do this by inferring statistical distributions of the underlying biochemical events that generate T-cell receptor coding sequences from the statistics of the observed sequences. This inferred model quantitatively describes the potential repertoire of T-cell receptors that can be produced by an individual, providing insight into its potential diversity and the probability of generation of any specific T-cell receptor. Then in chapter 3, we present work on understanding the functioning of regulatory DNA sequences in both prokaryotes and eukaryotes. Here we use experiments that measure the transcriptional activity of large libraries of mutagenized promoters and enhancers and infer models of the sequence-function relationship from this data. For the bacterial promoter, we infer a physically motivated 'thermodynamic' model of the interaction of DNA-binding proteins and RNA polymerase determining the transcription rate of the downstream gene. For the eukaryotic enhancers, we infer heuristic models of the sequence-function relationship and use these models to find synthetic enhancer sequences that optimize inducibility of expression. Both projects demonstrate the utility of sequence information in conjunction with sophisticated statistical inference techniques for dissecting underlying biophysical mechanisms.

Exclusion probabilities and likelihood ratios with applications to kinship problems.

PubMed

Slooten, Klaas-Jan; Egeland, Thore

2014-05-01

In forensic genetics, DNA profiles are compared in order to make inferences, paternity cases being a standard example. The statistical evidence can be summarized and reported in several ways. For example, in a paternity case, the likelihood ratio (LR) and the probability of not excluding a random man as father (RMNE) are two common summary statistics. There has been a long debate on the merits of the two statistics, also in the context of DNA mixture interpretation, and no general consensus has been reached. In this paper, we show that the RMNE is a certain weighted average of inverse likelihood ratios. This is true in any forensic context. We show that the likelihood ratio in favor of the correct hypothesis is, in expectation, bigger than the reciprocal of the RMNE probability. However, with the exception of pathological cases, it is also possible to obtain smaller likelihood ratios. We illustrate this result for paternity cases. Moreover, some theoretical properties of the likelihood ratio for a large class of general pairwise kinship cases, including expected value and variance, are derived. The practical implications of the findings are discussed and exemplified.

Publication Bias ( The "File-Drawer Problem") in Scientific Inference

NASA Technical Reports Server (NTRS)

Scargle, Jeffrey D.; DeVincenzi, Donald (Technical Monitor)

1999-01-01

Publication bias arises whenever the probability that a study is published depends on the statistical significance of its results. This bias, often called the file-drawer effect since the unpublished results are imagined to be tucked away in researchers' file cabinets, is potentially a severe impediment to combining the statistical results of studies collected from the literature. With almost any reasonable quantitative model for publication bias, only a small number of studies lost in the file-drawer will produce a significant bias. This result contradicts the well known Fail Safe File Drawer (FSFD) method for setting limits on the potential harm of publication bias, widely used in social, medical and psychic research. This method incorrectly treats the file drawer as unbiased, and almost always miss-estimates the seriousness of publication bias. A large body of not only psychic research, but medical and social science studies, has mistakenly relied on this method to validate claimed discoveries. Statistical combination can be trusted only if it is known with certainty that all studies that have been carried out are included. Such certainty is virtually impossible to achieve in literature surveys.

A robust clustering algorithm for identifying problematic samples in genome-wide association studies.

PubMed

Bellenguez, Céline; Strange, Amy; Freeman, Colin; Donnelly, Peter; Spencer, Chris C A

2012-01-01

High-throughput genotyping arrays provide an efficient way to survey single nucleotide polymorphisms (SNPs) across the genome in large numbers of individuals. Downstream analysis of the data, for example in genome-wide association studies (GWAS), often involves statistical models of genotype frequencies across individuals. The complexities of the sample collection process and the potential for errors in the experimental assay can lead to biases and artefacts in an individual's inferred genotypes. Rather than attempting to model these complications, it has become a standard practice to remove individuals whose genome-wide data differ from the sample at large. Here we describe a simple, but robust, statistical algorithm to identify samples with atypical summaries of genome-wide variation. Its use as a semi-automated quality control tool is demonstrated using several summary statistics, selected to identify different potential problems, and it is applied to two different genotyping platforms and sample collections. The algorithm is written in R and is freely available at www.well.ox.ac.uk/chris-spencer chris.spencer@well.ox.ac.uk Supplementary data are available at Bioinformatics online.

Problem-Solving Software

NASA Technical Reports Server (NTRS)

1992-01-01

CBR Express software solves problems by adapting sorted solutions to new problems specified by a user. It is applicable to a wide range of situations. The technology was originally developed by Inference Corporation for Johnson Space Center's Advanced Software Development Workstation. The project focused on the reuse of software designs, and Inference used CBR as part of the ACCESS prototype software. The commercial CBR Express is used as a "help desk" for customer support, enabling reuse of existing information when necessary. It has been adopted by several companies, among them American Airlines, which uses it to solve reservation system software problems.

CADDIS Volume 4. Data Analysis: PECBO Appendix - R Scripts for Non-Parametric Regressions

EPA Pesticide Factsheets

Script for computing nonparametric regression analysis. Overview of using scripts to infer environmental conditions from biological observations, statistically estimating species-environment relationships, statistical scripts.

An evaluation of the performance and suitability of R × C methods for ecological inference with known true values.

PubMed

Plescia, Carolina; De Sio, Lorenzo

2018-01-01

Ecological inference refers to the study of individuals using aggregate data and it is used in an impressive number of studies; it is well known, however, that the study of individuals using group data suffers from an ecological fallacy problem (Robinson in Am Sociol Rev 15:351-357, 1950). This paper evaluates the accuracy of two recent methods, the Rosen et al. (Stat Neerl 55:134-156, 2001) and the Greiner and Quinn (J R Stat Soc Ser A (Statistics in Society) 172:67-81, 2009) and the long-standing Goodman's (Am Sociol Rev 18:663-664, 1953; Am J Sociol 64:610-625, 1959) method designed to estimate all cells of R × C tables simultaneously by employing exclusively aggregate data. To conduct these tests we leverage on extensive electoral data for which the true quantities of interest are known. In particular, we focus on examining the extent to which the confidence intervals provided by the three methods contain the true values. The paper also provides important guidelines regarding the appropriate contexts for employing these models.

Integrating Genetic and Functional Genomic Data to Elucidate Common Disease Tra

NASA Astrophysics Data System (ADS)

Schadt, Eric

2005-03-01

The reconstruction of genetic networks in mammalian systems is one of the primary goals in biological research, especially as such reconstructions relate to elucidating not only common, polygenic human diseases, but living systems more generally. Here I present a statistical procedure for inferring causal relationships between gene expression traits and more classic clinical traits, including complex disease traits. This procedure has been generalized to the gene network reconstruction problem, where naturally occurring genetic variations in segregating mouse populations are used as a source of perturbations to elucidate tissue-specific gene networks. Differences in the extent of genetic control between genders and among four different tissues are highlighted. I also demonstrate that the networks derived from expression data in segregating mouse populations using the novel network reconstruction algorithm are able to capture causal associations between genes that result in increased predictive power, compared to more classically reconstructed networks derived from the same data. This approach to causal inference in large segregating mouse populations over multiple tissues not only elucidates fundamental aspects of transcriptional control, it also allows for the objective identification of key drivers of common human diseases.

p-Curve and p-Hacking in Observational Research.

PubMed

Bruns, Stephan B; Ioannidis, John P A

2016-01-01

The p-curve, the distribution of statistically significant p-values of published studies, has been used to make inferences on the proportion of true effects and on the presence of p-hacking in the published literature. We analyze the p-curve for observational research in the presence of p-hacking. We show by means of simulations that even with minimal omitted-variable bias (e.g., unaccounted confounding) p-curves based on true effects and p-curves based on null-effects with p-hacking cannot be reliably distinguished. We also demonstrate this problem using as practical example the evaluation of the effect of malaria prevalence on economic growth between 1960 and 1996. These findings call recent studies into question that use the p-curve to infer that most published research findings are based on true effects in the medical literature and in a wide range of disciplines. p-values in observational research may need to be empirically calibrated to be interpretable with respect to the commonly used significance threshold of 0.05. Violations of randomization in experimental studies may also result in situations where the use of p-curves is similarly unreliable.

A null model for Pearson coexpression networks.

PubMed

Gobbi, Andrea; Jurman, Giuseppe

2015-01-01

Gene coexpression networks inferred by correlation from high-throughput profiling such as microarray data represent simple but effective structures for discovering and interpreting linear gene relationships. In recent years, several approaches have been proposed to tackle the problem of deciding when the resulting correlation values are statistically significant. This is most crucial when the number of samples is small, yielding a non-negligible chance that even high correlation values are due to random effects. Here we introduce a novel hard thresholding solution based on the assumption that a coexpression network inferred by randomly generated data is expected to be empty. The threshold is theoretically derived by means of an analytic approach and, as a deterministic independent null model, it depends only on the dimensions of the starting data matrix, with assumptions on the skewness of the data distribution compatible with the structure of gene expression levels data. We show, on synthetic and array datasets, that the proposed threshold is effective in eliminating all false positive links, with an offsetting cost in terms of false negative detected edges.

Test Theory Reconceived.

ERIC Educational Resources Information Center

Mislevy, Robert J.

Educational test theory consists of statistical and methodological tools to support inferences about examinees' knowledge, skills, and accomplishments. The evolution of test theory has been shaped by the nature of users' inferences which, until recently, have been framed almost exclusively in terms of trait and behavioral psychology. Progress in…

Data-driven sensitivity inference for Thomson scattering electron density measurement systems.

PubMed

Fujii, Keisuke; Yamada, Ichihiro; Hasuo, Masahiro

2017-01-01

We developed a method to infer the calibration parameters of multichannel measurement systems, such as channel variations of sensitivity and noise amplitude, from experimental data. We regard such uncertainties of the calibration parameters as dependent noise. The statistical properties of the dependent noise and that of the latent functions were modeled and implemented in the Gaussian process kernel. Based on their statistical difference, both parameters were inferred from the data. We applied this method to the electron density measurement system by Thomson scattering for the Large Helical Device plasma, which is equipped with 141 spatial channels. Based on the 210 sets of experimental data, we evaluated the correction factor of the sensitivity and noise amplitude for each channel. The correction factor varies by ≈10%, and the random noise amplitude is ≈2%, i.e., the measurement accuracy increases by a factor of 5 after this sensitivity correction. The certainty improvement in the spatial derivative inference was demonstrated.

Learning probability distributions from smooth observables and the maximum entropy principle: some remarks

NASA Astrophysics Data System (ADS)

Obuchi, Tomoyuki; Monasson, Rémi

2015-09-01

The maximum entropy principle (MEP) is a very useful working hypothesis in a wide variety of inference problems, ranging from biological to engineering tasks. To better understand the reasons of the success of MEP, we propose a statistical-mechanical formulation to treat the space of probability distributions constrained by the measures of (experimental) observables. In this paper we first review the results of a detailed analysis of the simplest case of randomly chosen observables. In addition, we investigate by numerical and analytical means the case of smooth observables, which is of practical relevance. Our preliminary results are presented and discussed with respect to the efficiency of the MEP.

Evaluating sufficient similarity for drinking-water disinfection by-product (DBP) mixtures with bootstrap hypothesis test procedures.

PubMed

Feder, Paul I; Ma, Zhenxu J; Bull, Richard J; Teuschler, Linda K; Rice, Glenn

2009-01-01

In chemical mixtures risk assessment, the use of dose-response data developed for one mixture to estimate risk posed by a second mixture depends on whether the two mixtures are sufficiently similar. While evaluations of similarity may be made using qualitative judgments, this article uses nonparametric statistical methods based on the "bootstrap" resampling technique to address the question of similarity among mixtures of chemical disinfectant by-products (DBP) in drinking water. The bootstrap resampling technique is a general-purpose, computer-intensive approach to statistical inference that substitutes empirical sampling for theoretically based parametric mathematical modeling. Nonparametric, bootstrap-based inference involves fewer assumptions than parametric normal theory based inference. The bootstrap procedure is appropriate, at least in an asymptotic sense, whether or not the parametric, distributional assumptions hold, even approximately. The statistical analysis procedures in this article are initially illustrated with data from 5 water treatment plants (Schenck et al., 2009), and then extended using data developed from a study of 35 drinking-water utilities (U.S. EPA/AMWA, 1989), which permits inclusion of a greater number of water constituents and increased structure in the statistical models.

Statistical framework for the utilization of simultaneous pupil plane and focal plane telemetry for exoplanet imaging. I. Accounting for aberrations in multiple planes.

PubMed

Frazin, Richard A

2016-04-01

A new generation of telescopes with mirror diameters of 20 m or more, called extremely large telescopes (ELTs), has the potential to provide unprecedented imaging and spectroscopy of exoplanetary systems, if the difficulties in achieving the extremely high dynamic range required to differentiate the planetary signal from the star can be overcome to a sufficient degree. Fully utilizing the potential of ELTs for exoplanet imaging will likely require simultaneous and self-consistent determination of both the planetary image and the unknown aberrations in multiple planes of the optical system, using statistical inference based on the wavefront sensor and science camera data streams. This approach promises to overcome the most important systematic errors inherent in the various schemes based on differential imaging, such as angular differential imaging and spectral differential imaging. This paper is the first in a series on this subject, in which a formalism is established for the exoplanet imaging problem, setting the stage for the statistical inference methods to follow in the future. Every effort has been made to be rigorous and complete, so that validity of approximations to be made later can be assessed. Here, the polarimetric image is expressed in terms of aberrations in the various planes of a polarizing telescope with an adaptive optics system. Further, it is shown that current methods that utilize focal plane sensing to correct the speckle field, e.g., electric field conjugation, rely on the tacit assumption that aberrations on multiple optical surfaces can be represented as aberration on a single optical surface, ultimately limiting their potential effectiveness for ground-based astronomy.

Two approaches to incorporate clinical data uncertainty into multiple criteria decision analysis for benefit-risk assessment of medicinal products.

PubMed

Wen, Shihua; Zhang, Lanju; Yang, Bo

2014-07-01

The Problem formulation, Objectives, Alternatives, Consequences, Trade-offs, Uncertainties, Risk attitude, and Linked decisions (PrOACT-URL) framework and multiple criteria decision analysis (MCDA) have been recommended by the European Medicines Agency for structured benefit-risk assessment of medicinal products undergoing regulatory review. The objective of this article was to provide solutions to incorporate the uncertainty from clinical data into the MCDA model when evaluating the overall benefit-risk profiles among different treatment options. Two statistical approaches, the δ-method approach and the Monte-Carlo approach, were proposed to construct the confidence interval of the overall benefit-risk score from the MCDA model as well as other probabilistic measures for comparing the benefit-risk profiles between treatment options. Both approaches can incorporate the correlation structure between clinical parameters (criteria) in the MCDA model and are straightforward to implement. The two proposed approaches were applied to a case study to evaluate the benefit-risk profile of an add-on therapy for rheumatoid arthritis (drug X) relative to placebo. It demonstrated a straightforward way to quantify the impact of the uncertainty from clinical data to the benefit-risk assessment and enabled statistical inference on evaluating the overall benefit-risk profiles among different treatment options. The δ-method approach provides a closed form to quantify the variability of the overall benefit-risk score in the MCDA model, whereas the Monte-Carlo approach is more computationally intensive but can yield its true sampling distribution for statistical inference. The obtained confidence intervals and other probabilistic measures from the two approaches enhance the benefit-risk decision making of medicinal products. Copyright © 2014 International Society for Pharmacoeconomics and Outcomes Research (ISPOR). Published by Elsevier Inc. All rights reserved.

Local dependence in random graph models: characterization, properties and statistical inference

PubMed Central

Schweinberger, Michael; Handcock, Mark S.

2015-01-01

Summary Dependent phenomena, such as relational, spatial and temporal phenomena, tend to be characterized by local dependence in the sense that units which are close in a well-defined sense are dependent. In contrast with spatial and temporal phenomena, though, relational phenomena tend to lack a natural neighbourhood structure in the sense that it is unknown which units are close and thus dependent. Owing to the challenge of characterizing local dependence and constructing random graph models with local dependence, many conventional exponential family random graph models induce strong dependence and are not amenable to statistical inference. We take first steps to characterize local dependence in random graph models, inspired by the notion of finite neighbourhoods in spatial statistics and M-dependence in time series, and we show that local dependence endows random graph models with desirable properties which make them amenable to statistical inference. We show that random graph models with local dependence satisfy a natural domain consistency condition which every model should satisfy, but conventional exponential family random graph models do not satisfy. In addition, we establish a central limit theorem for random graph models with local dependence, which suggests that random graph models with local dependence are amenable to statistical inference. We discuss how random graph models with local dependence can be constructed by exploiting either observed or unobserved neighbourhood structure. In the absence of observed neighbourhood structure, we take a Bayesian view and express the uncertainty about the neighbourhood structure by specifying a prior on a set of suitable neighbourhood structures. We present simulation results and applications to two real world networks with ‘ground truth’. PMID:26560142

Statistical inference, the bootstrap, and neural-network modeling with application to foreign exchange rates.

PubMed

White, H; Racine, J

2001-01-01

We propose tests for individual and joint irrelevance of network inputs. Such tests can be used to determine whether an input or group of inputs "belong" in a particular model, thus permitting valid statistical inference based on estimated feedforward neural-network models. The approaches employ well-known statistical resampling techniques. We conduct a small Monte Carlo experiment showing that our tests have reasonable level and power behavior, and we apply our methods to examine whether there are predictable regularities in foreign exchange rates. We find that exchange rates do appear to contain information that is exploitable for enhanced point prediction, but the nature of the predictive relations evolves through time.

FUNSTAT and statistical image representations

NASA Technical Reports Server (NTRS)

Parzen, E.

1983-01-01

General ideas of functional statistical inference analysis of one sample and two samples, univariate and bivariate are outlined. ONESAM program is applied to analyze the univariate probability distributions of multi-spectral image data.

Testing AGN unification via inference from large catalogs

NASA Astrophysics Data System (ADS)

Nikutta, Robert; Ivezic, Zeljko; Elitzur, Moshe; Nenkova, Maia

2018-01-01

Source orientation and clumpiness of the central dust are the main factors in AGN classification. Type-1 QSOs are easy to observe and large samples are available (e.g. in SDSS), but obscured type-2 AGN are dimmer and redder as our line of sight is more obscured, making it difficult to obtain a complete sample. WISE has found up to a million QSOs. With only 4 bands and a relatively small aperture the analysis of individual sources is challenging, but the large sample allows inference of bulk properties at a very significant level.CLUMPY (www.clumpy.org) is arguably the most popular database of AGN torus SEDs. We model the ensemble properties of the entire WISE AGN content using regularized linear regression, with orientation-dependent CLUMPY color-color-magnitude (CCM) tracks as basis functions. We can reproduce the observed number counts per CCM bin with percent-level accuracy, and simultaneously infer the probability distributions of all torus parameters, redshifts, additional SED components, and identify type-1/2 AGN populations through their IR properties alone. We increase the statistical power of our AGN unification tests even further, by adding other datasets as axes in the regression problem. To this end, we make use of the NOAO Data Lab (datalab.noao.edu), which hosts several high-level large datasets and provides very powerful tools for handling large data, e.g. cross-matched catalogs, fast remote queries, etc.

Application of Non-Kolmogorovian Probability and Quantum Adaptive Dynamics to Unconscious Inference in Visual Perception Process

NASA Astrophysics Data System (ADS)

Accardi, Luigi; Khrennikov, Andrei; Ohya, Masanori; Tanaka, Yoshiharu; Yamato, Ichiro

2016-07-01

Recently a novel quantum information formalism — quantum adaptive dynamics — was developed and applied to modelling of information processing by bio-systems including cognitive phenomena: from molecular biology (glucose-lactose metabolism for E.coli bacteria, epigenetic evolution) to cognition, psychology. From the foundational point of view quantum adaptive dynamics describes mutual adapting of the information states of two interacting systems (physical or biological) as well as adapting of co-observations performed by the systems. In this paper we apply this formalism to model unconscious inference: the process of transition from sensation to perception. The paper combines theory and experiment. Statistical data collected in an experimental study on recognition of a particular ambiguous figure, the Schröder stairs, support the viability of the quantum(-like) model of unconscious inference including modelling of biases generated by rotation-contexts. From the probabilistic point of view, we study (for concrete experimental data) the problem of contextuality of probability, its dependence on experimental contexts. Mathematically contextuality leads to non-Komogorovness: probability distributions generated by various rotation contexts cannot be treated in the Kolmogorovian framework. At the same time they can be embedded in a “big Kolmogorov space” as conditional probabilities. However, such a Kolmogorov space has too complex structure and the operational quantum formalism in the form of quantum adaptive dynamics simplifies the modelling essentially.

Solving geosteering inverse problems by stochastic Hybrid Monte Carlo method

DOE PAGES

Shen, Qiuyang; Wu, Xuqing; Chen, Jiefu; ...

2017-11-20

The inverse problems arise in almost all fields of science where the real-world parameters are extracted from a set of measured data. The geosteering inversion plays an essential role in the accurate prediction of oncoming strata as well as a reliable guidance to adjust the borehole position on the fly to reach one or more geological targets. This mathematical treatment is not easy to solve, which requires finding an optimum solution among a large solution space, especially when the problem is non-linear and non-convex. Nowadays, a new generation of logging-while-drilling (LWD) tools has emerged on the market. The so-called azimuthalmore » resistivity LWD tools have azimuthal sensitivity and a large depth of investigation. Hence, the associated inverse problems become much more difficult since the earth model to be inverted will have more detailed structures. The conventional deterministic methods are incapable to solve such a complicated inverse problem, where they suffer from the local minimum trap. Alternatively, stochastic optimizations are in general better at finding global optimal solutions and handling uncertainty quantification. In this article, we investigate the Hybrid Monte Carlo (HMC) based statistical inversion approach and suggest that HMC based inference is more efficient in dealing with the increased complexity and uncertainty faced by the geosteering problems.« less

Building Intuitions about Statistical Inference Based on Resampling

ERIC Educational Resources Information Center

Watson, Jane; Chance, Beth

2012-01-01

Formal inference, which makes theoretical assumptions about distributions and applies hypothesis testing procedures with null and alternative hypotheses, is notoriously difficult for tertiary students to master. The debate about whether this content should appear in Years 11 and 12 of the "Australian Curriculum: Mathematics" has gone on…

Theory-based Bayesian models of inductive learning and reasoning.

PubMed

Tenenbaum, Joshua B; Griffiths, Thomas L; Kemp, Charles

2006-07-01

Inductive inference allows humans to make powerful generalizations from sparse data when learning about word meanings, unobserved properties, causal relationships, and many other aspects of the world. Traditional accounts of induction emphasize either the power of statistical learning, or the importance of strong constraints from structured domain knowledge, intuitive theories or schemas. We argue that both components are necessary to explain the nature, use and acquisition of human knowledge, and we introduce a theory-based Bayesian framework for modeling inductive learning and reasoning as statistical inferences over structured knowledge representations.

Data free inference with processed data products

DOE PAGES

Chowdhary, K.; Najm, H. N.

2014-07-12

Here, we consider the context of probabilistic inference of model parameters given error bars or confidence intervals on model output values, when the data is unavailable. We introduce a class of algorithms in a Bayesian framework, relying on maximum entropy arguments and approximate Bayesian computation methods, to generate consistent data with the given summary statistics. Once we obtain consistent data sets, we pool the respective posteriors, to arrive at a single, averaged density on the parameters. This approach allows us to perform accurate forward uncertainty propagation consistent with the reported statistics.

Statistics at the Chinese Universities.

DTIC Science & Technology

1981-09-01

education in China in the postwar years is pro- vided to give some perspective. My observa- tions on statistics at the Chinese universities are necessarily...has been accepted as a member society of ISI. 3. Education in China Understanding of statistics in universities in China will be enhanced through some...programaming), Statistical Mathematics (infer- ence, data analysis, industrial statistics , information theory), tiathematical Physics (dif- ferential

The role of familiarity in binary choice inferences.

PubMed

Honda, Hidehito; Abe, Keiga; Matsuka, Toshihiko; Yamagishi, Kimihiko

2011-07-01

In research on the recognition heuristic (Goldstein & Gigerenzer, Psychological Review, 109, 75-90, 2002), knowledge of recognized objects has been categorized as "recognized" or "unrecognized" without regard to the degree of familiarity of the recognized object. In the present article, we propose a new inference model--familiarity-based inference. We hypothesize that when subjective knowledge levels (familiarity) of recognized objects differ, the degree of familiarity of recognized objects will influence inferences. Specifically, people are predicted to infer that the more familiar object in a pair of two objects has a higher criterion value on the to-be-judged dimension. In two experiments, using a binary choice task, we examined inferences about populations in a pair of two cities. Results support predictions of familiarity-based inference. Participants inferred that the more familiar city in a pair was more populous. Statistical modeling showed that individual differences in familiarity-based inference lie in the sensitivity to differences in familiarity. In addition, we found that familiarity-based inference can be generally regarded as an ecologically rational inference. Furthermore, when cue knowledge about the inference criterion was available, participants made inferences based on the cue knowledge about population instead of familiarity. Implications of the role of familiarity in psychological processes are discussed.

Inference of the sparse kinetic Ising model using the decimation method

NASA Astrophysics Data System (ADS)

Decelle, Aurélien; Zhang, Pan

2015-05-01

In this paper we study the inference of the kinetic Ising model on sparse graphs by the decimation method. The decimation method, which was first proposed in Decelle and Ricci-Tersenghi [Phys. Rev. Lett. 112, 070603 (2014), 10.1103/PhysRevLett.112.070603] for the static inverse Ising problem, tries to recover the topology of the inferred system by setting the weakest couplings to zero iteratively. During the decimation process the likelihood function is maximized over the remaining couplings. Unlike the ℓ1-optimization-based methods, the decimation method does not use the Laplace distribution as a heuristic choice of prior to select a sparse solution. In our case, the whole process can be done auto-matically without fixing any parameters by hand. We show that in the dynamical inference problem, where the task is to reconstruct the couplings of an Ising model given the data, the decimation process can be applied naturally into a maximum-likelihood optimization algorithm, as opposed to the static case where pseudolikelihood method needs to be adopted. We also use extensive numerical studies to validate the accuracy of our methods in dynamical inference problems. Our results illustrate that, on various topologies and with different distribution of couplings, the decimation method outperforms the widely used ℓ1-optimization-based methods.

The hippocampus and memory for orderly stimulus relations

PubMed Central

Dusek, Jeffery A.; Eichenbaum, Howard

1997-01-01

Human declarative memory involves a systematic organization of information that supports generalizations and inferences from acquired knowledge. This kind of memory depends on the hippocampal region in humans, but the extent to which animals also have declarative memory, and whether inferential expression of memory depends on the hippocampus in animals, remains a major challenge in cognitive neuroscience. To examine these issues, we used a test of transitive inference pioneered by Piaget to assess capacities for systematic organization of knowledge and logical inference in children. In our adaptation of the test, rats were trained on a set of four overlapping odor discrimination problems that could be encoded either separately or as a single representation of orderly relations among the odor stimuli. Normal rats learned the problems and demonstrated the relational memory organization through appropriate transitive inferences about items not presented together during training. By contrast, after disconnection of the hippocampus from either its cortical or subcortical pathway, rats succeeded in acquiring the separate discrimination problems but did not demonstrate transitive inference, indicating that they had failed to develop or could not inferentially express the orderly organization of the stimulus elements. These findings strongly support the view that the hippocampus mediates a general declarative memory capacity in animals, as it does in humans. PMID:9192700

Statistical modeling of software reliability

NASA Technical Reports Server (NTRS)

Miller, Douglas R.

1992-01-01

This working paper discusses the statistical simulation part of a controlled software development experiment being conducted under the direction of the System Validation Methods Branch, Information Systems Division, NASA Langley Research Center. The experiment uses guidance and control software (GCS) aboard a fictitious planetary landing spacecraft: real-time control software operating on a transient mission. Software execution is simulated to study the statistical aspects of reliability and other failure characteristics of the software during development, testing, and random usage. Quantification of software reliability is a major goal. Various reliability concepts are discussed. Experiments are described for performing simulations and collecting appropriate simulated software performance and failure data. This data is then used to make statistical inferences about the quality of the software development and verification processes as well as inferences about the reliability of software versions and reliability growth under random testing and debugging.

Final Report: Quantification of Uncertainty in Extreme Scale Computations (QUEST)

DOE Office of Scientific and Technical Information (OSTI.GOV)

Marzouk, Youssef; Conrad, Patrick; Bigoni, Daniele

QUEST (\\url{www.quest-scidac.org}) is a SciDAC Institute that is focused on uncertainty quantification (UQ) in large-scale scientific computations. Our goals are to (1) advance the state of the art in UQ mathematics, algorithms, and software; and (2) provide modeling, algorithmic, and general UQ expertise, together with software tools, to other SciDAC projects, thereby enabling and guiding a broad range of UQ activities in their respective contexts. QUEST is a collaboration among six institutions (Sandia National Laboratories, Los Alamos National Laboratory, the University of Southern California, Massachusetts Institute of Technology, the University of Texas at Austin, and Duke University) with a historymore » of joint UQ research. Our vision encompasses all aspects of UQ in leadership-class computing. This includes the well-founded setup of UQ problems; characterization of the input space given available data/information; local and global sensitivity analysis; adaptive dimensionality and order reduction; forward and inverse propagation of uncertainty; handling of application code failures, missing data, and hardware/software fault tolerance; and model inadequacy, comparison, validation, selection, and averaging. The nature of the UQ problem requires the seamless combination of data, models, and information across this landscape in a manner that provides a self-consistent quantification of requisite uncertainties in predictions from computational models. Accordingly, our UQ methods and tools span an interdisciplinary space across applied math, information theory, and statistics. The MIT QUEST effort centers on statistical inference and methods for surrogate or reduced-order modeling. MIT personnel have been responsible for the development of adaptive sampling methods, methods for approximating computationally intensive models, and software for both forward uncertainty propagation and statistical inverse problems. A key software product of the MIT QUEST effort is the MIT Uncertainty Quantification library, called MUQ (\\url{muq.mit.edu}).« less

A new statistical framework to assess structural alignment quality using information compression

PubMed Central

Collier, James H.; Allison, Lloyd; Lesk, Arthur M.; Garcia de la Banda, Maria; Konagurthu, Arun S.

2014-01-01

Motivation: Progress in protein biology depends on the reliability of results from a handful of computational techniques, structural alignments being one. Recent reviews have highlighted substantial inconsistencies and differences between alignment results generated by the ever-growing stock of structural alignment programs. The lack of consensus on how the quality of structural alignments must be assessed has been identified as the main cause for the observed differences. Current methods assess structural alignment quality by constructing a scoring function that attempts to balance conflicting criteria, mainly alignment coverage and fidelity of structures under superposition. This traditional approach to measuring alignment quality, the subject of considerable literature, has failed to solve the problem. Further development along the same lines is unlikely to rectify the current deficiencies in the field. Results: This paper proposes a new statistical framework to assess structural alignment quality and significance based on lossless information compression. This is a radical departure from the traditional approach of formulating scoring functions. It links the structural alignment problem to the general class of statistical inductive inference problems, solved using the information-theoretic criterion of minimum message length. Based on this, we developed an efficient and reliable measure of structural alignment quality, I-value. The performance of I-value is demonstrated in comparison with a number of popular scoring functions, on a large collection of competing alignments. Our analysis shows that I-value provides a rigorous and reliable quantification of structural alignment quality, addressing a major gap in the field. Availability: http://lcb.infotech.monash.edu.au/I-value Contact: arun.konagurthu@monash.edu Supplementary information: Online supplementary data are available at http://lcb.infotech.monash.edu.au/I-value/suppl.html PMID:25161241

Representations of the language recognition problem for a theorem prover

NASA Technical Reports Server (NTRS)

Minker, J.; Vanderbrug, G. J.

1972-01-01

Two representations of the language recognition problem for a theorem prover in first order logic are presented and contrasted. One of the representations is based on the familiar method of generating sentential forms of the language, and the other is based on the Cocke parsing algorithm. An augmented theorem prover is described which permits recognition of recursive languages. The state-transformation method developed by Cordell Green to construct problem solutions in resolution-based systems can be used to obtain the parse tree. In particular, the end-order traversal of the parse tree is derived in one of the representations. An inference system, termed the cycle inference system, is defined which makes it possible for the theorem prover to model the method on which the representation is based. The general applicability of the cycle inference system to state space problems is discussed. Given an unsatisfiable set S, where each clause has at most one positive literal, it is shown that there exists an input proof. The clauses for the two representations satisfy these conditions, as do many state space problems.

Why environmental scientists are becoming Bayesians

Treesearch

James S. Clark

2005-01-01

Advances in computational statistics provide a general framework for the high dimensional models typically needed for ecological inference and prediction. Hierarchical Bayes (HB) represents a modelling structure with capacity to exploit diverse sources of information, to accommodate influences that are unknown (or unknowable), and to draw inference on large numbers of...

Pseudocontingencies and Choice Behavior in Probabilistic Environments with Context-Dependent Outcomes

ERIC Educational Resources Information Center

Meiser, Thorsten; Rummel, Jan; Fleig, Hanna

2018-01-01

Pseudocontingencies are inferences about correlations in the environment that are formed on the basis of statistical regularities like skewed base rates or varying base rates across environmental contexts. Previous research has demonstrated that pseudocontingencies provide a pervasive mechanism of inductive inference in numerous social judgment…

Cross-Situational Learning of Minimal Word Pairs

ERIC Educational Resources Information Center

Escudero, Paola; Mulak, Karen E.; Vlach, Haley A.

2016-01-01

"Cross-situational statistical learning" of words involves tracking co-occurrences of auditory words and objects across time to infer word-referent mappings. Previous research has demonstrated that learners can infer referents across sets of very phonologically distinct words (e.g., WUG, DAX), but it remains unknown whether learners can…

Inferring Social Influence of Anti-Tobacco Mass Media Campaign.

PubMed

Zhan, Qianyi; Zhang, Jiawei; Yu, Philip S; Emery, Sherry; Xie, Junyuan

2017-07-01

Anti-tobacco mass media campaigns are designed to influence tobacco users. It has been proved that campaigns will produce users' changes in awareness, knowledge, and attitudes, and also produce meaningful behavior change of audience. Anti-smoking television advertising is the most important part in the campaign. Meanwhile, nowadays, successful online social networks are creating new media environment, however, little is known about the relation between social conversations and anti-tobacco campaigns. This paper aims to infer social influence of these campaigns, and the problem is formally referred to as the Social Influence inference of anti-Tobacco mass mEdia campaigns (Site) problem. To address the Site problem, a novel influence inference framework, TV advertising social influence estimation (Asie), is proposed based on our analysis of two real anti-tobacco campaigns. Asie divides audience attitudes toward TV ads into three distinct stages: 1) cognitive; 2) affective; and 3) conative. Audience online reactions at each of these three stages are depicted by Asie with specific probabilistic models based on the synergistic influences from both online social friends and offline TV ads. Extensive experiments demonstrate the effectiveness of Asie.

Model-based branching point detection in single-cell data by K-branches clustering

PubMed Central

Chlis, Nikolaos K.; Wolf, F. Alexander; Theis, Fabian J.

2017-01-01

Abstract Motivation The identification of heterogeneities in cell populations by utilizing single-cell technologies such as single-cell RNA-Seq, enables inference of cellular development and lineage trees. Several methods have been proposed for such inference from high-dimensional single-cell data. They typically assign each cell to a branch in a differentiation trajectory. However, they commonly assume specific geometries such as tree-like developmental hierarchies and lack statistically sound methods to decide on the number of branching events. Results We present K-Branches, a solution to the above problem by locally fitting half-lines to single-cell data, introducing a clustering algorithm similar to K-Means. These halflines are proxies for branches in the differentiation trajectory of cells. We propose a modified version of the GAP statistic for model selection, in order to decide on the number of lines that best describe the data locally. In this manner, we identify the location and number of subgroups of cells that are associated with branching events and full differentiation, respectively. We evaluate the performance of our method on single-cell RNA-Seq data describing the differentiation of myeloid progenitors during hematopoiesis, single-cell qPCR data of mouse blastocyst development, single-cell qPCR data of human myeloid monocytic leukemia and artificial data. Availability and implementation An R implementation of K-Branches is freely available at https://github.com/theislab/kbranches. Contact fabian.theis@helmholtz-muenchen.de Supplementary information Supplementary data are available at Bioinformatics online. PMID:28582478

SubClonal Hierarchy Inference from Somatic Mutations: Automatic Reconstruction of Cancer Evolutionary Trees from Multi-region Next Generation Sequencing

PubMed Central

Niknafs, Noushin; Beleva-Guthrie, Violeta; Naiman, Daniel Q.; Karchin, Rachel

2015-01-01

Recent improvements in next-generation sequencing of tumor samples and the ability to identify somatic mutations at low allelic fractions have opened the way for new approaches to model the evolution of individual cancers. The power and utility of these models is increased when tumor samples from multiple sites are sequenced. Temporal ordering of the samples may provide insight into the etiology of both primary and metastatic lesions and rationalizations for tumor recurrence and therapeutic failures. Additional insights may be provided by temporal ordering of evolving subclones—cellular subpopulations with unique mutational profiles. Current methods for subclone hierarchy inference tightly couple the problem of temporal ordering with that of estimating the fraction of cancer cells harboring each mutation. We present a new framework that includes a rigorous statistical hypothesis test and a collection of tools that make it possible to decouple these problems, which we believe will enable substantial progress in the field of subclone hierarchy inference. The methods presented here can be flexibly combined with methods developed by others addressing either of these problems. We provide tools to interpret hypothesis test results, which inform phylogenetic tree construction, and we introduce the first genetic algorithm designed for this purpose. The utility of our framework is systematically demonstrated in simulations. For most tested combinations of tumor purity, sequencing coverage, and tree complexity, good power (≥ 0.8) can be achieved and Type 1 error is well controlled when at least three tumor samples are available from a patient. Using data from three published multi-region tumor sequencing studies of (murine) small cell lung cancer, acute myeloid leukemia, and chronic lymphocytic leukemia, in which the authors reconstructed subclonal phylogenetic trees by manual expert curation, we show how different configurations of our tools can identify either a single tree in agreement with the authors, or a small set of trees, which include the authors’ preferred tree. Our results have implications for improved modeling of tumor evolution and the importance of multi-region tumor sequencing. PMID:26436540

Statistical analysis of fNIRS data: a comprehensive review.

PubMed

Tak, Sungho; Ye, Jong Chul

2014-01-15

Functional near-infrared spectroscopy (fNIRS) is a non-invasive method to measure brain activities using the changes of optical absorption in the brain through the intact skull. fNIRS has many advantages over other neuroimaging modalities such as positron emission tomography (PET), functional magnetic resonance imaging (fMRI), or magnetoencephalography (MEG), since it can directly measure blood oxygenation level changes related to neural activation with high temporal resolution. However, fNIRS signals are highly corrupted by measurement noises and physiology-based systemic interference. Careful statistical analyses are therefore required to extract neuronal activity-related signals from fNIRS data. In this paper, we provide an extensive review of historical developments of statistical analyses of fNIRS signal, which include motion artifact correction, short source-detector separation correction, principal component analysis (PCA)/independent component analysis (ICA), false discovery rate (FDR), serially-correlated errors, as well as inference techniques such as the standard t-test, F-test, analysis of variance (ANOVA), and statistical parameter mapping (SPM) framework. In addition, to provide a unified view of various existing inference techniques, we explain a linear mixed effect model with restricted maximum likelihood (ReML) variance estimation, and show that most of the existing inference methods for fNIRS analysis can be derived as special cases. Some of the open issues in statistical analysis are also described. Copyright © 2013 Elsevier Inc. All rights reserved.

Accounting for measurement error: a critical but often overlooked process.

PubMed

Harris, Edward F; Smith, Richard N

2009-12-01

Due to instrument imprecision and human inconsistencies, measurements are not free of error. Technical error of measurement (TEM) is the variability encountered between dimensions when the same specimens are measured at multiple sessions. A goal of a data collection regimen is to minimise TEM. The few studies that actually quantify TEM, regardless of discipline, report that it is substantial and can affect results and inferences. This paper reviews some statistical approaches for identifying and controlling TEM. Statistically, TEM is part of the residual ('unexplained') variance in a statistical test, so accounting for TEM, which requires repeated measurements, enhances the chances of finding a statistically significant difference if one exists. The aim of this paper was to review and discuss common statistical designs relating to types of error and statistical approaches to error accountability. This paper addresses issues of landmark location, validity, technical and systematic error, analysis of variance, scaled measures and correlation coefficients in order to guide the reader towards correct identification of true experimental differences. Researchers commonly infer characteristics about populations from comparatively restricted study samples. Most inferences are statistical and, aside from concerns about adequate accounting for known sources of variation with the research design, an important source of variability is measurement error. Variability in locating landmarks that define variables is obvious in odontometrics, cephalometrics and anthropometry, but the same concerns about measurement accuracy and precision extend to all disciplines. With increasing accessibility to computer-assisted methods of data collection, the ease of incorporating repeated measures into statistical designs has improved. Accounting for this technical source of variation increases the chance of finding biologically true differences when they exist.

Developing a statistically powerful measure for quartet tree inference using phylogenetic identities and Markov invariants.

PubMed

Sumner, Jeremy G; Taylor, Amelia; Holland, Barbara R; Jarvis, Peter D

2017-12-01

Recently there has been renewed interest in phylogenetic inference methods based on phylogenetic invariants, alongside the related Markov invariants. Broadly speaking, both these approaches give rise to polynomial functions of sequence site patterns that, in expectation value, either vanish for particular evolutionary trees (in the case of phylogenetic invariants) or have well understood transformation properties (in the case of Markov invariants). While both approaches have been valued for their intrinsic mathematical interest, it is not clear how they relate to each other, and to what extent they can be used as practical tools for inference of phylogenetic trees. In this paper, by focusing on the special case of binary sequence data and quartets of taxa, we are able to view these two different polynomial-based approaches within a common framework. To motivate the discussion, we present three desirable statistical properties that we argue any invariant-based phylogenetic method should satisfy: (1) sensible behaviour under reordering of input sequences; (2) stability as the taxa evolve independently according to a Markov process; and (3) explicit dependence on the assumption of a continuous-time process. Motivated by these statistical properties, we develop and explore several new phylogenetic inference methods. In particular, we develop a statistically bias-corrected version of the Markov invariants approach which satisfies all three properties. We also extend previous work by showing that the phylogenetic invariants can be implemented in such a way as to satisfy property (3). A simulation study shows that, in comparison to other methods, our new proposed approach based on bias-corrected Markov invariants is extremely powerful for phylogenetic inference. The binary case is of particular theoretical interest as-in this case only-the Markov invariants can be expressed as linear combinations of the phylogenetic invariants. A wider implication of this is that, for models with more than two states-for example DNA sequence alignments with four-state models-we find that methods which rely on phylogenetic invariants are incapable of satisfying all three of the stated statistical properties. This is because in these cases the relevant Markov invariants belong to a class of polynomials independent from the phylogenetic invariants.

Imputation approaches for animal movement modeling

USGS Publications Warehouse

Scharf, Henry; Hooten, Mevin B.; Johnson, Devin S.

2017-01-01

The analysis of telemetry data is common in animal ecological studies. While the collection of telemetry data for individual animals has improved dramatically, the methods to properly account for inherent uncertainties (e.g., measurement error, dependence, barriers to movement) have lagged behind. Still, many new statistical approaches have been developed to infer unknown quantities affecting animal movement or predict movement based on telemetry data. Hierarchical statistical models are useful to account for some of the aforementioned uncertainties, as well as provide population-level inference, but they often come with an increased computational burden. For certain types of statistical models, it is straightforward to provide inference if the latent true animal trajectory is known, but challenging otherwise. In these cases, approaches related to multiple imputation have been employed to account for the uncertainty associated with our knowledge of the latent trajectory. Despite the increasing use of imputation approaches for modeling animal movement, the general sensitivity and accuracy of these methods have not been explored in detail. We provide an introduction to animal movement modeling and describe how imputation approaches may be helpful for certain types of models. We also assess the performance of imputation approaches in two simulation studies. Our simulation studies suggests that inference for model parameters directly related to the location of an individual may be more accurate than inference for parameters associated with higher-order processes such as velocity or acceleration. Finally, we apply these methods to analyze a telemetry data set involving northern fur seals (Callorhinus ursinus) in the Bering Sea. Supplementary materials accompanying this paper appear online.

Mathematical properties and bounds on haplotyping populations by pure parsimony.

PubMed

Wang, I-Lin; Chang, Chia-Yuan

2011-06-01

Although the haplotype data can be used to analyze the function of DNA, due to the significant efforts required in collecting the haplotype data, usually the genotype data is collected and then the population haplotype inference (PHI) problem is solved to infer haplotype data from genotype data for a population. This paper investigates the PHI problem based on the pure parsimony criterion (HIPP), which seeks the minimum number of distinct haplotypes to infer a given genotype data. We analyze the mathematical structure and properties for the HIPP problem, propose techniques to reduce the given genotype data into an equivalent one of much smaller size, and analyze the relations of genotype data using a compatible graph. Based on the mathematical properties in the compatible graph, we propose a maximal clique heuristic to obtain an upper bound, and a new polynomial-sized integer linear programming formulation to obtain a lower bound for the HIPP problem. Copyright © 2011 Elsevier Inc. All rights reserved.

Decision-theoretic control of EUVE telescope scheduling

NASA Technical Reports Server (NTRS)

Hansson, Othar; Mayer, Andrew

1993-01-01

This paper describes a decision theoretic scheduler (DTS) designed to employ state-of-the-art probabilistic inference technology to speed the search for efficient solutions to constraint-satisfaction problems. Our approach involves assessing the performance of heuristic control strategies that are normally hard-coded into scheduling systems and using probabilistic inference to aggregate this information in light of the features of a given problem. The Bayesian Problem-Solver (BPS) introduced a similar approach to solving single agent and adversarial graph search patterns yielding orders-of-magnitude improvement over traditional techniques. Initial efforts suggest that similar improvements will be realizable when applied to typical constraint-satisfaction scheduling problems.

Data analytics for simplifying thermal efficiency planning in cities.

PubMed

Abdolhosseini Qomi, Mohammad Javad; Noshadravan, Arash; Sobstyl, Jake M; Toole, Jameson; Ferreira, Joseph; Pellenq, Roland J-M; Ulm, Franz-Josef; Gonzalez, Marta C

2016-04-01

More than 44% of building energy consumption in the USA is used for space heating and cooling, and this accounts for 20% of national CO2emissions. This prompts the need to identify among the 130 million households in the USA those with the greatest energy-saving potential and the associated costs of the path to reach that goal. Whereas current solutions address this problem by analysing each building in detail, we herein reduce the dimensionality of the problem by simplifying the calculations of energy losses in buildings. We present a novel inference method that can be used via a ranking algorithm that allows us to estimate the potential energy saving for heating purposes. To that end, we only need consumption from records of gas bills integrated with a building's footprint. The method entails a statistical screening of the intricate interplay between weather, infrastructural and residents' choice variables to determine building gas consumption and potential savings at a city scale. We derive a general statistical pattern of consumption in an urban settlement, reducing it to a set of the most influential buildings' parameters that operate locally. By way of example, the implications are explored using records of a set of (N= 6200) buildings in Cambridge, MA, USA, which indicate that retrofitting only 16% of buildings entails a 40% reduction in gas consumption of the whole building stock. We find that the inferred heat loss rate of buildings exhibits a power-law data distribution akin to Zipf's law, which provides a means to map an optimum path for gas savings per retrofit at a city scale. These findings have implications for improving the thermal efficiency of cities' building stock, as outlined by current policy efforts seeking to reduce home heating and cooling energy consumption and lower associated greenhouse gas emissions. © 2016 The Author(s).

Design-based and model-based inference in surveys of freshwater mollusks

USGS Publications Warehouse

Dorazio, R.M.

1999-01-01

Well-known concepts in statistical inference and sampling theory are used to develop recommendations for planning and analyzing the results of quantitative surveys of freshwater mollusks. Two methods of inference commonly used in survey sampling (design-based and model-based) are described and illustrated using examples relevant in surveys of freshwater mollusks. The particular objectives of a survey and the type of information observed in each unit of sampling can be used to help select the sampling design and the method of inference. For example, the mean density of a sparsely distributed population of mollusks can be estimated with higher precision by using model-based inference or by using design-based inference with adaptive cluster sampling than by using design-based inference with conventional sampling. More experience with quantitative surveys of natural assemblages of freshwater mollusks is needed to determine the actual benefits of different sampling designs and inferential procedures.

Bayesian inference for joint modelling of longitudinal continuous, binary and ordinal events.

PubMed

Li, Qiuju; Pan, Jianxin; Belcher, John

2016-12-01

In medical studies, repeated measurements of continuous, binary and ordinal outcomes are routinely collected from the same patient. Instead of modelling each outcome separately, in this study we propose to jointly model the trivariate longitudinal responses, so as to take account of the inherent association between the different outcomes and thus improve statistical inferences. This work is motivated by a large cohort study in the North West of England, involving trivariate responses from each patient: Body Mass Index, Depression (Yes/No) ascertained with cut-off score not less than 8 at the Hospital Anxiety and Depression Scale, and Pain Interference generated from the Medical Outcomes Study 36-item short-form health survey with values returned on an ordinal scale 1-5. There are some well-established methods for combined continuous and binary, or even continuous and ordinal responses, but little work was done on the joint analysis of continuous, binary and ordinal responses. We propose conditional joint random-effects models, which take into account the inherent association between the continuous, binary and ordinal outcomes. Bayesian analysis methods are used to make statistical inferences. Simulation studies show that, by jointly modelling the trivariate outcomes, standard deviations of the estimates of parameters in the models are smaller and much more stable, leading to more efficient parameter estimates and reliable statistical inferences. In the real data analysis, the proposed joint analysis yields a much smaller deviance information criterion value than the separate analysis, and shows other good statistical properties too. © The Author(s) 2014.

State-space models’ dirty little secrets: even simple linear Gaussian models can have estimation problems

NASA Astrophysics Data System (ADS)

Auger-Méthé, Marie; Field, Chris; Albertsen, Christoffer M.; Derocher, Andrew E.; Lewis, Mark A.; Jonsen, Ian D.; Mills Flemming, Joanna

2016-05-01

State-space models (SSMs) are increasingly used in ecology to model time-series such as animal movement paths and population dynamics. This type of hierarchical model is often structured to account for two levels of variability: biological stochasticity and measurement error. SSMs are flexible. They can model linear and nonlinear processes using a variety of statistical distributions. Recent ecological SSMs are often complex, with a large number of parameters to estimate. Through a simulation study, we show that even simple linear Gaussian SSMs can suffer from parameter- and state-estimation problems. We demonstrate that these problems occur primarily when measurement error is larger than biological stochasticity, the condition that often drives ecologists to use SSMs. Using an animal movement example, we show how these estimation problems can affect ecological inference. Biased parameter estimates of a SSM describing the movement of polar bears (Ursus maritimus) result in overestimating their energy expenditure. We suggest potential solutions, but show that it often remains difficult to estimate parameters. While SSMs are powerful tools, they can give misleading results and we urge ecologists to assess whether the parameters can be estimated accurately before drawing ecological conclusions from their results.

Finding undetected protein associations in cell signaling by belief propagation.

PubMed

Bailly-Bechet, M; Borgs, C; Braunstein, A; Chayes, J; Dagkessamanskaia, A; François, J-M; Zecchina, R

2011-01-11

External information propagates in the cell mainly through signaling cascades and transcriptional activation, allowing it to react to a wide spectrum of environmental changes. High-throughput experiments identify numerous molecular components of such cascades that may, however, interact through unknown partners. Some of them may be detected using data coming from the integration of a protein-protein interaction network and mRNA expression profiles. This inference problem can be mapped onto the problem of finding appropriate optimal connected subgraphs of a network defined by these datasets. The optimization procedure turns out to be computationally intractable in general. Here we present a new distributed algorithm for this task, inspired from statistical physics, and apply this scheme to alpha factor and drug perturbations data in yeast. We identify the role of the COS8 protein, a member of a gene family of previously unknown function, and validate the results by genetic experiments. The algorithm we present is specially suited for very large datasets, can run in parallel, and can be adapted to other problems in systems biology. On renowned benchmarks it outperforms other algorithms in the field.

Active inference, communication and hermeneutics☆

PubMed Central

Friston, Karl J.; Frith, Christopher D.

2015-01-01

Hermeneutics refers to interpretation and translation of text (typically ancient scriptures) but also applies to verbal and non-verbal communication. In a psychological setting it nicely frames the problem of inferring the intended content of a communication. In this paper, we offer a solution to the problem of neural hermeneutics based upon active inference. In active inference, action fulfils predictions about how we will behave (e.g., predicting we will speak). Crucially, these predictions can be used to predict both self and others – during speaking and listening respectively. Active inference mandates the suppression of prediction errors by updating an internal model that generates predictions – both at fast timescales (through perceptual inference) and slower timescales (through perceptual learning). If two agents adopt the same model, then – in principle – they can predict each other and minimise their mutual prediction errors. Heuristically, this ensures they are singing from the same hymn sheet. This paper builds upon recent work on active inference and communication to illustrate perceptual learning using simulated birdsongs. Our focus here is the neural hermeneutics implicit in learning, where communication facilitates long-term changes in generative models that are trying to predict each other. In other words, communication induces perceptual learning and enables others to (literally) change our minds and vice versa. PMID:25957007

Active inference, communication and hermeneutics.

PubMed

Friston, Karl J; Frith, Christopher D

2015-07-01

Hermeneutics refers to interpretation and translation of text (typically ancient scriptures) but also applies to verbal and non-verbal communication. In a psychological setting it nicely frames the problem of inferring the intended content of a communication. In this paper, we offer a solution to the problem of neural hermeneutics based upon active inference. In active inference, action fulfils predictions about how we will behave (e.g., predicting we will speak). Crucially, these predictions can be used to predict both self and others--during speaking and listening respectively. Active inference mandates the suppression of prediction errors by updating an internal model that generates predictions--both at fast timescales (through perceptual inference) and slower timescales (through perceptual learning). If two agents adopt the same model, then--in principle--they can predict each other and minimise their mutual prediction errors. Heuristically, this ensures they are singing from the same hymn sheet. This paper builds upon recent work on active inference and communication to illustrate perceptual learning using simulated birdsongs. Our focus here is the neural hermeneutics implicit in learning, where communication facilitates long-term changes in generative models that are trying to predict each other. In other words, communication induces perceptual learning and enables others to (literally) change our minds and vice versa. Copyright © 2015 The Authors. Published by Elsevier Ltd.. All rights reserved.

Neuronal couplings between retinal ganglion cells inferred by efficient inverse statistical physics methods

PubMed Central

Cocco, Simona; Leibler, Stanislas; Monasson, Rémi

2009-01-01

Complexity of neural systems often makes impracticable explicit measurements of all interactions between their constituents. Inverse statistical physics approaches, which infer effective couplings between neurons from their spiking activity, have been so far hindered by their computational complexity. Here, we present 2 complementary, computationally efficient inverse algorithms based on the Ising and “leaky integrate-and-fire” models. We apply those algorithms to reanalyze multielectrode recordings in the salamander retina in darkness and under random visual stimulus. We find strong positive couplings between nearby ganglion cells common to both stimuli, whereas long-range couplings appear under random stimulus only. The uncertainty on the inferred couplings due to limitations in the recordings (duration, small area covered on the retina) is discussed. Our methods will allow real-time evaluation of couplings for large assemblies of neurons. PMID:19666487

Confidence crisis of results in biomechanics research.

PubMed

Knudson, Duane

2017-11-01

Many biomechanics studies have small sample sizes and incorrect statistical analyses, so reporting of inaccurate inferences and inflated magnitude of effects are common in the field. This review examines these issues in biomechanics research and summarises potential solutions from research in other fields to increase the confidence in the experimental effects reported in biomechanics. Authors, reviewers and editors of biomechanics research reports are encouraged to improve sample sizes and the resulting statistical power, improve reporting transparency, improve the rigour of statistical analyses used, and increase the acceptance of replication studies to improve the validity of inferences from data in biomechanics research. The application of sports biomechanics research results would also improve if a larger percentage of unbiased effects and their uncertainty were reported in the literature.

Cognitive Transfer Outcomes for a Simulation-Based Introductory Statistics Curriculum

ERIC Educational Resources Information Center

Backman, Matthew D.; Delmas, Robert C.; Garfield, Joan

2017-01-01

Cognitive transfer is the ability to apply learned skills and knowledge to new applications and contexts. This investigation evaluates cognitive transfer outcomes for a tertiary-level introductory statistics course using the CATALST curriculum, which exclusively used simulation-based methods to develop foundations of statistical inference. A…

The Role of the Sampling Distribution in Understanding Statistical Inference

ERIC Educational Resources Information Center

Lipson, Kay

2003-01-01

Many statistics educators believe that few students develop the level of conceptual understanding essential for them to apply correctly the statistical techniques at their disposal and to interpret their outcomes appropriately. It is also commonly believed that the sampling distribution plays an important role in developing this understanding.…

A statistical method for lung tumor segmentation uncertainty in PET images based on user inference.

PubMed

Zheng, Chaojie; Wang, Xiuying; Feng, Dagan

2015-01-01

PET has been widely accepted as an effective imaging modality for lung tumor diagnosis and treatment. However, standard criteria for delineating tumor boundary from PET are yet to develop largely due to relatively low quality of PET images, uncertain tumor boundary definition, and variety of tumor characteristics. In this paper, we propose a statistical solution to segmentation uncertainty on the basis of user inference. We firstly define the uncertainty segmentation band on the basis of segmentation probability map constructed from Random Walks (RW) algorithm; and then based on the extracted features of the user inference, we use Principle Component Analysis (PCA) to formulate the statistical model for labeling the uncertainty band. We validated our method on 10 lung PET-CT phantom studies from the public RIDER collections [1] and 16 clinical PET studies where tumors were manually delineated by two experienced radiologists. The methods were validated using Dice similarity coefficient (DSC) to measure the spatial volume overlap. Our method achieved an average DSC of 0.878 ± 0.078 on phantom studies and 0.835 ± 0.039 on clinical studies.

Empirical evidence for acceleration-dependent amplification factors

USGS Publications Warehouse

Borcherdt, R.D.

2002-01-01

Site-specific amplification factors, Fa and Fv, used in current U.S. building codes decrease with increasing base acceleration level as implied by the Loma Prieta earthquake at 0.1g and extrapolated using numerical models and laboratory results. The Northridge earthquake recordings of 17 January 1994 and subsequent geotechnical data permit empirical estimates of amplification at base acceleration levels up to 0.5g. Distance measures and normalization procedures used to infer amplification ratios from soil-rock pairs in predetermined azimuth-distance bins significantly influence the dependence of amplification estimates on base acceleration. Factors inferred using a hypocentral distance norm do not show a statistically significant dependence on base acceleration. Factors inferred using norms implied by the attenuation functions of Abrahamson and Silva show a statistically significant decrease with increasing base acceleration. The decrease is statistically more significant for stiff clay and sandy soil (site class D) sites than for stiffer sites underlain by gravely soils and soft rock (site class C). The decrease in amplification with increasing base acceleration is more pronounced for the short-period amplification factor, Fa, than for the midperiod factor, Fv.

Karl Pearson and eugenics: personal opinions and scientific rigor.

PubMed

Delzell, Darcie A P; Poliak, Cathy D

2013-09-01

The influence of personal opinions and biases on scientific conclusions is a threat to the advancement of knowledge. Expertise and experience does not render one immune to this temptation. In this work, one of the founding fathers of statistics, Karl Pearson, is used as an illustration of how even the most talented among us can produce misleading results when inferences are made without caution or reference to potential bias and other analysis limitations. A study performed by Pearson on British Jewish schoolchildren is examined in light of ethical and professional statistical practice. The methodology used and inferences made by Pearson and his coauthor are sometimes questionable and offer insight into how Pearson's support of eugenics and his own British nationalism could have potentially influenced his often careless and far-fetched inferences. A short background into Pearson's work and beliefs is provided, along with an in-depth examination of the authors' overall experimental design and statistical practices. In addition, portions of the study regarding intelligence and tuberculosis are discussed in more detail, along with historical reactions to their work.

Particle Filter with State Permutations for Solving Image Jigsaw Puzzles

PubMed Central

Yang, Xingwei; Adluru, Nagesh; Latecki, Longin Jan

2016-01-01

We deal with an image jigsaw puzzle problem, which is defined as reconstructing an image from a set of square and non-overlapping image patches. It is known that a general instance of this problem is NP-complete, and it is also challenging for humans, since in the considered setting the original image is not given. Recently a graphical model has been proposed to solve this and related problems. The target label probability function is then maximized using loopy belief propagation. We also formulate the problem as maximizing a label probability function and use exactly the same pairwise potentials. Our main contribution is a novel inference approach in the sampling framework of Particle Filter (PF). Usually in the PF framework it is assumed that the observations arrive sequentially, e.g., the observations are naturally ordered by their time stamps in the tracking scenario. Based on this assumption, the posterior density over the corresponding hidden states is estimated. In the jigsaw puzzle problem all observations (puzzle pieces) are given at once without any particular order. Therefore, we relax the assumption of having ordered observations and extend the PF framework to estimate the posterior density by exploring different orders of observations and selecting the most informative permutations of observations. This significantly broadens the scope of applications of the PF inference. Our experimental results demonstrate that the proposed inference framework significantly outperforms the loopy belief propagation in solving the image jigsaw puzzle problem. In particular, the extended PF inference triples the accuracy of the label assignment compared to that using loopy belief propagation. PMID:27795660

Acoustic emissions diagnosis of rotor-stator rubs using the KS statistic

NASA Astrophysics Data System (ADS)

Hall, L. D.; Mba, D.

2004-07-01

Acoustic emission (AE) measurement at the bearings of rotating machinery has become a useful tool for diagnosing incipient fault conditions. In particular, AE can be used to detect unwanted intermittent or partial rubbing between a rotating central shaft and surrounding stationary components. This is a particular problem encountered in turbines used for power generation. For successful fault diagnosis, it is important to adopt AE signal analysis techniques capable of distinguishing between various types of rub mechanisms. It is also useful to develop techniques for inferring information such as the severity of rubbing or the type of seal material making contact on the shaft. It is proposed that modelling the cumulative distribution function of rub-induced AE signals with respect to appropriate theoretical distributions, and quantifying the goodness of fit with the Kolmogorov-Smirnov (KS) statistic, offers a suitable signal feature for diagnosis. This paper demonstrates the successful use of the KS feature for discriminating different classes of shaft-seal rubbing.

Order-restricted inference for means with missing values.

PubMed

Wang, Heng; Zhong, Ping-Shou

2017-09-01

Missing values appear very often in many applications, but the problem of missing values has not received much attention in testing order-restricted alternatives. Under the missing at random (MAR) assumption, we impute the missing values nonparametrically using kernel regression. For data with imputation, the classical likelihood ratio test designed for testing the order-restricted means is no longer applicable since the likelihood does not exist. This article proposes a novel method for constructing test statistics for assessing means with an increasing order or a decreasing order based on jackknife empirical likelihood (JEL) ratio. It is shown that the JEL ratio statistic evaluated under the null hypothesis converges to a chi-bar-square distribution, whose weights depend on missing probabilities and nonparametric imputation. Simulation study shows that the proposed test performs well under various missing scenarios and is robust for normally and nonnormally distributed data. The proposed method is applied to an Alzheimer's disease neuroimaging initiative data set for finding a biomarker for the diagnosis of the Alzheimer's disease. © 2017, The International Biometric Society.

Adjusting Beliefs via Transformed Fuzzy Priors

NASA Astrophysics Data System (ADS)

Rattanadamrongaksorn, T.; Sirikanchanarak, D.; Sirisrisakulchai, J.; Sriboonchitta, S.

2018-02-01

Instead of leaving a decision to a pure data-driven system, intervention and collaboration by human would be preferred to fill the gap that machine cannot perform well. In financial applications, for instance, the inference and prediction during structural changes by critical factors; such as market conditions, administrative styles, political policies, etc.; have significant influences to investment strategies. With the conditions differing from the past, we believe that the decision should not be made by only the historical data but also with human estimation. In this study, the updating process by data fusion between expert opinions and statistical observations is thus proposed. The expert’s linguistic terms can be translated into mathematical expressions by the predefined fuzzy numbers and utilized as the initial knowledge for Bayesian statistical framework via the possibility-to-probability transformation. The artificial samples on five scenarios were tested in the univariate problem to demonstrate the methodology. The results showed the shifts and variations appeared on the parameters of the distributions and, as a consequence, adjust the degrees of belief accordingly.

Activity inference for Ambient Intelligence through handling artifacts in a healthcare environment.

PubMed

Martínez-Pérez, Francisco E; González-Fraga, Jose Ángel; Cuevas-Tello, Juan C; Rodríguez, Marcela D

2012-01-01

Human activity inference is not a simple process due to distinct ways of performing it. Our proposal presents the SCAN framework for activity inference. SCAN is divided into three modules: (1) artifact recognition, (2) activity inference, and (3) activity representation, integrating three important elements of Ambient Intelligence (AmI) (artifact-behavior modeling, event interpretation and context extraction). The framework extends the roaming beat (RB) concept by obtaining the representation using three kinds of technologies for activity inference. The RB is based on both analysis and recognition from artifact behavior for activity inference. A practical case is shown in a nursing home where a system affording 91.35% effectiveness was implemented in situ. Three examples are shown using RB representation for activity representation. Framework description, RB description and CALog system overcome distinct problems such as the feasibility to implement AmI systems, and to show the feasibility for accomplishing the challenges related to activity recognition based on artifact recognition. We discuss how the use of RBs might positively impact the problems faced by designers and developers for recovering information in an easier manner and thus they can develop tools focused on the user.

Activity Inference for Ambient Intelligence Through Handling Artifacts in a Healthcare Environment

PubMed Central

Martínez-Pérez, Francisco E.; González-Fraga, Jose Ángel; Cuevas-Tello, Juan C.; Rodríguez, Marcela D.

2012-01-01

Human activity inference is not a simple process due to distinct ways of performing it. Our proposal presents the SCAN framework for activity inference. SCAN is divided into three modules: (1) artifact recognition, (2) activity inference, and (3) activity representation, integrating three important elements of Ambient Intelligence (AmI) (artifact-behavior modeling, event interpretation and context extraction). The framework extends the roaming beat (RB) concept by obtaining the representation using three kinds of technologies for activity inference. The RB is based on both analysis and recognition from artifact behavior for activity inference. A practical case is shown in a nursing home where a system affording 91.35% effectiveness was implemented in situ. Three examples are shown using RB representation for activity representation. Framework description, RB description and CALog system overcome distinct problems such as the feasibility to implement AmI systems, and to show the feasibility for accomplishing the challenges related to activity recognition based on artifact recognition. We discuss how the use of RBs might positively impact the problems faced by designers and developers for recovering information in an easier manner and thus they can develop tools focused on the user. PMID:22368512

In silico model-based inference: a contemporary approach for hypothesis testing in network biology

PubMed Central

Klinke, David J.

2014-01-01

Inductive inference plays a central role in the study of biological systems where one aims to increase their understanding of the system by reasoning backwards from uncertain observations to identify causal relationships among components of the system. These causal relationships are postulated from prior knowledge as a hypothesis or simply a model. Experiments are designed to test the model. Inferential statistics are used to establish a level of confidence in how well our postulated model explains the acquired data. This iterative process, commonly referred to as the scientific method, either improves our confidence in a model or suggests that we revisit our prior knowledge to develop a new model. Advances in technology impact how we use prior knowledge and data to formulate models of biological networks and how we observe cellular behavior. However, the approach for model-based inference has remained largely unchanged since Fisher, Neyman and Pearson developed the ideas in the early 1900’s that gave rise to what is now known as classical statistical hypothesis (model) testing. Here, I will summarize conventional methods for model-based inference and suggest a contemporary approach to aid in our quest to discover how cells dynamically interpret and transmit information for therapeutic aims that integrates ideas drawn from high performance computing, Bayesian statistics, and chemical kinetics. PMID:25139179

In silico model-based inference: a contemporary approach for hypothesis testing in network biology.

PubMed

Klinke, David J

2014-01-01

Inductive inference plays a central role in the study of biological systems where one aims to increase their understanding of the system by reasoning backwards from uncertain observations to identify causal relationships among components of the system. These causal relationships are postulated from prior knowledge as a hypothesis or simply a model. Experiments are designed to test the model. Inferential statistics are used to establish a level of confidence in how well our postulated model explains the acquired data. This iterative process, commonly referred to as the scientific method, either improves our confidence in a model or suggests that we revisit our prior knowledge to develop a new model. Advances in technology impact how we use prior knowledge and data to formulate models of biological networks and how we observe cellular behavior. However, the approach for model-based inference has remained largely unchanged since Fisher, Neyman and Pearson developed the ideas in the early 1900s that gave rise to what is now known as classical statistical hypothesis (model) testing. Here, I will summarize conventional methods for model-based inference and suggest a contemporary approach to aid in our quest to discover how cells dynamically interpret and transmit information for therapeutic aims that integrates ideas drawn from high performance computing, Bayesian statistics, and chemical kinetics. © 2014 American Institute of Chemical Engineers.

Spatio-temporal conditional inference and hypothesis tests for neural ensemble spiking precision

PubMed Central

Harrison, Matthew T.; Amarasingham, Asohan; Truccolo, Wilson

2014-01-01

The collective dynamics of neural ensembles create complex spike patterns with many spatial and temporal scales. Understanding the statistical structure of these patterns can help resolve fundamental questions about neural computation and neural dynamics. Spatio-temporal conditional inference (STCI) is introduced here as a semiparametric statistical framework for investigating the nature of precise spiking patterns from collections of neurons that is robust to arbitrarily complex and nonstationary coarse spiking dynamics. The main idea is to focus statistical modeling and inference, not on the full distribution of the data, but rather on families of conditional distributions of precise spiking given different types of coarse spiking. The framework is then used to develop families of hypothesis tests for probing the spatio-temporal precision of spiking patterns. Relationships among different conditional distributions are used to improve multiple hypothesis testing adjustments and to design novel Monte Carlo spike resampling algorithms. Of special note are algorithms that can locally jitter spike times while still preserving the instantaneous peri-stimulus time histogram (PSTH) or the instantaneous total spike count from a group of recorded neurons. The framework can also be used to test whether first-order maximum entropy models with possibly random and time-varying parameters can account for observed patterns of spiking. STCI provides a detailed example of the generic principle of conditional inference, which may be applicable in other areas of neurostatistical analysis. PMID:25380339

A Parallel Finite Set Statistical Simulator for Multi-Target Detection and Tracking

NASA Astrophysics Data System (ADS)

Hussein, I.; MacMillan, R.

2014-09-01

Finite Set Statistics (FISST) is a powerful Bayesian inference tool for the joint detection, classification and tracking of multi-target environments. FISST is capable of handling phenomena such as clutter, misdetections, and target birth and decay. Implicit within the approach are solutions to the data association and target label-tracking problems. Finally, FISST provides generalized information measures that can be used for sensor allocation across different types of tasks such as: searching for new targets, and classification and tracking of known targets. These FISST capabilities have been demonstrated on several small-scale illustrative examples. However, for implementation in a large-scale system as in the Space Situational Awareness problem, these capabilities require a lot of computational power. In this paper, we implement FISST in a parallel environment for the joint detection and tracking of multi-target systems. In this implementation, false alarms and misdetections will be modeled. Target birth and decay will not be modeled in the present paper. We will demonstrate the success of the method for as many targets as we possibly can in a desktop parallel environment. Performance measures will include: number of targets in the simulation, certainty of detected target tracks, computational time as a function of clutter returns and number of targets, among other factors.

Behavioral pattern identification for structural health monitoring in complex systems

NASA Astrophysics Data System (ADS)

Gupta, Shalabh

Estimation of structural damage and quantification of structural integrity are critical for safe and reliable operation of human-engineered complex systems, such as electromechanical, thermofluid, and petrochemical systems. Damage due to fatigue crack is one of the most commonly encountered sources of structural degradation in mechanical systems. Early detection of fatigue damage is essential because the resulting structural degradation could potentially cause catastrophic failures, leading to loss of expensive equipment and human life. Therefore, for reliable operation and enhanced availability, it is necessary to develop capabilities for prognosis and estimation of impending failures, such as the onset of wide-spread fatigue crack damage in mechanical structures. This dissertation presents information-based online sensing of fatigue damage using the analytical tools of symbolic time series analysis ( STSA). Anomaly detection using STSA is a pattern recognition method that has been recently developed based upon a fixed-structure, fixed-order Markov chain. The analysis procedure is built upon the principles of Symbolic Dynamics, Information Theory and Statistical Pattern Recognition. The dissertation demonstrates real-time fatigue damage monitoring based on time series data of ultrasonic signals. Statistical pattern changes are measured using STSA to monitor the evolution of fatigue damage. Real-time anomaly detection is presented as a solution to the forward (analysis) problem and the inverse (synthesis) problem. (1) the forward problem - The primary objective of the forward problem is identification of the statistical changes in the time series data of ultrasonic signals due to gradual evolution of fatigue damage. (2) the inverse problem - The objective of the inverse problem is to infer the anomalies from the observed time series data in real time based on the statistical information generated during the forward problem. A computer-controlled special-purpose fatigue test apparatus, equipped with multiple sensing devices (e.g., ultrasonics and optical microscope) for damage analysis, has been used to experimentally validate the STSA method for early detection of anomalous behavior. The sensor information is integrated with a software module consisting of the STSA algorithm for real-time monitoring of fatigue damage. Experiments have been conducted under different loading conditions on specimens constructed from the ductile aluminium alloy 7075 - T6. The dissertation has also investigated the application of the STSA method for early detection of anomalies in other engineering disciplines. Two primary applications include combustion instability in a generic thermal pulse combustor model and whirling phenomenon in a typical misaligned shaft.

Data mining and statistical inference in selective laser melting

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kamath, Chandrika

Selective laser melting (SLM) is an additive manufacturing process that builds a complex three-dimensional part, layer-by-layer, using a laser beam to fuse fine metal powder together. The design freedom afforded by SLM comes associated with complexity. As the physical phenomena occur over a broad range of length and time scales, the computational cost of modeling the process is high. At the same time, the large number of parameters that control the quality of a part make experiments expensive. In this paper, we describe ways in which we can use data mining and statistical inference techniques to intelligently combine simulations andmore » experiments to build parts with desired properties. We start with a brief summary of prior work in finding process parameters for high-density parts. We then expand on this work to show how we can improve the approach by using feature selection techniques to identify important variables, data-driven surrogate models to reduce computational costs, improved sampling techniques to cover the design space adequately, and uncertainty analysis for statistical inference. Here, our results indicate that techniques from data mining and statistics can complement those from physical modeling to provide greater insight into complex processes such as selective laser melting.« less

Data mining and statistical inference in selective laser melting

DOE PAGES

Kamath, Chandrika

2016-01-11

Selective laser melting (SLM) is an additive manufacturing process that builds a complex three-dimensional part, layer-by-layer, using a laser beam to fuse fine metal powder together. The design freedom afforded by SLM comes associated with complexity. As the physical phenomena occur over a broad range of length and time scales, the computational cost of modeling the process is high. At the same time, the large number of parameters that control the quality of a part make experiments expensive. In this paper, we describe ways in which we can use data mining and statistical inference techniques to intelligently combine simulations andmore » experiments to build parts with desired properties. We start with a brief summary of prior work in finding process parameters for high-density parts. We then expand on this work to show how we can improve the approach by using feature selection techniques to identify important variables, data-driven surrogate models to reduce computational costs, improved sampling techniques to cover the design space adequately, and uncertainty analysis for statistical inference. Here, our results indicate that techniques from data mining and statistics can complement those from physical modeling to provide greater insight into complex processes such as selective laser melting.« less

Fully Bayesian inference for structural MRI: application to segmentation and statistical analysis of T2-hypointensities.

PubMed

Schmidt, Paul; Schmid, Volker J; Gaser, Christian; Buck, Dorothea; Bührlen, Susanne; Förschler, Annette; Mühlau, Mark

2013-01-01

Aiming at iron-related T2-hypointensity, which is related to normal aging and neurodegenerative processes, we here present two practicable approaches, based on Bayesian inference, for preprocessing and statistical analysis of a complex set of structural MRI data. In particular, Markov Chain Monte Carlo methods were used to simulate posterior distributions. First, we rendered a segmentation algorithm that uses outlier detection based on model checking techniques within a Bayesian mixture model. Second, we rendered an analytical tool comprising a Bayesian regression model with smoothness priors (in the form of Gaussian Markov random fields) mitigating the necessity to smooth data prior to statistical analysis. For validation, we used simulated data and MRI data of 27 healthy controls (age: [Formula: see text]; range, [Formula: see text]). We first observed robust segmentation of both simulated T2-hypointensities and gray-matter regions known to be T2-hypointense. Second, simulated data and images of segmented T2-hypointensity were analyzed. We found not only robust identification of simulated effects but also a biologically plausible age-related increase of T2-hypointensity primarily within the dentate nucleus but also within the globus pallidus, substantia nigra, and red nucleus. Our results indicate that fully Bayesian inference can successfully be applied for preprocessing and statistical analysis of structural MRI data.

A Comparison of Phasing Algorithms for Trios and Unrelated Individuals

PubMed Central

Marchini, Jonathan; Cutler, David; Patterson, Nick; Stephens, Matthew; Eskin, Eleazar; Halperin, Eran; Lin, Shin; Qin, Zhaohui S.; Munro, Heather M.; Abecasis, Gonçalo R.; Donnelly, Peter

2006-01-01

Knowledge of haplotype phase is valuable for many analysis methods in the study of disease, population, and evolutionary genetics. Considerable research effort has been devoted to the development of statistical and computational methods that infer haplotype phase from genotype data. Although a substantial number of such methods have been developed, they have focused principally on inference from unrelated individuals, and comparisons between methods have been rather limited. Here, we describe the extension of five leading algorithms for phase inference for handling father-mother-child trios. We performed a comprehensive assessment of the methods applied to both trios and to unrelated individuals, with a focus on genomic-scale problems, using both simulated data and data from the HapMap project. The most accurate algorithm was PHASE (v2.1). For this method, the percentages of genotypes whose phase was incorrectly inferred were 0.12%, 0.05%, and 0.16% for trios from simulated data, HapMap Centre d'Etude du Polymorphisme Humain (CEPH) trios, and HapMap Yoruban trios, respectively, and 5.2% and 5.9% for unrelated individuals in simulated data and the HapMap CEPH data, respectively. The other methods considered in this work had comparable but slightly worse error rates. The error rates for trios are similar to the levels of genotyping error and missing data expected. We thus conclude that all the methods considered will provide highly accurate estimates of haplotypes when applied to trio data sets. Running times differ substantially between methods. Although it is one of the slowest methods, PHASE (v2.1) was used to infer haplotypes for the 1 million–SNP HapMap data set. Finally, we evaluated methods of estimating the value of r2 between a pair of SNPs and concluded that all methods estimated r2 well when the estimated value was ⩾0.8. PMID:16465620

Drug target inference through pathway analysis of genomics data

PubMed Central

Ma, Haisu; Zhao, Hongyu

2013-01-01

Statistical modeling coupled with bioinformatics is commonly used for drug discovery. Although there exist many approaches for single target based drug design and target inference, recent years have seen a paradigm shift to system-level pharmacological research. Pathway analysis of genomics data represents one promising direction for computational inference of drug targets. This article aims at providing a comprehensive review on the evolving issues is this field, covering methodological developments, their pros and cons, as well as future research directions. PMID:23369829

Applications of statistics to medical science, II overview of statistical procedures for general use.

PubMed

Watanabe, Hiroshi

2012-01-01

Procedures of statistical analysis are reviewed to provide an overview of applications of statistics for general use. Topics that are dealt with are inference on a population, comparison of two populations with respect to means and probabilities, and multiple comparisons. This study is the second part of series in which we survey medical statistics. Arguments related to statistical associations and regressions will be made in subsequent papers.

PROBABILITY SAMPLING AND POPULATION INFERENCE IN MONITORING PROGRAMS

EPA Science Inventory

A fundamental difference between probability sampling and conventional statistics is that "sampling" deals with real, tangible populations, whereas "conventional statistics" usually deals with hypothetical populations that have no real-world realization. he focus here is on real ...

Conceptual Challenges in Coordinating Theoretical and Data-Centered Estimates of Probability

ERIC Educational Resources Information Center

Konold, Cliff; Madden, Sandra; Pollatsek, Alexander; Pfannkuch, Maxine; Wild, Chris; Ziedins, Ilze; Finzer, William; Horton, Nicholas J.; Kazak, Sibel

2011-01-01

A core component of informal statistical inference is the recognition that judgments based on sample data are inherently uncertain. This implies that instruction aimed at developing informal inference needs to foster basic probabilistic reasoning. In this article, we analyze and critique the now-common practice of introducing students to both…

Campbell's and Rubin's Perspectives on Causal Inference

ERIC Educational Resources Information Center

West, Stephen G.; Thoemmes, Felix

2010-01-01

Donald Campbell's approach to causal inference (D. T. Campbell, 1957; W. R. Shadish, T. D. Cook, & D. T. Campbell, 2002) is widely used in psychology and education, whereas Donald Rubin's causal model (P. W. Holland, 1986; D. B. Rubin, 1974, 2005) is widely used in economics, statistics, medicine, and public health. Campbell's approach focuses on…

Direct Evidence for a Dual Process Model of Deductive Inference

ERIC Educational Resources Information Center

Markovits, Henry; Brunet, Marie-Laurence; Thompson, Valerie; Brisson, Janie

2013-01-01

In 2 experiments, we tested a strong version of a dual process theory of conditional inference (cf. Verschueren et al., 2005a, 2005b) that assumes that most reasoners have 2 strategies available, the choice of which is determined by situational variables, cognitive capacity, and metacognitive control. The statistical strategy evaluates inferences…

From Blickets to Synapses: Inferring Temporal Causal Networks by Observation

ERIC Educational Resources Information Center

Fernando, Chrisantha

2013-01-01

How do human infants learn the causal dependencies between events? Evidence suggests that this remarkable feat can be achieved by observation of only a handful of examples. Many computational models have been produced to explain how infants perform causal inference without explicit teaching about statistics or the scientific method. Here, we…

It's a Girl! Random Numbers, Simulations, and the Law of Large Numbers

ERIC Educational Resources Information Center

Goodwin, Chris; Ortiz, Enrique

2015-01-01

Modeling using mathematics and making inferences about mathematical situations are becoming more prevalent in most fields of study. Descriptive statistics cannot be used to generalize about a population or make predictions of what can occur. Instead, inference must be used. Simulation and sampling are essential in building a foundation for…

Hypothesis-Testing Demands Trustworthy Data—A Simulation Approach to Inferential Statistics Advocating the Research Program Strategy

PubMed Central

Krefeld-Schwalb, Antonia; Witte, Erich H.; Zenker, Frank

2018-01-01

In psychology as elsewhere, the main statistical inference strategy to establish empirical effects is null-hypothesis significance testing (NHST). The recent failure to replicate allegedly well-established NHST-results, however, implies that such results lack sufficient statistical power, and thus feature unacceptably high error-rates. Using data-simulation to estimate the error-rates of NHST-results, we advocate the research program strategy (RPS) as a superior methodology. RPS integrates Frequentist with Bayesian inference elements, and leads from a preliminary discovery against a (random) H0-hypothesis to a statistical H1-verification. Not only do RPS-results feature significantly lower error-rates than NHST-results, RPS also addresses key-deficits of a “pure” Frequentist and a standard Bayesian approach. In particular, RPS aggregates underpowered results safely. RPS therefore provides a tool to regain the trust the discipline had lost during the ongoing replicability-crisis. PMID:29740363

NIRS-SPM: statistical parametric mapping for near infrared spectroscopy

NASA Astrophysics Data System (ADS)

Tak, Sungho; Jang, Kwang Eun; Jung, Jinwook; Jang, Jaeduck; Jeong, Yong; Ye, Jong Chul

2008-02-01

Even though there exists a powerful statistical parametric mapping (SPM) tool for fMRI, similar public domain tools are not available for near infrared spectroscopy (NIRS). In this paper, we describe a new public domain statistical toolbox called NIRS-SPM for quantitative analysis of NIRS signals. Specifically, NIRS-SPM statistically analyzes the NIRS data using GLM and makes inference as the excursion probability which comes from the random field that are interpolated from the sparse measurement. In order to obtain correct inference, NIRS-SPM offers the pre-coloring and pre-whitening method for temporal correlation estimation. For simultaneous recording NIRS signal with fMRI, the spatial mapping between fMRI image and real coordinate in 3-D digitizer is estimated using Horn's algorithm. These powerful tools allows us the super-resolution localization of the brain activation which is not possible using the conventional NIRS analysis tools.

Hypothesis-Testing Demands Trustworthy Data-A Simulation Approach to Inferential Statistics Advocating the Research Program Strategy.

PubMed

Krefeld-Schwalb, Antonia; Witte, Erich H; Zenker, Frank

2018-01-01

In psychology as elsewhere, the main statistical inference strategy to establish empirical effects is null-hypothesis significance testing (NHST). The recent failure to replicate allegedly well-established NHST-results, however, implies that such results lack sufficient statistical power, and thus feature unacceptably high error-rates. Using data-simulation to estimate the error-rates of NHST-results, we advocate the research program strategy (RPS) as a superior methodology. RPS integrates Frequentist with Bayesian inference elements, and leads from a preliminary discovery against a (random) H 0 -hypothesis to a statistical H 1 -verification. Not only do RPS-results feature significantly lower error-rates than NHST-results, RPS also addresses key-deficits of a "pure" Frequentist and a standard Bayesian approach. In particular, RPS aggregates underpowered results safely. RPS therefore provides a tool to regain the trust the discipline had lost during the ongoing replicability-crisis.

Application of Bayesian inference to the study of hierarchical organization in self-organized complex adaptive systems

NASA Astrophysics Data System (ADS)

Knuth, K. H.

2001-05-01

We consider the application of Bayesian inference to the study of self-organized structures in complex adaptive systems. In particular, we examine the distribution of elements, agents, or processes in systems dominated by hierarchical structure. We demonstrate that results obtained by Caianiello [1] on Hierarchical Modular Systems (HMS) can be found by applying Jaynes' Principle of Group Invariance [2] to a few key assumptions about our knowledge of hierarchical organization. Subsequent application of the Principle of Maximum Entropy allows inferences to be made about specific systems. The utility of the Bayesian method is considered by examining both successes and failures of the hierarchical model. We discuss how Caianiello's original statements suffer from the Mind Projection Fallacy [3] and we restate his assumptions thus widening the applicability of the HMS model. The relationship between inference and statistical physics, described by Jaynes [4], is reiterated with the expectation that this realization will aid the field of complex systems research by moving away from often inappropriate direct application of statistical mechanics to a more encompassing inferential methodology.

Conditional statistical inference with multistage testing designs.

PubMed

Zwitser, Robert J; Maris, Gunter

2015-03-01

In this paper it is demonstrated how statistical inference from multistage test designs can be made based on the conditional likelihood. Special attention is given to parameter estimation, as well as the evaluation of model fit. Two reasons are provided why the fit of simple measurement models is expected to be better in adaptive designs, compared to linear designs: more parameters are available for the same number of observations; and undesirable response behavior, like slipping and guessing, might be avoided owing to a better match between item difficulty and examinee proficiency. The results are illustrated with simulated data, as well as with real data.

Use of Tests of Statistical Significance and Other Analytic Choices in a School Psychology Journal: Review of Practices and Suggested Alternatives.

ERIC Educational Resources Information Center

Snyder, Patricia A.; Thompson, Bruce

The use of tests of statistical significance was explored, first by reviewing some criticisms of contemporary practice in the use of statistical tests as reflected in a series of articles in the "American Psychologist" and in the appointment of a "Task Force on Statistical Inference" by the American Psychological Association…

Bayesian parameter inference for stochastic biochemical network models using particle Markov chain Monte Carlo

PubMed Central

Golightly, Andrew; Wilkinson, Darren J.

2011-01-01

Computational systems biology is concerned with the development of detailed mechanistic models of biological processes. Such models are often stochastic and analytically intractable, containing uncertain parameters that must be estimated from time course data. In this article, we consider the task of inferring the parameters of a stochastic kinetic model defined as a Markov (jump) process. Inference for the parameters of complex nonlinear multivariate stochastic process models is a challenging problem, but we find here that algorithms based on particle Markov chain Monte Carlo turn out to be a very effective computationally intensive approach to the problem. Approximations to the inferential model based on stochastic differential equations (SDEs) are considered, as well as improvements to the inference scheme that exploit the SDE structure. We apply the methodology to a Lotka–Volterra system and a prokaryotic auto-regulatory network. PMID:23226583

Standard deviation and standard error of the mean.

PubMed

Lee, Dong Kyu; In, Junyong; Lee, Sangseok

2015-06-01

In most clinical and experimental studies, the standard deviation (SD) and the estimated standard error of the mean (SEM) are used to present the characteristics of sample data and to explain statistical analysis results. However, some authors occasionally muddle the distinctive usage between the SD and SEM in medical literature. Because the process of calculating the SD and SEM includes different statistical inferences, each of them has its own meaning. SD is the dispersion of data in a normal distribution. In other words, SD indicates how accurately the mean represents sample data. However the meaning of SEM includes statistical inference based on the sampling distribution. SEM is the SD of the theoretical distribution of the sample means (the sampling distribution). While either SD or SEM can be applied to describe data and statistical results, one should be aware of reasonable methods with which to use SD and SEM. We aim to elucidate the distinctions between SD and SEM and to provide proper usage guidelines for both, which summarize data and describe statistical results.

Standard deviation and standard error of the mean

PubMed Central

In, Junyong; Lee, Sangseok

2015-01-01

In most clinical and experimental studies, the standard deviation (SD) and the estimated standard error of the mean (SEM) are used to present the characteristics of sample data and to explain statistical analysis results. However, some authors occasionally muddle the distinctive usage between the SD and SEM in medical literature. Because the process of calculating the SD and SEM includes different statistical inferences, each of them has its own meaning. SD is the dispersion of data in a normal distribution. In other words, SD indicates how accurately the mean represents sample data. However the meaning of SEM includes statistical inference based on the sampling distribution. SEM is the SD of the theoretical distribution of the sample means (the sampling distribution). While either SD or SEM can be applied to describe data and statistical results, one should be aware of reasonable methods with which to use SD and SEM. We aim to elucidate the distinctions between SD and SEM and to provide proper usage guidelines for both, which summarize data and describe statistical results. PMID:26045923

Semisupervised learning using Bayesian interpretation: application to LS-SVM.

PubMed

Adankon, Mathias M; Cheriet, Mohamed; Biem, Alain

2011-04-01

Bayesian reasoning provides an ideal basis for representing and manipulating uncertain knowledge, with the result that many interesting algorithms in machine learning are based on Bayesian inference. In this paper, we use the Bayesian approach with one and two levels of inference to model the semisupervised learning problem and give its application to the successful kernel classifier support vector machine (SVM) and its variant least-squares SVM (LS-SVM). Taking advantage of Bayesian interpretation of LS-SVM, we develop a semisupervised learning algorithm for Bayesian LS-SVM using our approach based on two levels of inference. Experimental results on both artificial and real pattern recognition problems show the utility of our method.

Optimal Recall from Bounded Metaplastic Synapses: Predicting Functional Adaptations in Hippocampal Area CA3

PubMed Central

Savin, Cristina; Dayan, Peter; Lengyel, Máté

2014-01-01

A venerable history of classical work on autoassociative memory has significantly shaped our understanding of several features of the hippocampus, and most prominently of its CA3 area, in relation to memory storage and retrieval. However, existing theories of hippocampal memory processing ignore a key biological constraint affecting memory storage in neural circuits: the bounded dynamical range of synapses. Recent treatments based on the notion of metaplasticity provide a powerful model for individual bounded synapses; however, their implications for the ability of the hippocampus to retrieve memories well and the dynamics of neurons associated with that retrieval are both unknown. Here, we develop a theoretical framework for memory storage and recall with bounded synapses. We formulate the recall of a previously stored pattern from a noisy recall cue and limited-capacity (and therefore lossy) synapses as a probabilistic inference problem, and derive neural dynamics that implement approximate inference algorithms to solve this problem efficiently. In particular, for binary synapses with metaplastic states, we demonstrate for the first time that memories can be efficiently read out with biologically plausible network dynamics that are completely constrained by the synaptic plasticity rule, and the statistics of the stored patterns and of the recall cue. Our theory organises into a coherent framework a wide range of existing data about the regulation of excitability, feedback inhibition, and network oscillations in area CA3, and makes novel and directly testable predictions that can guide future experiments. PMID:24586137

Exact solutions for species tree inference from discordant gene trees.

PubMed

Chang, Wen-Chieh; Górecki, Paweł; Eulenstein, Oliver

2013-10-01

Phylogenetic analysis has to overcome the grant challenge of inferring accurate species trees from evolutionary histories of gene families (gene trees) that are discordant with the species tree along whose branches they have evolved. Two well studied approaches to cope with this challenge are to solve either biologically informed gene tree parsimony (GTP) problems under gene duplication, gene loss, and deep coalescence, or the classic RF supertree problem that does not rely on any biological model. Despite the potential of these problems to infer credible species trees, they are NP-hard. Therefore, these problems are addressed by heuristics that typically lack any provable accuracy and precision. We describe fast dynamic programming algorithms that solve the GTP problems and the RF supertree problem exactly, and demonstrate that our algorithms can solve instances with data sets consisting of as many as 22 taxa. Extensions of our algorithms can also report the number of all optimal species trees, as well as the trees themselves. To better asses the quality of the resulting species trees that best fit the given gene trees, we also compute the worst case species trees, their numbers, and optimization score for each of the computational problems. Finally, we demonstrate the performance of our exact algorithms using empirical and simulated data sets, and analyze the quality of heuristic solutions for the studied problems by contrasting them with our exact solutions.

Statistical analysis and interpolation of compositional data in materials science.

PubMed

Pesenson, Misha Z; Suram, Santosh K; Gregoire, John M

2015-02-09

Compositional data are ubiquitous in chemistry and materials science: analysis of elements in multicomponent systems, combinatorial problems, etc., lead to data that are non-negative and sum to a constant (for example, atomic concentrations). The constant sum constraint restricts the sampling space to a simplex instead of the usual Euclidean space. Since statistical measures such as mean and standard deviation are defined for the Euclidean space, traditional correlation studies, multivariate analysis, and hypothesis testing may lead to erroneous dependencies and incorrect inferences when applied to compositional data. Furthermore, composition measurements that are used for data analytics may not include all of the elements contained in the material; that is, the measurements may be subcompositions of a higher-dimensional parent composition. Physically meaningful statistical analysis must yield results that are invariant under the number of composition elements, requiring the application of specialized statistical tools. We present specifics and subtleties of compositional data processing through discussion of illustrative examples. We introduce basic concepts, terminology, and methods required for the analysis of compositional data and utilize them for the spatial interpolation of composition in a sputtered thin film. The results demonstrate the importance of this mathematical framework for compositional data analysis (CDA) in the fields of materials science and chemistry.

Statistics and Informatics in Space Astrophysics

NASA Astrophysics Data System (ADS)

Feigelson, E.

2017-12-01

The interest in statistical and computational methodology has seen rapid growth in space-based astrophysics, parallel to the growth seen in Earth remote sensing. There is widespread agreement that scientific interpretation of the cosmic microwave background, discovery of exoplanets, and classifying multiwavelength surveys is too complex to be accomplished with traditional techniques. NASA operates several well-functioning Science Archive Research Centers providing 0.5 PBy datasets to the research community. These databases are integrated with full-text journal articles in the NASA Astrophysics Data System (200K pageviews/day). Data products use interoperable formats and protocols established by the International Virtual Observatory Alliance. NASA supercomputers also support complex astrophysical models of systems such as accretion disks and planet formation. Academic researcher interest in methodology has significantly grown in areas such as Bayesian inference and machine learning, and statistical research is underway to treat problems such as irregularly spaced time series and astrophysical model uncertainties. Several scholarly societies have created interest groups in astrostatistics and astroinformatics. Improvements are needed on several fronts. Community education in advanced methodology is not sufficiently rapid to meet the research needs. Statistical procedures within NASA science analysis software are sometimes not optimal, and pipeline development may not use modern software engineering techniques. NASA offers few grant opportunities supporting research in astroinformatics and astrostatistics.

Visual shape perception as Bayesian inference of 3D object-centered shape representations.

PubMed

Erdogan, Goker; Jacobs, Robert A

2017-11-01

Despite decades of research, little is known about how people visually perceive object shape. We hypothesize that a promising approach to shape perception is provided by a "visual perception as Bayesian inference" framework which augments an emphasis on visual representation with an emphasis on the idea that shape perception is a form of statistical inference. Our hypothesis claims that shape perception of unfamiliar objects can be characterized as statistical inference of 3D shape in an object-centered coordinate system. We describe a computational model based on our theoretical framework, and provide evidence for the model along two lines. First, we show that, counterintuitively, the model accounts for viewpoint-dependency of object recognition, traditionally regarded as evidence against people's use of 3D object-centered shape representations. Second, we report the results of an experiment using a shape similarity task, and present an extensive evaluation of existing models' abilities to account for the experimental data. We find that our shape inference model captures subjects' behaviors better than competing models. Taken as a whole, our experimental and computational results illustrate the promise of our approach and suggest that people's shape representations of unfamiliar objects are probabilistic, 3D, and object-centered. (PsycINFO Database Record (c) 2017 APA, all rights reserved).

Approximate message passing with restricted Boltzmann machine priors

NASA Astrophysics Data System (ADS)

Tramel, Eric W.; Drémeau, Angélique; Krzakala, Florent

2016-07-01

Approximate message passing (AMP) has been shown to be an excellent statistical approach to signal inference and compressed sensing problems. The AMP framework provides modularity in the choice of signal prior; here we propose a hierarchical form of the Gauss-Bernoulli prior which utilizes a restricted Boltzmann machine (RBM) trained on the signal support to push reconstruction performance beyond that of simple i.i.d. priors for signals whose support can be well represented by a trained binary RBM. We present and analyze two methods of RBM factorization and demonstrate how these affect signal reconstruction performance within our proposed algorithm. Finally, using the MNIST handwritten digit dataset, we show experimentally that using an RBM allows AMP to approach oracle-support performance.

Incorporating imperfect detection into joint models of communites: A response to Warton et al.

USGS Publications Warehouse

Beissinger, Steven R.; Iknayan, Kelly J.; Guillera-Arroita, Gurutzeta; Zipkin, Elise; Dorazio, Robert; Royle, Andy; Kery, Marc

2016-01-01

Warton et al. [1] advance community ecology by describing a statistical framework that can jointly model abundances (or distributions) across many taxa to quantify how community properties respond to environmental variables. This framework specifies the effects of both measured and unmeasured (latent) variables on the abundance (or occurrence) of each species. Latent variables are random effects that capture the effects of both missing environmental predictors and correlations in parameter values among different species. As presented in Warton et al., however, the joint modeling framework fails to account for the common problem of detection or measurement errors that always accompany field sampling of abundance or occupancy, and are well known to obscure species- and community-level inferences.

Restoration of HST images with missing data

NASA Technical Reports Server (NTRS)

Adorf, Hans-Martin

1992-01-01

Missing data are a fairly common problem when restoring Hubble Space Telescope observations of extended sources. On Wide Field and Planetary Camera images cosmic ray hits and CCD hot spots are the prevalent causes of data losses, whereas on Faint Object Camera images data are lossed due to reseaux marks, blemishes, areas of saturation and the omnipresent frame edges. This contribution discusses a technique for 'filling in' missing data by statistical inference using information from the surrounding pixels. The major gain consists in minimizing adverse spill-over effects to the restoration in areas neighboring those where data are missing. When the mask delineating the support of 'missing data' is made dynamic, cosmic ray hits, etc. can be detected on the fly during restoration.

Statistical inferences with jointly type-II censored samples from two Pareto distributions

NASA Astrophysics Data System (ADS)

Abu-Zinadah, Hanaa H.

2017-08-01

In the several fields of industries the product comes from more than one production line, which is required to work the comparative life tests. This problem requires sampling of the different production lines, then the joint censoring scheme is appeared. In this article we consider the life time Pareto distribution with jointly type-II censoring scheme. The maximum likelihood estimators (MLE) and the corresponding approximate confidence intervals as well as the bootstrap confidence intervals of the model parameters are obtained. Also Bayesian point and credible intervals of the model parameters are presented. The life time data set is analyzed for illustrative purposes. Monte Carlo results from simulation studies are presented to assess the performance of our proposed method.

Statistics and bioinformatics in nutritional sciences: analysis of complex data in the era of systems biology⋆

PubMed Central

Fu, Wenjiang J.; Stromberg, Arnold J.; Viele, Kert; Carroll, Raymond J.; Wu, Guoyao

2009-01-01

Over the past two decades, there have been revolutionary developments in life science technologies characterized by high throughput, high efficiency, and rapid computation. Nutritionists now have the advanced methodologies for the analysis of DNA, RNA, protein, low-molecular-weight metabolites, as well as access to bioinformatics databases. Statistics, which can be defined as the process of making scientific inferences from data that contain variability, has historically played an integral role in advancing nutritional sciences. Currently, in the era of systems biology, statistics has become an increasingly important tool to quantitatively analyze information about biological macromolecules. This article describes general terms used in statistical analysis of large, complex experimental data. These terms include experimental design, power analysis, sample size calculation, and experimental errors (type I and II errors) for nutritional studies at population, tissue, cellular, and molecular levels. In addition, we highlighted various sources of experimental variations in studies involving microarray gene expression, real-time polymerase chain reaction, proteomics, and other bioinformatics technologies. Moreover, we provided guidelines for nutritionists and other biomedical scientists to plan and conduct studies and to analyze the complex data. Appropriate statistical analyses are expected to make an important contribution to solving major nutrition-associated problems in humans and animals (including obesity, diabetes, cardiovascular disease, cancer, ageing, and intrauterine fetal retardation). PMID:20233650

Robust inference for group sequential trials.

PubMed

Ganju, Jitendra; Lin, Yunzhi; Zhou, Kefei

2017-03-01

For ethical reasons, group sequential trials were introduced to allow trials to stop early in the event of extreme results. Endpoints in such trials are usually mortality or irreversible morbidity. For a given endpoint, the norm is to use a single test statistic and to use that same statistic for each analysis. This approach is risky because the test statistic has to be specified before the study is unblinded, and there is loss in power if the assumptions that ensure optimality for each analysis are not met. To minimize the risk of moderate to substantial loss in power due to a suboptimal choice of a statistic, a robust method was developed for nonsequential trials. The concept is analogous to diversification of financial investments to minimize risk. The method is based on combining P values from multiple test statistics for formal inference while controlling the type I error rate at its designated value.This article evaluates the performance of 2 P value combining methods for group sequential trials. The emphasis is on time to event trials although results from less complex trials are also included. The gain or loss in power with the combination method relative to a single statistic is asymmetric in its favor. Depending on the power of each individual test, the combination method can give more power than any single test or give power that is closer to the test with the most power. The versatility of the method is that it can combine P values from different test statistics for analysis at different times. The robustness of results suggests that inference from group sequential trials can be strengthened with the use of combined tests. Copyright © 2017 John Wiley & Sons, Ltd.

Solving large-scale PDE-constrained Bayesian inverse problems with Riemann manifold Hamiltonian Monte Carlo

NASA Astrophysics Data System (ADS)

Bui-Thanh, T.; Girolami, M.

2014-11-01

We consider the Riemann manifold Hamiltonian Monte Carlo (RMHMC) method for solving statistical inverse problems governed by partial differential equations (PDEs). The Bayesian framework is employed to cast the inverse problem into the task of statistical inference whose solution is the posterior distribution in infinite dimensional parameter space conditional upon observation data and Gaussian prior measure. We discretize both the likelihood and the prior using the H1-conforming finite element method together with a matrix transfer technique. The power of the RMHMC method is that it exploits the geometric structure induced by the PDE constraints of the underlying inverse problem. Consequently, each RMHMC posterior sample is almost uncorrelated/independent from the others providing statistically efficient Markov chain simulation. However this statistical efficiency comes at a computational cost. This motivates us to consider computationally more efficient strategies for RMHMC. At the heart of our construction is the fact that for Gaussian error structures the Fisher information matrix coincides with the Gauss-Newton Hessian. We exploit this fact in considering a computationally simplified RMHMC method combining state-of-the-art adjoint techniques and the superiority of the RMHMC method. Specifically, we first form the Gauss-Newton Hessian at the maximum a posteriori point and then use it as a fixed constant metric tensor throughout RMHMC simulation. This eliminates the need for the computationally costly differential geometric Christoffel symbols, which in turn greatly reduces computational effort at a corresponding loss of sampling efficiency. We further reduce the cost of forming the Fisher information matrix by using a low rank approximation via a randomized singular value decomposition technique. This is efficient since a small number of Hessian-vector products are required. The Hessian-vector product in turn requires only two extra PDE solves using the adjoint technique. Various numerical results up to 1025 parameters are presented to demonstrate the ability of the RMHMC method in exploring the geometric structure of the problem to propose (almost) uncorrelated/independent samples that are far away from each other, and yet the acceptance rate is almost unity. The results also suggest that for the PDE models considered the proposed fixed metric RMHMC can attain almost as high a quality performance as the original RMHMC, i.e. generating (almost) uncorrelated/independent samples, while being two orders of magnitude less computationally expensive.

Long-term strategy for the statistical design of a forest health monitoring system

Treesearch

Hans T. Schreuder; Raymond L. Czaplewski

1993-01-01

A conceptual framework is given for a broad-scale survey of forest health that accomplishes three objectives: generate descriptive statistics; detect changes in such statistics; and simplify analytical inferences that identify, and possibly establish cause-effect relationships. Our paper discusses the development of sampling schemes to satisfy these three objectives,...

Assessing Understanding of Sampling Distributions and Differences in Learning amongst Different Learning Styles

ERIC Educational Resources Information Center

Beeman, Jennifer Leigh Sloan

2013-01-01

Research has found that students successfully complete an introductory course in statistics without fully comprehending the underlying theory or being able to exhibit statistical reasoning. This is particularly true for the understanding about the sampling distribution of the mean, a crucial concept for statistical inference. This study…

Using Action Research to Develop a Course in Statistical Inference for Workplace-Based Adults

ERIC Educational Resources Information Center

Forbes, Sharleen

2014-01-01

Many adults who need an understanding of statistical concepts have limited mathematical skills. They need a teaching approach that includes as little mathematical context as possible. Iterative participatory qualitative research (action research) was used to develop a statistical literacy course for adult learners informed by teaching in…

Applying Statistical Process Control to Clinical Data: An Illustration.

ERIC Educational Resources Information Center

Pfadt, Al; And Others

1992-01-01

Principles of statistical process control are applied to a clinical setting through the use of control charts to detect changes, as part of treatment planning and clinical decision-making processes. The logic of control chart analysis is derived from principles of statistical inference. Sample charts offer examples of evaluating baselines and…

Efficiency Analysis: Enhancing the Statistical and Evaluative Power of the Regression-Discontinuity Design.

ERIC Educational Resources Information Center

Madhere, Serge

An analytic procedure, efficiency analysis, is proposed for improving the utility of quantitative program evaluation for decision making. The three features of the procedure are explained: (1) for statistical control, it adopts and extends the regression-discontinuity design; (2) for statistical inferences, it de-emphasizes hypothesis testing in…

Statistical dynamo theory: Mode excitation.

PubMed

Hoyng, P

2009-04-01

We compute statistical properties of the lowest-order multipole coefficients of the magnetic field generated by a dynamo of arbitrary shape. To this end we expand the field in a complete biorthogonal set of base functions, viz. B= summation operator_{k}a;{k}(t)b;{k}(r) . The properties of these biorthogonal function sets are treated in detail. We consider a linear problem and the statistical properties of the fluid flow are supposed to be given. The turbulent convection may have an arbitrary distribution of spatial scales. The time evolution of the expansion coefficients a;{k} is governed by a stochastic differential equation from which we infer their averages a;{k} , autocorrelation functions a;{k}(t)a;{k *}(t+tau) , and an equation for the cross correlations a;{k}a;{l *} . The eigenfunctions of the dynamo equation (with eigenvalues lambda_{k} ) turn out to be a preferred set in terms of which our results assume their simplest form. The magnetic field of the dynamo is shown to consist of transiently excited eigenmodes whose frequency and coherence time is given by Ilambda_{k} and -1/Rlambda_{k} , respectively. The relative rms excitation level of the eigenmodes, and hence the distribution of magnetic energy over spatial scales, is determined by linear theory. An expression is derived for |a;{k}|;{2}/|a;{0}|;{2} in case the fundamental mode b;{0} has a dominant amplitude, and we outline how this expression may be evaluated. It is estimated that |a;{k}|;{2}/|a;{0}|;{2} approximately 1/N , where N is the number of convective cells in the dynamo. We show that the old problem of a short correlation time (or first-order smoothing approximation) has been partially eliminated. Finally we prove that for a simple statistically steady dynamo with finite resistivity all eigenvalues obey Rlambda_{k}<0 .

The penumbra of learning: a statistical theory of synaptic tagging and capture.

PubMed

Gershman, Samuel J

2014-01-01

Learning in humans and animals is accompanied by a penumbra: Learning one task benefits from learning an unrelated task shortly before or after. At the cellular level, the penumbra of learning appears when weak potentiation of one synapse is amplified by strong potentiation of another synapse on the same neuron during a critical time window. Weak potentiation sets a molecular tag that enables the synapse to capture plasticity-related proteins synthesized in response to strong potentiation at another synapse. This paper describes a computational model which formalizes synaptic tagging and capture in terms of statistical learning mechanisms. According to this model, synaptic strength encodes a probabilistic inference about the dynamically changing association between pre- and post-synaptic firing rates. The rate of change is itself inferred, coupling together different synapses on the same neuron. When the inputs to one synapse change rapidly, the inferred rate of change increases, amplifying learning at other synapses.

Inference of missing data and chemical model parameters using experimental statistics

NASA Astrophysics Data System (ADS)

Casey, Tiernan; Najm, Habib

2017-11-01

A method for determining the joint parameter density of Arrhenius rate expressions through the inference of missing experimental data is presented. This approach proposes noisy hypothetical data sets from target experiments and accepts those which agree with the reported statistics, in the form of nominal parameter values and their associated uncertainties. The data exploration procedure is formalized using Bayesian inference, employing maximum entropy and approximate Bayesian computation methods to arrive at a joint density on data and parameters. The method is demonstrated in the context of reactions in the H2-O2 system for predictive modeling of combustion systems of interest. Work supported by the US DOE BES CSGB. Sandia National Labs is a multimission lab managed and operated by Nat. Technology and Eng'g Solutions of Sandia, LLC., a wholly owned subsidiary of Honeywell Intl, for the US DOE NCSA under contract DE-NA-0003525.

Statistical numeracy as a moderator of (pseudo)contingency effects on decision behavior.

PubMed

Fleig, Hanna; Meiser, Thorsten; Ettlin, Florence; Rummel, Jan

2017-03-01

Pseudocontingencies denote contingency estimates inferred from base rates rather than from cell frequencies. We examined the role of statistical numeracy for effects of such fallible but adaptive inferences on choice behavior. In Experiment 1, we provided information on single observations as well as on base rates and tracked participants' eye movements. In Experiment 2, we manipulated the availability of information on cell frequencies and base rates between conditions. Our results demonstrate that a focus on base rates rather than cell frequencies benefits pseudocontingency effects. Learners who are more proficient in (conditional) probability calculation prefer to rely on cell frequencies in order to judge contingencies, though, as was evident from their gaze behavior. If cell frequencies are available in summarized format, they may infer the true contingency between options and outcomes. Otherwise, however, even highly numerate learners are susceptible to pseudocontingency effects. Copyright © 2017 Elsevier B.V. All rights reserved.

Doubly robust nonparametric inference on the average treatment effect.

PubMed

Benkeser, D; Carone, M; Laan, M J Van Der; Gilbert, P B

2017-12-01

Doubly robust estimators are widely used to draw inference about the average effect of a treatment. Such estimators are consistent for the effect of interest if either one of two nuisance parameters is consistently estimated. However, if flexible, data-adaptive estimators of these nuisance parameters are used, double robustness does not readily extend to inference. We present a general theoretical study of the behaviour of doubly robust estimators of an average treatment effect when one of the nuisance parameters is inconsistently estimated. We contrast different methods for constructing such estimators and investigate the extent to which they may be modified to also allow doubly robust inference. We find that while targeted minimum loss-based estimation can be used to solve this problem very naturally, common alternative frameworks appear to be inappropriate for this purpose. We provide a theoretical study and a numerical evaluation of the alternatives considered. Our simulations highlight the need for and usefulness of these approaches in practice, while our theoretical developments have broad implications for the construction of estimators that permit doubly robust inference in other problems.

MULTINEST: an efficient and robust Bayesian inference tool for cosmology and particle physics

NASA Astrophysics Data System (ADS)

Feroz, F.; Hobson, M. P.; Bridges, M.

2009-10-01

We present further development and the first public release of our multimodal nested sampling algorithm, called MULTINEST. This Bayesian inference tool calculates the evidence, with an associated error estimate, and produces posterior samples from distributions that may contain multiple modes and pronounced (curving) degeneracies in high dimensions. The developments presented here lead to further substantial improvements in sampling efficiency and robustness, as compared to the original algorithm presented in Feroz & Hobson, which itself significantly outperformed existing Markov chain Monte Carlo techniques in a wide range of astrophysical inference problems. The accuracy and economy of the MULTINEST algorithm are demonstrated by application to two toy problems and to a cosmological inference problem focusing on the extension of the vanilla Λ cold dark matter model to include spatial curvature and a varying equation of state for dark energy. The MULTINEST software, which is fully parallelized using MPI and includes an interface to COSMOMC, is available at http://www.mrao.cam.ac.uk/software/multinest/. It will also be released as part of the SUPERBAYES package, for the analysis of supersymmetric theories of particle physics, at http://www.superbayes.org.

Comment on ‘Are physicists afraid of mathematics?’

NASA Astrophysics Data System (ADS)

Higginson, Andrew D.; Fawcett, Tim W.

2016-11-01

In 2012, we showed that the citation count for articles in ecology and evolutionary biology declines with increasing density of equations. Kollmer et al (2015 New J. Phys. 17 013036) claim this effect is an artefact of the manner in which we plotted the data. They also present citation data from Physical Review Letters and argue, based on graphs, that citation counts are unrelated to equation density. Here we show that both claims are misguided. We identified the effects in biology not by visual means, but using the most appropriate statistical analysis. Since Kollmer et al did not carry out any statistical analysis, they cannot draw reliable inferences about the citation patterns in physics. We show that when statistically analysed their data actually do provide evidence that in physics, as in biology, citation counts are lower for articles with a high density of equations. This indicates that a negative relationship between equation density and citations may extend across the breadth of the sciences, even those in which researchers are well accustomed to mathematical descriptions of natural phenomena. We restate our assessment that this is a genuine problem and discuss what we think should be done about it.

DnaSAM: Software to perform neutrality testing for large datasets with complex null models.

PubMed

Eckert, Andrew J; Liechty, John D; Tearse, Brandon R; Pande, Barnaly; Neale, David B

2010-05-01

Patterns of DNA sequence polymorphisms can be used to understand the processes of demography and adaptation within natural populations. High-throughput generation of DNA sequence data has historically been the bottleneck with respect to data processing and experimental inference. Advances in marker technologies have largely solved this problem. Currently, the limiting step is computational, with most molecular population genetic software allowing a gene-by-gene analysis through a graphical user interface. An easy-to-use analysis program that allows both high-throughput processing of multiple sequence alignments along with the flexibility to simulate data under complex demographic scenarios is currently lacking. We introduce a new program, named DnaSAM, which allows high-throughput estimation of DNA sequence diversity and neutrality statistics from experimental data along with the ability to test those statistics via Monte Carlo coalescent simulations. These simulations are conducted using the ms program, which is able to incorporate several genetic parameters (e.g. recombination) and demographic scenarios (e.g. population bottlenecks). The output is a set of diversity and neutrality statistics with associated probability values under a user-specified null model that are stored in easy to manipulate text file. © 2009 Blackwell Publishing Ltd.

Networking—a statistical physics perspective

NASA Astrophysics Data System (ADS)

Yeung, Chi Ho; Saad, David

2013-03-01

Networking encompasses a variety of tasks related to the communication of information on networks; it has a substantial economic and societal impact on a broad range of areas including transportation systems, wired and wireless communications and a range of Internet applications. As transportation and communication networks become increasingly more complex, the ever increasing demand for congestion control, higher traffic capacity, quality of service, robustness and reduced energy consumption requires new tools and methods to meet these conflicting requirements. The new methodology should serve for gaining better understanding of the properties of networking systems at the macroscopic level, as well as for the development of new principled optimization and management algorithms at the microscopic level. Methods of statistical physics seem best placed to provide new approaches as they have been developed specifically to deal with nonlinear large-scale systems. This review aims at presenting an overview of tools and methods that have been developed within the statistical physics community and that can be readily applied to address the emerging problems in networking. These include diffusion processes, methods from disordered systems and polymer physics, probabilistic inference, which have direct relevance to network routing, file and frequency distribution, the exploration of network structures and vulnerability, and various other practical networking applications.

Statistical modelling of networked human-automation performance using working memory capacity.

PubMed

Ahmed, Nisar; de Visser, Ewart; Shaw, Tyler; Mohamed-Ameen, Amira; Campbell, Mark; Parasuraman, Raja

2014-01-01

This study examines the challenging problem of modelling the interaction between individual attentional limitations and decision-making performance in networked human-automation system tasks. Analysis of real experimental data from a task involving networked supervision of multiple unmanned aerial vehicles by human participants shows that both task load and network message quality affect performance, but that these effects are modulated by individual differences in working memory (WM) capacity. These insights were used to assess three statistical approaches for modelling and making predictions with real experimental networked supervisory performance data: classical linear regression, non-parametric Gaussian processes and probabilistic Bayesian networks. It is shown that each of these approaches can help designers of networked human-automated systems cope with various uncertainties in order to accommodate future users by linking expected operating conditions and performance from real experimental data to observable cognitive traits like WM capacity. Practitioner Summary: Working memory (WM) capacity helps account for inter-individual variability in operator performance in networked unmanned aerial vehicle supervisory tasks. This is useful for reliable performance prediction near experimental conditions via linear models; robust statistical prediction beyond experimental conditions via Gaussian process models and probabilistic inference about unknown task conditions/WM capacities via Bayesian network models.

Inferring Characteristics of Sensorimotor Behavior by Quantifying Dynamics of Animal Locomotion

NASA Astrophysics Data System (ADS)

Leung, KaWai

Locomotion is one of the most well-studied topics in animal behavioral studies. Many fundamental and clinical research make use of the locomotion of an animal model to explore various aspects in sensorimotor behavior. In the past, most of these studies focused on population average of a specific trait due to limitation of data collection and processing power. With recent advance in computer vision and statistical modeling techniques, it is now possible to track and analyze large amounts of behavioral data. In this thesis, I present two projects that aim to infer the characteristics of sensorimotor behavior by quantifying the dynamics of locomotion of nematode Caenorhabditis elegans and fruit fly Drosophila melanogaster, shedding light on statistical dependence between sensing and behavior. In the first project, I investigate the possibility of inferring noxious sensory information from the behavior of Caenorhabditis elegans. I develop a statistical model to infer the heat stimulus level perceived by individual animals from their stereotyped escape responses after stimulation by an IR laser. The model allows quantification of analgesic-like effects of chemical agents or genetic mutations in the worm. At the same time, the method is able to differentiate perturbations of locomotion behavior that are beyond affecting the sensory system. With this model I propose experimental designs that allows statistically significant identification of analgesic-like effects. In the second project, I investigate the relationship of energy budget and stability of locomotion in determining the walking speed distribution of Drosophila melanogaster during aging. The locomotion stability at different age groups is estimated from video recordings using Floquet theory. I calculate the power consumption of different locomotion speed using a biomechanics model. In conclusion, the power consumption, not stability, predicts the locomotion speed distribution at different ages.

Towards a Phylogenetic Approach to the Composition of Species Complexes in the North and Central American Triatoma, Vectors of Chagas Disease

PubMed Central

de la Rúa, Nicholas M.; Bustamante, Dulce M.; Menes, Marianela; Stevens, Lori; Monroy, Carlota; Kilpatrick, William; Rizzo, Donna; Klotz, Stephen A.; Schmidt, Justin; Axen, Heather J.; Dorn, Patricia L.

2014-01-01

Phylogenetic relationships of insect vectors of parasitic diseases are important for understanding the evolution of epidemiologically relevant traits, and may be useful in vector control. The subfamily Triatominae (Hemiptera:Reduviidae) includes ~140 extant species arranged in five tribes comprised of 15 genera. The genus Triatoma is the most species-rich and contains important vectors of Trypanosoma cruzi, the causative agent of Chagas disease. Triatoma species were grouped into complexes originally by morphology and more recently with the addition of information from molecular phylogenetics (the four-complex hypothesis); however, without a strict adherence to monophyly. To date, the validity of proposed species complexes has not been tested by statistical tests of topology. The goal of this study was to clarify the systematics of 19 Triatoma species from North and Central America. We inferred their evolutionary relatedness using two independent data sets: the complete nuclear Internal Transcribed Spacer-2 ribosomal DNA (ITS-2 rDNA) and head morphometrics. In addition, we used the Shimodaira-Hasegawa statistical test of topology to assess the fit of the data to a set of competing systematic hypotheses (topologies). An unconstrained topology inferred from the ITS-2 data was compared to topologies constrained based on the four-complex hypothesis or one inferred from our morphometry results. The unconstrained topology represents a statistically significant better fit of the molecular data than either the four-complex or the morphometric topology. We propose an update to the composition of species complexes in the North and Central American Triatoma, based on a phylogeny inferred from ITS-2 as a first step towards updating the phylogeny of the complexes based on monophyly and statistical tests of topologies. PMID:24681261

Emerging Concepts of Data Integration in Pathogen Phylodynamics.

PubMed

Baele, Guy; Suchard, Marc A; Rambaut, Andrew; Lemey, Philippe

2017-01-01

Phylodynamics has become an increasingly popular statistical framework to extract evolutionary and epidemiological information from pathogen genomes. By harnessing such information, epidemiologists aim to shed light on the spatio-temporal patterns of spread and to test hypotheses about the underlying interaction of evolutionary and ecological dynamics in pathogen populations. Although the field has witnessed a rich development of statistical inference tools with increasing levels of sophistication, these tools initially focused on sequences as their sole primary data source. Integrating various sources of information, however, promises to deliver more precise insights in infectious diseases and to increase opportunities for statistical hypothesis testing. Here, we review how the emerging concept of data integration is stimulating new advances in Bayesian evolutionary inference methodology which formalize a marriage of statistical thinking and evolutionary biology. These approaches include connecting sequence to trait evolution, such as for host, phenotypic and geographic sampling information, but also the incorporation of covariates of evolutionary and epidemic processes in the reconstruction procedures. We highlight how a full Bayesian approach to covariate modeling and testing can generate further insights into sequence evolution, trait evolution, and population dynamics in pathogen populations. Specific examples demonstrate how such approaches can be used to test the impact of host on rabies and HIV evolutionary rates, to identify the drivers of influenza dispersal as well as the determinants of rabies cross-species transmissions, and to quantify the evolutionary dynamics of influenza antigenicity. Finally, we briefly discuss how data integration is now also permeating through the inference of transmission dynamics, leading to novel insights into tree-generative processes and detailed reconstructions of transmission trees. [Bayesian inference; birth–death models; coalescent models; continuous trait evolution; covariates; data integration; discrete trait evolution; pathogen phylodynamics.

Emerging Concepts of Data Integration in Pathogen Phylodynamics

PubMed Central

Baele, Guy; Suchard, Marc A.; Rambaut, Andrew; Lemey, Philippe

2017-01-01

Phylodynamics has become an increasingly popular statistical framework to extract evolutionary and epidemiological information from pathogen genomes. By harnessing such information, epidemiologists aim to shed light on the spatio-temporal patterns of spread and to test hypotheses about the underlying interaction of evolutionary and ecological dynamics in pathogen populations. Although the field has witnessed a rich development of statistical inference tools with increasing levels of sophistication, these tools initially focused on sequences as their sole primary data source. Integrating various sources of information, however, promises to deliver more precise insights in infectious diseases and to increase opportunities for statistical hypothesis testing. Here, we review how the emerging concept of data integration is stimulating new advances in Bayesian evolutionary inference methodology which formalize a marriage of statistical thinking and evolutionary biology. These approaches include connecting sequence to trait evolution, such as for host, phenotypic and geographic sampling information, but also the incorporation of covariates of evolutionary and epidemic processes in the reconstruction procedures. We highlight how a full Bayesian approach to covariate modeling and testing can generate further insights into sequence evolution, trait evolution, and population dynamics in pathogen populations. Specific examples demonstrate how such approaches can be used to test the impact of host on rabies and HIV evolutionary rates, to identify the drivers of influenza dispersal as well as the determinants of rabies cross-species transmissions, and to quantify the evolutionary dynamics of influenza antigenicity. Finally, we briefly discuss how data integration is now also permeating through the inference of transmission dynamics, leading to novel insights into tree-generative processes and detailed reconstructions of transmission trees. [Bayesian inference; birth–death models; coalescent models; continuous trait evolution; covariates; data integration; discrete trait evolution; pathogen phylodynamics. PMID:28173504

Evaluation of Subjective Measurement Systems with Focus on Workmanship Scratches and Characterization

DOE Office of Scientific and Technical Information (OSTI.GOV)

Fitzgerald, Jesse

2011-02-24

The presence of workmanship defects at the Kansas City Plant (KCP) is not a new problem nor is it an easy one to remedy. The lack of well defined parameters, subjective evaluations, and operator dependency makes this problem difficult to analyze. At the time of project assignment, workmanship defects comprised approximately 50% of all non-conformance reports for internally produced products. Not all of these non-conformances result in product rejections, thus inferring that inconsistency in evaluations were present. The purpose of this study was to identify a method for evaluating an operator’s ability to properly characterize subjective defects. Since the scopemore » of the project was limited to no funding, scratch depth was selected as the only criteria to evaluate. It was determined that the introduction of a reference standard coupled with a predefined gate-sorting technique approved by the customer can statistically improve an operators ability to perform subjective evaluations.« less

DOE Office of Scientific and Technical Information (OSTI.GOV)

Romano, J.D.; Woan, G.

Data from the Laser Interferometer Space Antenna (LISA) is expected to be dominated by frequency noise from its lasers. However, the noise from any one laser appears more than once in the data and there are combinations of the data that are insensitive to this noise. These combinations, called time delay interferometry (TDI) variables, have received careful study and point the way to how LISA data analysis may be performed. Here we approach the problem from the direction of statistical inference, and show that these variables are a direct consequence of a principal component analysis of the problem. We presentmore » a formal analysis for a simple LISA model and show that there are eigenvectors of the noise covariance matrix that do not depend on laser frequency noise. Importantly, these orthogonal basis vectors correspond to linear combinations of TDI variables. As a result we show that the likelihood function for source parameters using LISA data can be based on TDI combinations of the data without loss of information.« less

Statistical genetics concepts and approaches in schizophrenia and related neuropsychiatric research.

PubMed

Schork, Nicholas J; Greenwood, Tiffany A; Braff, David L

2007-01-01

Statistical genetics is a research field that focuses on mathematical models and statistical inference methodologies that relate genetic variations (ie, naturally occurring human DNA sequence variations or "polymorphisms") to particular traits or diseases (phenotypes) usually from data collected on large samples of families or individuals. The ultimate goal of such analysis is the identification of genes and genetic variations that influence disease susceptibility. Although of extreme interest and importance, the fact that many genes and environmental factors contribute to neuropsychiatric diseases of public health importance (eg, schizophrenia, bipolar disorder, and depression) complicates relevant studies and suggests that very sophisticated mathematical and statistical modeling may be required. In addition, large-scale contemporary human DNA sequencing and related projects, such as the Human Genome Project and the International HapMap Project, as well as the development of high-throughput DNA sequencing and genotyping technologies have provided statistical geneticists with a great deal of very relevant and appropriate information and resources. Unfortunately, the use of these resources and their interpretation are not straightforward when applied to complex, multifactorial diseases such as schizophrenia. In this brief and largely nonmathematical review of the field of statistical genetics, we describe many of the main concepts, definitions, and issues that motivate contemporary research. We also provide a discussion of the most pressing contemporary problems that demand further research if progress is to be made in the identification of genes and genetic variations that predispose to complex neuropsychiatric diseases.

Beyond P Values and Hypothesis Testing: Using the Minimum Bayes Factor to Teach Statistical Inference in Undergraduate Introductory Statistics Courses

ERIC Educational Resources Information Center

Page, Robert; Satake, Eiki

2017-01-01

While interest in Bayesian statistics has been growing in statistics education, the treatment of the topic is still inadequate in both textbooks and the classroom. Because so many fields of study lead to careers that involve a decision-making process requiring an understanding of Bayesian methods, it is becoming increasingly clear that Bayesian…

Practical limits for reverse engineering of dynamical systems: a statistical analysis of sensitivity and parameter inferability in systems biology models.

PubMed

Erguler, Kamil; Stumpf, Michael P H

2011-05-01

The size and complexity of cellular systems make building predictive models an extremely difficult task. In principle dynamical time-course data can be used to elucidate the structure of the underlying molecular mechanisms, but a central and recurring problem is that many and very different models can be fitted to experimental data, especially when the latter are limited and subject to noise. Even given a model, estimating its parameters remains challenging in real-world systems. Here we present a comprehensive analysis of 180 systems biology models, which allows us to classify the parameters with respect to their contribution to the overall dynamical behaviour of the different systems. Our results reveal candidate elements of control in biochemical pathways that differentially contribute to dynamics. We introduce sensitivity profiles that concisely characterize parameter sensitivity and demonstrate how this can be connected to variability in data. Systematically linking data and model sloppiness allows us to extract features of dynamical systems that determine how well parameters can be estimated from time-course measurements, and associates the extent of data required for parameter inference with the model structure, and also with the global dynamical state of the system. The comprehensive analysis of so many systems biology models reaffirms the inability to estimate precisely most model or kinetic parameters as a generic feature of dynamical systems, and provides safe guidelines for performing better inferences and model predictions in the context of reverse engineering of mathematical models for biological systems.

Human Inferences about Sequences: A Minimal Transition Probability Model

PubMed Central

2016-01-01

The brain constantly infers the causes of the inputs it receives and uses these inferences to generate statistical expectations about future observations. Experimental evidence for these expectations and their violations include explicit reports, sequential effects on reaction times, and mismatch or surprise signals recorded in electrophysiology and functional MRI. Here, we explore the hypothesis that the brain acts as a near-optimal inference device that constantly attempts to infer the time-varying matrix of transition probabilities between the stimuli it receives, even when those stimuli are in fact fully unpredictable. This parsimonious Bayesian model, with a single free parameter, accounts for a broad range of findings on surprise signals, sequential effects and the perception of randomness. Notably, it explains the pervasive asymmetry between repetitions and alternations encountered in those studies. Our analysis suggests that a neural machinery for inferring transition probabilities lies at the core of human sequence knowledge. PMID:28030543

Weighted community detection and data clustering using message passing

NASA Astrophysics Data System (ADS)

Shi, Cheng; Liu, Yanchen; Zhang, Pan

2018-03-01

Grouping objects into clusters based on the similarities or weights between them is one of the most important problems in science and engineering. In this work, by extending message-passing algorithms and spectral algorithms proposed for an unweighted community detection problem, we develop a non-parametric method based on statistical physics, by mapping the problem to the Potts model at the critical temperature of spin-glass transition and applying belief propagation to solve the marginals corresponding to the Boltzmann distribution. Our algorithm is robust to over-fitting and gives a principled way to determine whether there are significant clusters in the data and how many clusters there are. We apply our method to different clustering tasks. In the community detection problem in weighted and directed networks, we show that our algorithm significantly outperforms existing algorithms. In the clustering problem, where the data were generated by mixture models in the sparse regime, we show that our method works all the way down to the theoretical limit of detectability and gives accuracy very close to that of the optimal Bayesian inference. In the semi-supervised clustering problem, our method only needs several labels to work perfectly in classic datasets. Finally, we further develop Thouless-Anderson-Palmer equations which heavily reduce the computation complexity in dense networks but give almost the same performance as belief propagation.