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.

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…

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…

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.

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...

Statistics for nuclear engineers and scientists. Part 1. Basic statistical inference

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

Beggs, W.J.

1981-02-01

This report is intended for the use of engineers and scientists working in the nuclear industry, especially at the Bettis Atomic Power Laboratory. It serves as the basis for several Bettis in-house statistics courses. The objectives of the report are to introduce the reader to the language and concepts of statistics and to provide a basic set of techniques to apply to problems of the collection and analysis of data. Part 1 covers subjects of basic inference. The subjects include: descriptive statistics; probability; simple inference for normally distributed populations, and for non-normal populations as well; comparison of two populations; themore » analysis of variance; quality control procedures; and linear regression analysis.« less

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…

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…

Faster Mass Spectrometry-based Protein Inference: Junction Trees are More Efficient than Sampling and Marginalization by Enumeration

PubMed Central

Serang, Oliver; Noble, William Stafford

2012-01-01

The problem of identifying the proteins in a complex mixture using tandem mass spectrometry can be framed as an inference problem on a graph that connects peptides to proteins. Several existing protein identification methods make use of statistical inference methods for graphical models, including expectation maximization, Markov chain Monte Carlo, and full marginalization coupled with approximation heuristics. We show that, for this problem, the majority of the cost of inference usually comes from a few highly connected subgraphs. Furthermore, we evaluate three different statistical inference methods using a common graphical model, and we demonstrate that junction tree inference substantially improves rates of convergence compared to existing methods. The python code used for this paper is available at http://noble.gs.washington.edu/proj/fido. PMID:22331862

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.

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…

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.

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.

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.

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.

A Coalitional Game for Distributed Inference in Sensor Networks With Dependent Observations

NASA Astrophysics Data System (ADS)

He, Hao; Varshney, Pramod K.

2016-04-01

We consider the problem of collaborative inference in a sensor network with heterogeneous and statistically dependent sensor observations. Each sensor aims to maximize its inference performance by forming a coalition with other sensors and sharing information within the coalition. It is proved that the inference performance is a nondecreasing function of the coalition size. However, in an energy constrained network, the energy consumption of inter-sensor communication also increases with increasing coalition size, which discourages the formation of the grand coalition (the set of all sensors). In this paper, the formation of non-overlapping coalitions with statistically dependent sensors is investigated under a specific communication constraint. We apply a game theoretical approach to fully explore and utilize the information contained in the spatial dependence among sensors to maximize individual sensor performance. Before formulating the distributed inference problem as a coalition formation game, we first quantify the gain and loss in forming a coalition by introducing the concepts of diversity gain and redundancy loss for both estimation and detection problems. These definitions, enabled by the statistical theory of copulas, allow us to characterize the influence of statistical dependence among sensor observations on inference performance. An iterative algorithm based on merge-and-split operations is proposed for the solution and the stability of the proposed algorithm is analyzed. Numerical results are provided to demonstrate the superiority of our proposed game theoretical approach.

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,…

Inference and the Introductory Statistics Course

ERIC Educational Resources Information Center

Pfannkuch, Maxine; Regan, Matt; Wild, Chris; Budgett, Stephanie; Forbes, Sharleen; Harraway, John; Parsonage, Ross

2011-01-01

This article sets out some of the rationale and arguments for making major changes to the teaching and learning of statistical inference in introductory courses at our universities by changing from a norm-based, mathematical approach to more conceptually accessible computer-based approaches. The core problem of the inferential argument with its…

"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.

Multi-Agent Inference in Social Networks: A Finite Population Learning Approach.

PubMed

Fan, Jianqing; Tong, Xin; Zeng, Yao

When people in a society want to make inference about some parameter, each person may want to use data collected by other people. Information (data) exchange in social networks is usually costly, so to make reliable statistical decisions, people need to trade off the benefits and costs of information acquisition. Conflicts of interests and coordination problems will arise in the process. Classical statistics does not consider people's incentives and interactions in the data collection process. To address this imperfection, this work explores multi-agent Bayesian inference problems with a game theoretic social network model. Motivated by our interest in aggregate inference at the societal level, we propose a new concept, finite population learning , to address whether with high probability, a large fraction of people in a given finite population network can make "good" inference. Serving as a foundation, this concept enables us to study the long run trend of aggregate inference quality as population grows.

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.

Statistical learning and selective inference.

PubMed

Taylor, Jonathan; Tibshirani, Robert J

2015-06-23

We describe the problem of "selective inference." This addresses the following challenge: Having mined a set of data to find potential associations, how do we properly assess the strength of these associations? The fact that we have "cherry-picked"--searched for the strongest associations--means that we must set a higher bar for declaring significant the associations that we see. This challenge becomes more important in the era of big data and complex statistical modeling. The cherry tree (dataset) can be very large and the tools for cherry picking (statistical learning methods) are now very sophisticated. We describe some recent new developments in selective inference and illustrate their use in forward stepwise regression, the lasso, and principal components analysis.

Variations on Bayesian Prediction and Inference

DTIC Science & Technology

2016-05-09

inference 2.2.1 Background There are a number of statistical inference problems that are not generally formulated via a full probability model...problem of inference about an unknown parameter, the Bayesian approach requires a full probability 1. REPORT DATE (DD-MM-YYYY) 4. TITLE AND...the problem of inference about an unknown parameter, the Bayesian approach requires a full probability model/likelihood which can be an obstacle

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...

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…

Multi-Agent Inference in Social Networks: A Finite Population Learning Approach

PubMed Central

Tong, Xin; Zeng, Yao

2016-01-01

When people in a society want to make inference about some parameter, each person may want to use data collected by other people. Information (data) exchange in social networks is usually costly, so to make reliable statistical decisions, people need to trade off the benefits and costs of information acquisition. Conflicts of interests and coordination problems will arise in the process. Classical statistics does not consider people’s incentives and interactions in the data collection process. To address this imperfection, this work explores multi-agent Bayesian inference problems with a game theoretic social network model. Motivated by our interest in aggregate inference at the societal level, we propose a new concept, finite population learning, to address whether with high probability, a large fraction of people in a given finite population network can make “good” inference. Serving as a foundation, this concept enables us to study the long run trend of aggregate inference quality as population grows. PMID:27076691

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.

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.

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.

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.

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…

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.

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.

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

Fair Inference on Outcomes

PubMed Central

Nabi, Razieh; Shpitser, Ilya

2017-01-01

In this paper, we consider the problem of fair statistical inference involving outcome variables. Examples include classification and regression problems, and estimating treatment effects in randomized trials or observational data. The issue of fairness arises in such problems where some covariates or treatments are “sensitive,” in the sense of having potential of creating discrimination. In this paper, we argue that the presence of discrimination can be formalized in a sensible way as the presence of an effect of a sensitive covariate on the outcome along certain causal pathways, a view which generalizes (Pearl 2009). A fair outcome model can then be learned by solving a constrained optimization problem. We discuss a number of complications that arise in classical statistical inference due to this view and provide workarounds based on recent work in causal and semi-parametric inference.

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".

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.

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.

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.

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

Protein and gene model inference based on statistical modeling in k-partite graphs.

PubMed

Gerster, Sarah; Qeli, Ermir; Ahrens, Christian H; Bühlmann, Peter

2010-07-06

One of the major goals of proteomics is the comprehensive and accurate description of a proteome. Shotgun proteomics, the method of choice for the analysis of complex protein mixtures, requires that experimentally observed peptides are mapped back to the proteins they were derived from. This process is also known as protein inference. We present Markovian Inference of Proteins and Gene Models (MIPGEM), a statistical model based on clearly stated assumptions to address the problem of protein and gene model inference for shotgun proteomics data. In particular, we are dealing with dependencies among peptides and proteins using a Markovian assumption on k-partite graphs. We are also addressing the problems of shared peptides and ambiguous proteins by scoring the encoding gene models. Empirical results on two control datasets with synthetic mixtures of proteins and on complex protein samples of Saccharomyces cerevisiae, Drosophila melanogaster, and Arabidopsis thaliana suggest that the results with MIPGEM are competitive with existing tools for protein inference.

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.

Computational statistics using the Bayesian Inference Engine

NASA Astrophysics Data System (ADS)

Weinberg, Martin D.

2013-09-01

This paper introduces the Bayesian Inference Engine (BIE), a general parallel, optimized software package for parameter inference and model selection. This package is motivated by the analysis needs of modern astronomical surveys and the need to organize and reuse expensive derived data. The BIE is the first platform for computational statistics designed explicitly to enable Bayesian update and model comparison for astronomical problems. Bayesian update is based on the representation of high-dimensional posterior distributions using metric-ball-tree based kernel density estimation. Among its algorithmic offerings, the BIE emphasizes hybrid tempered Markov chain Monte Carlo schemes that robustly sample multimodal posterior distributions in high-dimensional parameter spaces. Moreover, the BIE implements a full persistence or serialization system that stores the full byte-level image of the running inference and previously characterized posterior distributions for later use. Two new algorithms to compute the marginal likelihood from the posterior distribution, developed for and implemented in the BIE, enable model comparison for complex models and data sets. Finally, the BIE was designed to be a collaborative platform for applying Bayesian methodology to astronomy. It includes an extensible object-oriented and easily extended framework that implements every aspect of the Bayesian inference. By providing a variety of statistical algorithms for all phases of the inference problem, a scientist may explore a variety of approaches with a single model and data implementation. Additional technical details and download details are available from http://www.astro.umass.edu/bie. The BIE is distributed under the GNU General Public License.

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.

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.

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

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.

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.

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.

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

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.

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.

Hierarchical modeling and inference in ecology: The analysis of data from populations, metapopulations and communities

USGS Publications Warehouse

Royle, J. Andrew; Dorazio, Robert M.

2008-01-01

A guide to data collection, modeling and inference strategies for biological survey data using Bayesian and classical statistical methods. This book describes a general and flexible framework for modeling and inference in ecological systems based on hierarchical models, with a strict focus on the use of probability models and parametric inference. Hierarchical models represent a paradigm shift in the application of statistics to ecological inference problems because they combine explicit models of ecological system structure or dynamics with models of how ecological systems are observed. The principles of hierarchical modeling are developed and applied to problems in population, metapopulation, community, and metacommunity systems. The book provides the first synthetic treatment of many recent methodological advances in ecological modeling and unifies disparate methods and procedures. The authors apply principles of hierarchical modeling to ecological problems, including * occurrence or occupancy models for estimating species distribution * abundance models based on many sampling protocols, including distance sampling * capture-recapture models with individual effects * spatial capture-recapture models based on camera trapping and related methods * population and metapopulation dynamic models * models of biodiversity, community structure and dynamics.

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.

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.

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.

Statistics, Computation, and Modeling in Cosmology

NASA Astrophysics Data System (ADS)

Jewell, Jeff; Guiness, Joe; SAMSI 2016 Working Group in Cosmology

2017-01-01

Current and future ground and space based missions are designed to not only detect, but map out with increasing precision, details of the universe in its infancy to the present-day. As a result we are faced with the challenge of analyzing and interpreting observations from a wide variety of instruments to form a coherent view of the universe. Finding solutions to a broad range of challenging inference problems in cosmology is one of the goals of the “Statistics, Computation, and Modeling in Cosmology” workings groups, formed as part of the year long program on ‘Statistical, Mathematical, and Computational Methods for Astronomy’, hosted by the Statistical and Applied Mathematical Sciences Institute (SAMSI), a National Science Foundation funded institute. Two application areas have emerged for focused development in the cosmology working group involving advanced algorithmic implementations of exact Bayesian inference for the Cosmic Microwave Background, and statistical modeling of galaxy formation. The former includes study and development of advanced Markov Chain Monte Carlo algorithms designed to confront challenging inference problems including inference for spatial Gaussian random fields in the presence of sources of galactic emission (an example of a source separation problem). Extending these methods to future redshift survey data probing the nonlinear regime of large scale structure formation is also included in the working group activities. In addition, the working group is also focused on the study of ‘Galacticus’, a galaxy formation model applied to dark matter-only cosmological N-body simulations operating on time-dependent halo merger trees. The working group is interested in calibrating the Galacticus model to match statistics of galaxy survey observations; specifically stellar mass functions, luminosity functions, and color-color diagrams. The group will use subsampling approaches and fractional factorial designs to statistically and computationally efficiently explore the Galacticus parameter space. The group will also use the Galacticus simulations to study the relationship between the topological and physical structure of the halo merger trees and the properties of the resulting galaxies.

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.

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.

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.

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.

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.

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.

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.

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.

Quantum-Like Representation of Non-Bayesian Inference

NASA Astrophysics Data System (ADS)

Asano, M.; Basieva, I.; Khrennikov, A.; Ohya, M.; Tanaka, Y.

2013-01-01

This research is related to the problem of "irrational decision making or inference" that have been discussed in cognitive psychology. There are some experimental studies, and these statistical data cannot be described by classical probability theory. The process of decision making generating these data cannot be reduced to the classical Bayesian inference. For this problem, a number of quantum-like coginitive models of decision making was proposed. Our previous work represented in a natural way the classical Bayesian inference in the frame work of quantum mechanics. By using this representation, in this paper, we try to discuss the non-Bayesian (irrational) inference that is biased by effects like the quantum interference. Further, we describe "psychological factor" disturbing "rationality" as an "environment" correlating with the "main system" of usual Bayesian inference.

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…

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.

Using a Five-Step Procedure for Inferential Statistical Analyses

ERIC Educational Resources Information Center

Kamin, Lawrence F.

2010-01-01

Many statistics texts pose inferential statistical problems in a disjointed way. By using a simple five-step procedure as a template for statistical inference problems, the student can solve problems in an organized fashion. The problem and its solution will thus be a stand-by-itself organic whole and a single unit of thought and effort. The…

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.

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.

The Empirical Nature and Statistical Treatment of Missing Data

ERIC Educational Resources Information Center

Tannenbaum, Christyn E.

2009-01-01

Introduction. Missing data is a common problem in research and can produce severely misleading analyses, including biased estimates of statistical parameters, and erroneous conclusions. In its 1999 report, the APA Task Force on Statistical Inference encouraged authors to report complications such as missing data and discouraged the use of…

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.

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

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.

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 ...

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,…

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…

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…

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…

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…

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…

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

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).

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.

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…

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.

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.

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.

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'.

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

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

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…

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

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…

Stan: A Probabilistic Programming Language for Bayesian Inference and Optimization

ERIC Educational Resources Information Center

Gelman, Andrew; Lee, Daniel; Guo, Jiqiang

2015-01-01

Stan is a free and open-source C++ program that performs Bayesian inference or optimization for arbitrary user-specified models and can be called from the command line, R, Python, Matlab, or Julia and has great promise for fitting large and complex statistical models in many areas of application. We discuss Stan from users' and developers'…

IMNN: Information Maximizing Neural Networks

NASA Astrophysics Data System (ADS)

Charnock, Tom; Lavaux, Guilhem; Wandelt, Benjamin D.

2018-04-01

This software trains artificial neural networks to find non-linear functionals of data that maximize Fisher information: information maximizing neural networks (IMNNs). As compressing large data sets vastly simplifies both frequentist and Bayesian inference, important information may be inadvertently missed. Likelihood-free inference based on automatically derived IMNN summaries produces summaries that are good approximations to sufficient statistics. IMNNs are robustly capable of automatically finding optimal, non-linear summaries of the data even in cases where linear compression fails: inferring the variance of Gaussian signal in the presence of noise, inferring cosmological parameters from mock simulations of the Lyman-α forest in quasar spectra, and inferring frequency-domain parameters from LISA-like detections of gravitational waveforms. In this final case, the IMNN summary outperforms linear data compression by avoiding the introduction of spurious likelihood maxima.

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.

Data Acquisition and Preprocessing in Studies on Humans: What Is Not Taught in Statistics Classes?

PubMed

Zhu, Yeyi; Hernandez, Ladia M; Mueller, Peter; Dong, Yongquan; Forman, Michele R

2013-01-01

The aim of this paper is to address issues in research that may be missing from statistics classes and important for (bio-)statistics students. In the context of a case study, we discuss data acquisition and preprocessing steps that fill the gap between research questions posed by subject matter scientists and statistical methodology for formal inference. Issues include participant recruitment, data collection training and standardization, variable coding, data review and verification, data cleaning and editing, and documentation. Despite the critical importance of these details in research, most of these issues are rarely discussed in an applied statistics program. One reason for the lack of more formal training is the difficulty in addressing the many challenges that can possibly arise in the course of a study in a systematic way. This article can help to bridge this gap between research questions and formal statistical inference by using an illustrative case study for a discussion. We hope that reading and discussing this paper and practicing data preprocessing exercises will sensitize statistics students to these important issues and achieve optimal conduct, quality control, analysis, and interpretation of a study.

An Artificial Intelligence Approach to Analyzing Student Errors in Statistics.

ERIC Educational Resources Information Center

Sebrechts, Marc M.; Schooler, Lael J.

1987-01-01

Describes the development of an artificial intelligence system called GIDE that analyzes student errors in statistics problems by inferring the students' intentions. Learning strategies involved in problem solving are discussed and the inclusion of goal structures is explained. (LRW)

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.

Reaction Time in Grade 5: Data Collection within the Practice of Statistics

ERIC Educational Resources Information Center

Watson, Jane; English, Lyn

2017-01-01

This study reports on a classroom activity for Grade 5 students investigating their reaction times. The investigation was part of a 3-year research project introducing students to informal inference and giving them experience carrying out the practice of statistics. For this activity the focus within the practice of statistics was on introducing…

An Inferentialist Perspective on the Coordination of Actions and Reasons Involved in Making a Statistical Inference

ERIC Educational Resources Information Center

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

2017-01-01

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…

Causal inference in biology networks with integrated belief propagation.

PubMed

Chang, Rui; Karr, Jonathan R; Schadt, Eric E

2015-01-01

Inferring causal relationships among molecular and higher order phenotypes is a critical step in elucidating the complexity of living systems. Here we propose a novel method for inferring causality that is no longer constrained by the conditional dependency arguments that limit the ability of statistical causal inference methods to resolve causal relationships within sets of graphical models that are Markov equivalent. Our method utilizes Bayesian belief propagation to infer the responses of perturbation events on molecular traits given a hypothesized graph structure. A distance measure between the inferred response distribution and the observed data is defined to assess the 'fitness' of the hypothesized causal relationships. To test our algorithm, we infer causal relationships within equivalence classes of gene networks in which the form of the functional interactions that are possible are assumed to be nonlinear, given synthetic microarray and RNA sequencing data. We also apply our method to infer causality in real metabolic network with v-structure and feedback loop. We show that our method can recapitulate the causal structure and recover the feedback loop only from steady-state data which conventional method cannot.

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.

Distinguishing between statistical significance and practical/clinical meaningfulness using statistical inference.

PubMed

Wilkinson, Michael

2014-03-01

Decisions about support for predictions of theories in light of data are made using statistical inference. The dominant approach in sport and exercise science is the Neyman-Pearson (N-P) significance-testing approach. When applied correctly it provides a reliable procedure for making dichotomous decisions for accepting or rejecting zero-effect null hypotheses with known and controlled long-run error rates. Type I and type II error rates must be specified in advance and the latter controlled by conducting an a priori sample size calculation. The N-P approach does not provide the probability of hypotheses or indicate the strength of support for hypotheses in light of data, yet many scientists believe it does. Outcomes of analyses allow conclusions only about the existence of non-zero effects, and provide no information about the likely size of true effects or their practical/clinical value. Bayesian inference can show how much support data provide for different hypotheses, and how personal convictions should be altered in light of data, but the approach is complicated by formulating probability distributions about prior subjective estimates of population effects. A pragmatic solution is magnitude-based inference, which allows scientists to estimate the true magnitude of population effects and how likely they are to exceed an effect magnitude of practical/clinical importance, thereby integrating elements of subjective Bayesian-style thinking. While this approach is gaining acceptance, progress might be hastened if scientists appreciate the shortcomings of traditional N-P null hypothesis significance testing.

Bayesian multimodel inference for dose-response studies

USGS Publications Warehouse

Link, W.A.; Albers, P.H.

2007-01-01

Statistical inference in dose?response studies is model-based: The analyst posits a mathematical model of the relation between exposure and response, estimates parameters of the model, and reports conclusions conditional on the model. Such analyses rarely include any accounting for the uncertainties associated with model selection. The Bayesian inferential system provides a convenient framework for model selection and multimodel inference. In this paper we briefly describe the Bayesian paradigm and Bayesian multimodel inference. We then present a family of models for multinomial dose?response data and apply Bayesian multimodel inferential methods to the analysis of data on the reproductive success of American kestrels (Falco sparveriuss) exposed to various sublethal dietary concentrations of methylmercury.

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.

ddClone: joint statistical inference of clonal populations from single cell and bulk tumour sequencing data.

PubMed

Salehi, Sohrab; Steif, Adi; Roth, Andrew; Aparicio, Samuel; Bouchard-Côté, Alexandre; Shah, Sohrab P

2017-03-01

Next-generation sequencing (NGS) of bulk tumour tissue can identify constituent cell populations in cancers and measure their abundance. This requires computational deconvolution of allelic counts from somatic mutations, which may be incapable of fully resolving the underlying population structure. Single cell sequencing (SCS) is a more direct method, although its replacement of NGS is impeded by technical noise and sampling limitations. We propose ddClone, which analytically integrates NGS and SCS data, leveraging their complementary attributes through joint statistical inference. We show on real and simulated datasets that ddClone produces more accurate results than can be achieved by either method alone.

The Heuristic Value of p in Inductive Statistical Inference

PubMed Central

Krueger, Joachim I.; Heck, Patrick R.

2017-01-01

Many statistical methods yield the probability of the observed data – or data more extreme – under the assumption that a particular hypothesis is true. This probability is commonly known as ‘the’ p-value. (Null Hypothesis) Significance Testing ([NH]ST) is the most prominent of these methods. The p-value has been subjected to much speculation, analysis, and criticism. We explore how well the p-value predicts what researchers presumably seek: the probability of the hypothesis being true given the evidence, and the probability of reproducing significant results. We also explore the effect of sample size on inferential accuracy, bias, and error. In a series of simulation experiments, we find that the p-value performs quite well as a heuristic cue in inductive inference, although there are identifiable limits to its usefulness. We conclude that despite its general usefulness, the p-value cannot bear the full burden of inductive inference; it is but one of several heuristic cues available to the data analyst. Depending on the inferential challenge at hand, investigators may supplement their reports with effect size estimates, Bayes factors, or other suitable statistics, to communicate what they think the data say. PMID:28649206

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.

The Heuristic Value of p in Inductive Statistical Inference.

PubMed

Krueger, Joachim I; Heck, Patrick R

2017-01-01

Many statistical methods yield the probability of the observed data - or data more extreme - under the assumption that a particular hypothesis is true. This probability is commonly known as 'the' p -value. (Null Hypothesis) Significance Testing ([NH]ST) is the most prominent of these methods. The p -value has been subjected to much speculation, analysis, and criticism. We explore how well the p -value predicts what researchers presumably seek: the probability of the hypothesis being true given the evidence, and the probability of reproducing significant results. We also explore the effect of sample size on inferential accuracy, bias, and error. In a series of simulation experiments, we find that the p -value performs quite well as a heuristic cue in inductive inference, although there are identifiable limits to its usefulness. We conclude that despite its general usefulness, the p -value cannot bear the full burden of inductive inference; it is but one of several heuristic cues available to the data analyst. Depending on the inferential challenge at hand, investigators may supplement their reports with effect size estimates, Bayes factors, or other suitable statistics, to communicate what they think the data say.

Statistical inference of seabed sound-speed structure in the Gulf of Oman Basin.

PubMed

Sagers, Jason D; Knobles, David P

2014-06-01

Addressed is the statistical inference of the sound-speed depth profile of a thick soft seabed from broadband sound propagation data recorded in the Gulf of Oman Basin in 1977. The acoustic data are in the form of time series signals recorded on a sparse vertical line array and generated by explosive sources deployed along a 280 km track. The acoustic data offer a unique opportunity to study a deep-water bottom-limited thickly sedimented environment because of the large number of time series measurements, very low seabed attenuation, and auxiliary measurements. A maximum entropy method is employed to obtain a conditional posterior probability distribution (PPD) for the sound-speed ratio and the near-surface sound-speed gradient. The multiple data samples allow for a determination of the average error constraint value required to uniquely specify the PPD for each data sample. Two complicating features of the statistical inference study are addressed: (1) the need to develop an error function that can both utilize the measured multipath arrival structure and mitigate the effects of data errors and (2) the effect of small bathymetric slopes on the structure of the bottom interacting arrivals.

Experimental and environmental factors affect spurious detection of ecological thresholds

USGS Publications Warehouse

Daily, Jonathan P.; Hitt, Nathaniel P.; Smith, David; Snyder, Craig D.

2012-01-01

Threshold detection methods are increasingly popular for assessing nonlinear responses to environmental change, but their statistical performance remains poorly understood. We simulated linear change in stream benthic macroinvertebrate communities and evaluated the performance of commonly used threshold detection methods based on model fitting (piecewise quantile regression [PQR]), data partitioning (nonparametric change point analysis [NCPA]), and a hybrid approach (significant zero crossings [SiZer]). We demonstrated that false detection of ecological thresholds (type I errors) and inferences on threshold locations are influenced by sample size, rate of linear change, and frequency of observations across the environmental gradient (i.e., sample-environment distribution, SED). However, the relative importance of these factors varied among statistical methods and between inference types. False detection rates were influenced primarily by user-selected parameters for PQR (τ) and SiZer (bandwidth) and secondarily by sample size (for PQR) and SED (for SiZer). In contrast, the location of reported thresholds was influenced primarily by SED. Bootstrapped confidence intervals for NCPA threshold locations revealed strong correspondence to SED. We conclude that the choice of statistical methods for threshold detection should be matched to experimental and environmental constraints to minimize false detection rates and avoid spurious inferences regarding threshold location.

Advances in Bayesian Modeling in Educational Research

ERIC Educational Resources Information Center

Levy, Roy

2016-01-01

In this article, I provide a conceptually oriented overview of Bayesian approaches to statistical inference and contrast them with frequentist approaches that currently dominate conventional practice in educational research. The features and advantages of Bayesian approaches are illustrated with examples spanning several statistical modeling…

Statistical Inference for Quality-Adjusted Survival Time

DTIC Science & Technology

2003-08-01

survival functions of QAL. If an influence function for a test statistic exists for complete data case, denoted as ’i, then a test statistic for...the survival function for the censoring variable. Zhao and Tsiatis (2001) proposed a test statistic where O is the influence function of the general...to 1 everywhere until a subject’s death. We have considered other forms of test statistics. One option is to use an influence function 0i that is

Intimate Partner Violence in the United States - 2010

MedlinePlus

... administration............................................................................. 9 Statistical testing and inference ................................................................... 9 Additional methodological information ..........................................................10 2. Prevalence and Frequency of Individual ...

Estimating the probability of rare events: addressing zero failure data.

PubMed

Quigley, John; Revie, Matthew

2011-07-01

Traditional statistical procedures for estimating the probability of an event result in an estimate of zero when no events are realized. Alternative inferential procedures have been proposed for the situation where zero events have been realized but often these are ad hoc, relying on selecting methods dependent on the data that have been realized. Such data-dependent inference decisions violate fundamental statistical principles, resulting in estimation procedures whose benefits are difficult to assess. In this article, we propose estimating the probability of an event occurring through minimax inference on the probability that future samples of equal size realize no more events than that in the data on which the inference is based. Although motivated by inference on rare events, the method is not restricted to zero event data and closely approximates the maximum likelihood estimate (MLE) for nonzero data. The use of the minimax procedure provides a risk adverse inferential procedure where there are no events realized. A comparison is made with the MLE and regions of the underlying probability are identified where this approach is superior. Moreover, a comparison is made with three standard approaches to supporting inference where no event data are realized, which we argue are unduly pessimistic. We show that for situations of zero events the estimator can be simply approximated with 1/2.5n, where n is the number of trials. © 2011 Society for Risk Analysis.

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.

Statistical primer: how to deal with missing data in scientific research?

PubMed

Papageorgiou, Grigorios; Grant, Stuart W; Takkenberg, Johanna J M; Mokhles, Mostafa M

2018-05-10

Missing data are a common challenge encountered in research which can compromise the results of statistical inference when not handled appropriately. This paper aims to introduce basic concepts of missing data to a non-statistical audience, list and compare some of the most popular approaches for handling missing data in practice and provide guidelines and recommendations for dealing with and reporting missing data in scientific research. Complete case analysis and single imputation are simple approaches for handling missing data and are popular in practice, however, in most cases they are not guaranteed to provide valid inferences. Multiple imputation is a robust and general alternative which is appropriate for data missing at random, surpassing the disadvantages of the simpler approaches, but should always be conducted with care. The aforementioned approaches are illustrated and compared in an example application using Cox regression.

Is the P-Value Really Dead? Assessing Inference Learning Outcomes for Social Science Students in an Introductory Statistics Course

ERIC Educational Resources Information Center

Lane-Getaz, Sharon

2017-01-01

In reaction to misuses and misinterpretations of p-values and confidence intervals, a social science journal editor banned p-values from its pages. This study aimed to show that education could address misuse and abuse. This study examines inference-related learning outcomes for social science students in an introductory course supplemented with…

Back to BaySICS: a user-friendly program for Bayesian Statistical Inference from Coalescent Simulations.

PubMed

Sandoval-Castellanos, Edson; Palkopoulou, Eleftheria; Dalén, Love

2014-01-01

Inference of population demographic history has vastly improved in recent years due to a number of technological and theoretical advances including the use of ancient DNA. Approximate Bayesian computation (ABC) stands among the most promising methods due to its simple theoretical fundament and exceptional flexibility. However, limited availability of user-friendly programs that perform ABC analysis renders it difficult to implement, and hence programming skills are frequently required. In addition, there is limited availability of programs able to deal with heterochronous data. Here we present the software BaySICS: Bayesian Statistical Inference of Coalescent Simulations. BaySICS provides an integrated and user-friendly platform that performs ABC analyses by means of coalescent simulations from DNA sequence data. It estimates historical demographic population parameters and performs hypothesis testing by means of Bayes factors obtained from model comparisons. Although providing specific features that improve inference from datasets with heterochronous data, BaySICS also has several capabilities making it a suitable tool for analysing contemporary genetic datasets. Those capabilities include joint analysis of independent tables, a graphical interface and the implementation of Markov-chain Monte Carlo without likelihoods.

STATISTICAL METHODOLOGY FOR THE SIMULTANEOUS ANALYSIS OF MULTIPLE TYPES OF OUTCOMES IN NONLINEAR THRESHOLD MODELS.

EPA Science Inventory

Multiple outcomes are often measured on each experimental unit in toxicology experiments. These multiple observations typically imply the existence of correlation between endpoints, and a statistical analysis that incorporates it may result in improved inference. When both disc...

The Love of Large Numbers: A Popularity Bias in Consumer Choice.

PubMed

Powell, Derek; Yu, Jingqi; DeWolf, Melissa; Holyoak, Keith J

2017-10-01

Social learning-the ability to learn from observing the decisions of other people and the outcomes of those decisions-is fundamental to human evolutionary and cultural success. The Internet now provides social evidence on an unprecedented scale. However, properly utilizing this evidence requires a capacity for statistical inference. We examined how people's interpretation of online review scores is influenced by the numbers of reviews-a potential indicator both of an item's popularity and of the precision of the average review score. Our task was designed to pit statistical information against social information. We modeled the behavior of an "intuitive statistician" using empirical prior information from millions of reviews posted on Amazon.com and then compared the model's predictions with the behavior of experimental participants. Under certain conditions, people preferred a product with more reviews to one with fewer reviews even though the statistical model indicated that the latter was likely to be of higher quality than the former. Overall, participants' judgments suggested that they failed to make meaningful statistical inferences.

Learning what to expect (in visual perception)

PubMed Central

Seriès, Peggy; Seitz, Aaron R.

2013-01-01

Expectations are known to greatly affect our experience of the world. A growing theory in computational neuroscience is that perception can be successfully described using Bayesian inference models and that the brain is “Bayes-optimal” under some constraints. In this context, expectations are particularly interesting, because they can be viewed as prior beliefs in the statistical inference process. A number of questions remain unsolved, however, for example: How fast do priors change over time? Are there limits in the complexity of the priors that can be learned? How do an individual’s priors compare to the true scene statistics? Can we unlearn priors that are thought to correspond to natural scene statistics? Where and what are the neural substrate of priors? Focusing on the perception of visual motion, we here review recent studies from our laboratories and others addressing these issues. We discuss how these data on motion perception fit within the broader literature on perceptual Bayesian priors, perceptual expectations, and statistical and perceptual learning and review the possible neural basis of priors. PMID:24187536

Statistical Inference for Porous Materials using Persistent Homology.

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

Moon, Chul; Heath, Jason E.; Mitchell, Scott A.

2017-12-01

We propose a porous materials analysis pipeline using persistent homology. We rst compute persistent homology of binarized 3D images of sampled material subvolumes. For each image we compute sets of homology intervals, which are represented as summary graphics called persistence diagrams. We convert persistence diagrams into image vectors in order to analyze the similarity of the homology of the material images using the mature tools for image analysis. Each image is treated as a vector and we compute its principal components to extract features. We t a statistical model using the loadings of principal components to estimate material porosity, permeability,more » anisotropy, and tortuosity. We also propose an adaptive version of the structural similarity index (SSIM), a similarity metric for images, as a measure to determine the statistical representative elementary volumes (sREV) for persistence homology. Thus we provide a capability for making a statistical inference of the uid ow and transport properties of porous materials based on their geometry and connectivity.« less

Philosophy and the practice of Bayesian statistics

PubMed Central

Gelman, Andrew; Shalizi, Cosma Rohilla

2015-01-01

A substantial school in the philosophy of science identifies Bayesian inference with inductive inference and even rationality as such, and seems to be strengthened by the rise and practical success of Bayesian statistics. We argue that the most successful forms of Bayesian statistics do not actually support that particular philosophy but rather accord much better with sophisticated forms of hypothetico-deductivism. We examine the actual role played by prior distributions in Bayesian models, and the crucial aspects of model checking and model revision, which fall outside the scope of Bayesian confirmation theory. We draw on the literature on the consistency of Bayesian updating and also on our experience of applied work in social science. Clarity about these matters should benefit not just philosophy of science, but also statistical practice. At best, the inductivist view has encouraged researchers to fit and compare models without checking them; at worst, theorists have actively discouraged practitioners from performing model checking because it does not fit into their framework. PMID:22364575

Philosophy and the practice of Bayesian statistics.

PubMed

Gelman, Andrew; Shalizi, Cosma Rohilla

2013-02-01

A substantial school in the philosophy of science identifies Bayesian inference with inductive inference and even rationality as such, and seems to be strengthened by the rise and practical success of Bayesian statistics. We argue that the most successful forms of Bayesian statistics do not actually support that particular philosophy but rather accord much better with sophisticated forms of hypothetico-deductivism. We examine the actual role played by prior distributions in Bayesian models, and the crucial aspects of model checking and model revision, which fall outside the scope of Bayesian confirmation theory. We draw on the literature on the consistency of Bayesian updating and also on our experience of applied work in social science. Clarity about these matters should benefit not just philosophy of science, but also statistical practice. At best, the inductivist view has encouraged researchers to fit and compare models without checking them; at worst, theorists have actively discouraged practitioners from performing model checking because it does not fit into their framework. © 2012 The British Psychological Society.

78 FR 24138 - Implementing Public Safety Broadband Provisions of the Middle Class Tax Relief and Job Creation...

Federal Register 2010, 2011, 2012, 2013, 2014

2013-04-24

... Bureau, Statistical Abstract of the United States: 2011, Table 427 (2007). \\28\\ The 2007 U.S Census data.... (U.S. CENSUS BUREAU, STATISTICAL ABSTRACT OF THE UNITED STATES 2011, Table 428.) The criterion by... Statistical Abstract of the U.S., that inference is further supported by the fact that in both Tables, many...

Augmenting Latent Dirichlet Allocation and Rank Threshold Detection with Ontologies

DTIC Science & Technology

2010-03-01

Probabilistic Latent Semantic Indexing (PLSI) is an automated indexing information retrieval model [20]. It is based on a statistical latent class model which is...uses a statistical foundation that is more accurate in finding hidden semantic relationships [20]. The model uses factor analysis of count data, number...principle of statistical infer- ence which asserts that all of the information in a sample is contained in the likelihood function [20]. The statistical

Inference Control Mechanism for Statistical Database: Frequency-Imposed Data Distortions.

ERIC Educational Resources Information Center

Liew, Chong K.; And Others

1985-01-01

Introduces two data distortion methods (Frequency-Imposed Distortion, Frequency-Imposed Probability Distortion) and uses a Monte Carlo study to compare their performance with that of other distortion methods (Point Distortion, Probability Distortion). Indications that data generated by these two methods produce accurate statistics and protect…

Notes on power of normality tests of error terms in regression models

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

Střelec, Luboš

2015-03-10

Normality is one of the basic assumptions in applying statistical procedures. For example in linear regression most of the inferential procedures are based on the assumption of normality, i.e. the disturbance vector is assumed to be normally distributed. Failure to assess non-normality of the error terms may lead to incorrect results of usual statistical inference techniques such as t-test or F-test. Thus, error terms should be normally distributed in order to allow us to make exact inferences. As a consequence, normally distributed stochastic errors are necessary in order to make a not misleading inferences which explains a necessity and importancemore » of robust tests of normality. Therefore, the aim of this contribution is to discuss normality testing of error terms in regression models. In this contribution, we introduce the general RT class of robust tests for normality, and present and discuss the trade-off between power and robustness of selected classical and robust normality tests of error terms in regression models.« less

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

An argument for mechanism-based statistical inference in cancer

PubMed Central

Ochs, Michael; Price, Nathan D.; Tomasetti, Cristian; Younes, Laurent

2015-01-01

Cancer is perhaps the prototypical systems disease, and as such has been the focus of extensive study in quantitative systems biology. However, translating these programs into personalized clinical care remains elusive and incomplete. In this perspective, we argue that realizing this agenda—in particular, predicting disease phenotypes, progression and treatment response for individuals—requires going well beyond standard computational and bioinformatics tools and algorithms. It entails designing global mathematical models over network-scale configurations of genomic states and molecular concentrations, and learning the model parameters from limited available samples of high-dimensional and integrative omics data. As such, any plausible design should accommodate: biological mechanism, necessary for both feasible learning and interpretable decision making; stochasticity, to deal with uncertainty and observed variation at many scales; and a capacity for statistical inference at the patient level. This program, which requires a close, sustained collaboration between mathematicians and biologists, is illustrated in several contexts, including learning bio-markers, metabolism, cell signaling, network inference and tumorigenesis. PMID:25381197

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

Bayesian Inference for Functional Dynamics Exploring in fMRI Data.

PubMed

Guo, Xuan; Liu, Bing; Chen, Le; Chen, Guantao; Pan, Yi; Zhang, Jing

2016-01-01

This paper aims to review state-of-the-art Bayesian-inference-based methods applied to functional magnetic resonance imaging (fMRI) data. Particularly, we focus on one specific long-standing challenge in the computational modeling of fMRI datasets: how to effectively explore typical functional interactions from fMRI time series and the corresponding boundaries of temporal segments. Bayesian inference is a method of statistical inference which has been shown to be a powerful tool to encode dependence relationships among the variables with uncertainty. Here we provide an introduction to a group of Bayesian-inference-based methods for fMRI data analysis, which were designed to detect magnitude or functional connectivity change points and to infer their functional interaction patterns based on corresponding temporal boundaries. We also provide a comparison of three popular Bayesian models, that is, Bayesian Magnitude Change Point Model (BMCPM), Bayesian Connectivity Change Point Model (BCCPM), and Dynamic Bayesian Variable Partition Model (DBVPM), and give a summary of their applications. We envision that more delicate Bayesian inference models will be emerging and play increasingly important roles in modeling brain functions in the years to come.

Modular Spectral Inference Framework Applied to Young Stars and Brown Dwarfs

NASA Technical Reports Server (NTRS)

Gully-Santiago, Michael A.; Marley, Mark S.

2017-01-01

In practice, synthetic spectral models are imperfect, causing inaccurate estimates of stellar parameters. Using forward modeling and statistical inference, we derive accurate stellar parameters for a given observed spectrum by emulating a grid of precomputed spectra to track uncertainties. Spectral inference as applied to brown dwarfs re: Synthetic spectral models (Marley et al 1996 and 2014) via the newest grid spans a massive multi-dimensional grid applied to IGRINS spectra, improving atmospheric models for JWST. When applied to young stars(10Myr) with large starpots, they can be measured spectroscopically, especially in the near-IR with IGRINS.

Inference of neuronal network spike dynamics and topology from calcium imaging data

PubMed Central

Lütcke, Henry; Gerhard, Felipe; Zenke, Friedemann; Gerstner, Wulfram; Helmchen, Fritjof

2013-01-01

Two-photon calcium imaging enables functional analysis of neuronal circuits by inferring action potential (AP) occurrence (“spike trains”) from cellular fluorescence signals. It remains unclear how experimental parameters such as signal-to-noise ratio (SNR) and acquisition rate affect spike inference and whether additional information about network structure can be extracted. Here we present a simulation framework for quantitatively assessing how well spike dynamics and network topology can be inferred from noisy calcium imaging data. For simulated AP-evoked calcium transients in neocortical pyramidal cells, we analyzed the quality of spike inference as a function of SNR and data acquisition rate using a recently introduced peeling algorithm. Given experimentally attainable values of SNR and acquisition rate, neural spike trains could be reconstructed accurately and with up to millisecond precision. We then applied statistical neuronal network models to explore how remaining uncertainties in spike inference affect estimates of network connectivity and topological features of network organization. We define the experimental conditions suitable for inferring whether the network has a scale-free structure and determine how well hub neurons can be identified. Our findings provide a benchmark for future calcium imaging studies that aim to reliably infer neuronal network properties. PMID:24399936

Type Ia Supernova Light Curve Inference: Hierarchical Models for Nearby SN Ia in the Optical and Near Infrared

NASA Astrophysics Data System (ADS)

Mandel, Kaisey; Kirshner, R. P.; Narayan, G.; Wood-Vasey, W. M.; Friedman, A. S.; Hicken, M.

2010-01-01

I have constructed a comprehensive statistical model for Type Ia supernova light curves spanning optical through near infrared data simultaneously. The near infrared light curves are found to be excellent standard candles (sigma(MH) = 0.11 +/- 0.03 mag) that are less vulnerable to systematic error from dust extinction, a major confounding factor for cosmological studies. A hierarchical statistical framework incorporates coherently multiple sources of randomness and uncertainty, including photometric error, intrinsic supernova light curve variations and correlations, dust extinction and reddening, peculiar velocity dispersion and distances, for probabilistic inference with Type Ia SN light curves. Inferences are drawn from the full probability density over individual supernovae and the SN Ia and dust populations, conditioned on a dataset of SN Ia light curves and redshifts. To compute probabilistic inferences with hierarchical models, I have developed BayeSN, a Markov Chain Monte Carlo algorithm based on Gibbs sampling. This code explores and samples the global probability density of parameters describing individual supernovae and the population. I have applied this hierarchical model to optical and near infrared data of over 100 nearby Type Ia SN from PAIRITEL, the CfA3 sample, and the literature. Using this statistical model, I find that SN with optical and NIR data have a smaller residual scatter in the Hubble diagram than SN with only optical data. The continued study of Type Ia SN in the near infrared will be important for improving their utility as precise and accurate cosmological distance indicators.

Statistical inference involving binomial and negative binomial parameters.

PubMed

García-Pérez, Miguel A; Núñez-Antón, Vicente

2009-05-01

Statistical inference about two binomial parameters implies that they are both estimated by binomial sampling. There are occasions in which one aims at testing the equality of two binomial parameters before and after the occurrence of the first success along a sequence of Bernoulli trials. In these cases, the binomial parameter before the first success is estimated by negative binomial sampling whereas that after the first success is estimated by binomial sampling, and both estimates are related. This paper derives statistical tools to test two hypotheses, namely, that both binomial parameters equal some specified value and that both parameters are equal though unknown. Simulation studies are used to show that in small samples both tests are accurate in keeping the nominal Type-I error rates, and also to determine sample size requirements to detect large, medium, and small effects with adequate power. Additional simulations also show that the tests are sufficiently robust to certain violations of their assumptions.

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.

Sampling and counting genome rearrangement scenarios

PubMed Central

2015-01-01

Background Even for moderate size inputs, there are a tremendous number of optimal rearrangement scenarios, regardless what the model is and which specific question is to be answered. Therefore giving one optimal solution might be misleading and cannot be used for statistical inferring. Statistically well funded methods are necessary to sample uniformly from the solution space and then a small number of samples are sufficient for statistical inferring. Contribution In this paper, we give a mini-review about the state-of-the-art of sampling and counting rearrangement scenarios, focusing on the reversal, DCJ and SCJ models. Above that, we also give a Gibbs sampler for sampling most parsimonious labeling of evolutionary trees under the SCJ model. The method has been implemented and tested on real life data. The software package together with example data can be downloaded from http://www.renyi.hu/~miklosi/SCJ-Gibbs/ PMID:26452124

Online Updating of Statistical Inference in the Big Data Setting.

PubMed

Schifano, Elizabeth D; Wu, Jing; Wang, Chun; Yan, Jun; Chen, Ming-Hui

2016-01-01

We present statistical methods for big data arising from online analytical processing, where large amounts of data arrive in streams and require fast analysis without storage/access to the historical data. In particular, we develop iterative estimating algorithms and statistical inferences for linear models and estimating equations that update as new data arrive. These algorithms are computationally efficient, minimally storage-intensive, and allow for possible rank deficiencies in the subset design matrices due to rare-event covariates. Within the linear model setting, the proposed online-updating framework leads to predictive residual tests that can be used to assess the goodness-of-fit of the hypothesized model. We also propose a new online-updating estimator under the estimating equation setting. Theoretical properties of the goodness-of-fit tests and proposed estimators are examined in detail. In simulation studies and real data applications, our estimator compares favorably with competing approaches under the estimating equation setting.

When mechanism matters: Bayesian forecasting using models of ecological diffusion

USGS Publications Warehouse

Hefley, Trevor J.; Hooten, Mevin B.; Russell, Robin E.; Walsh, Daniel P.; Powell, James A.

2017-01-01

Ecological diffusion is a theory that can be used to understand and forecast spatio-temporal processes such as dispersal, invasion, and the spread of disease. Hierarchical Bayesian modelling provides a framework to make statistical inference and probabilistic forecasts, using mechanistic ecological models. To illustrate, we show how hierarchical Bayesian models of ecological diffusion can be implemented for large data sets that are distributed densely across space and time. The hierarchical Bayesian approach is used to understand and forecast the growth and geographic spread in the prevalence of chronic wasting disease in white-tailed deer (Odocoileus virginianus). We compare statistical inference and forecasts from our hierarchical Bayesian model to phenomenological regression-based methods that are commonly used to analyse spatial occurrence data. The mechanistic statistical model based on ecological diffusion led to important ecological insights, obviated a commonly ignored type of collinearity, and was the most accurate method for forecasting.

Probabilistic Signal Recovery and Random Matrices

DTIC Science & Technology

2016-12-08

applications in statistics , biomedical data analysis, quantization, dimen- sion reduction, and networks science. 1. High-dimensional inference and geometry Our...low-rank approxima- tion, with applications to community detection in networks, Annals of Statistics 44 (2016), 373–400. [7] C. Le, E. Levina, R...approximation, with applications to community detection in networks, Annals of Statistics 44 (2016), 373–400. C. Le, E. Levina, R. Vershynin, Concentration

The Use of a Context-Based Information Retrieval Technique

DTIC Science & Technology

2009-07-01

provided in context. Latent Semantic Analysis (LSA) is a statistical technique for inferring contextual and structural information, and previous studies...WAIS). 10 DSTO-TR-2322 1.4.4 Latent Semantic Analysis LSA, which is also known as latent semantic indexing (LSI), uses a statistical and...1.4.6 Language Models In contrast, natural language models apply algorithms that combine statistical information with semantic information. Semantic

An Introduction to Confidence Intervals for Both Statistical Estimates and Effect Sizes.

ERIC Educational Resources Information Center

Capraro, Mary Margaret

This paper summarizes methods of estimating confidence intervals, including classical intervals and intervals for effect sizes. The recent American Psychological Association (APA) Task Force on Statistical Inference report suggested that confidence intervals should always be reported, and the fifth edition of the APA "Publication Manual"…

Balancing Treatment and Control Groups in Quasi-Experiments: An Introduction to Propensity Scoring

ERIC Educational Resources Information Center

Connelly, Brian S.; Sackett, Paul R.; Waters, Shonna D.

2013-01-01

Organizational and applied sciences have long struggled with improving causal inference in quasi-experiments. We introduce organizational researchers to propensity scoring, a statistical technique that has become popular in other applied sciences as a means for improving internal validity. Propensity scoring statistically models how individuals in…

Modeling Cross-Situational Word-Referent Learning: Prior Questions

ERIC Educational Resources Information Center

Yu, Chen; Smith, Linda B.

2012-01-01

Both adults and young children possess powerful statistical computation capabilities--they can infer the referent of a word from highly ambiguous contexts involving many words and many referents by aggregating cross-situational statistical information across contexts. This ability has been explained by models of hypothesis testing and by models of…

Temporal and Statistical Information in Causal Structure Learning

ERIC Educational Resources Information Center

McCormack, Teresa; Frosch, Caren; Patrick, Fiona; Lagnado, David

2015-01-01

Three experiments examined children's and adults' abilities to use statistical and temporal information to distinguish between common cause and causal chain structures. In Experiment 1, participants were provided with conditional probability information and/or temporal information and asked to infer the causal structure of a 3-variable mechanical…

Secondary Analysis of National Longitudinal Transition Study 2 Data

ERIC Educational Resources Information Center

Hicks, Tyler A.; Knollman, Greg A.

2015-01-01

This review examines published secondary analyses of National Longitudinal Transition Study 2 (NLTS2) data, with a primary focus upon statistical objectives, paradigms, inferences, and methods. Its primary purpose was to determine which statistical techniques have been common in secondary analyses of NLTS2 data. The review begins with an…

Some General Goals in Teaching Statistics.

ERIC Educational Resources Information Center

Blalock, H. M.

1987-01-01

States that regardless of the content or level of a statistics course, five goals to reach are: (1) overcoming fears, resistances, and tendencies to memorize; (2) the importance of intellectual honesty and integrity; (3) understanding relationship between deductive and inductive inferences; (4) learning to play role of reasonable critic; and (5)…

Propensity Score Analysis: An Alternative Statistical Approach for HRD Researchers

ERIC Educational Resources Information Center

Keiffer, Greggory L.; Lane, Forrest C.

2016-01-01

Purpose: This paper aims to introduce matching in propensity score analysis (PSA) as an alternative statistical approach for researchers looking to make causal inferences using intact groups. Design/methodology/approach: An illustrative example demonstrated the varying results of analysis of variance, analysis of covariance and PSA on a heuristic…

Technology Focus: Using Technology to Explore Statistical Inference

ERIC Educational Resources Information Center

Garofalo, Joe; Juersivich, Nicole

2007-01-01

There is much research that documents what many teachers know, that students struggle with many concepts in probability and statistics. This article presents two sample activities the authors use to help preservice teachers develop ideas about how they can use technology to promote their students' ability to understand mathematics and connect…

The Impact of an Instructional Intervention Designed to Support Development of Stochastic Understanding of Probability Distribution

ERIC Educational Resources Information Center

Conant, Darcy Lynn

2013-01-01

Stochastic understanding of probability distribution undergirds development of conceptual connections between probability and statistics and supports development of a principled understanding of statistical inference. This study investigated the impact of an instructional course intervention designed to support development of stochastic…

Basic Statistical Concepts and Methods for Earth Scientists

USGS Publications Warehouse

Olea, Ricardo A.

2008-01-01

INTRODUCTION Statistics is the science of collecting, analyzing, interpreting, modeling, and displaying masses of numerical data primarily for the characterization and understanding of incompletely known systems. Over the years, these objectives have lead to a fair amount of analytical work to achieve, substantiate, and guide descriptions and inferences.

Metacontrast Inferred from Reaction Time and Verbal Report: Replication and Comments on the Feher-Biederman Experiment

ERIC Educational Resources Information Center

Amundson, Vickie E.; Bernstein, Ira H.

1973-01-01

Authors note that Fehrer and Biederman's two statistical tests were not of equal power and that their conclusion could be a statistical artifact of both the lesser power of the verbal report comparison and the insensitivity of their particular verbal report indicator. (Editor)

Optimism bias leads to inconclusive results - an empirical study

PubMed Central

Djulbegovic, Benjamin; Kumar, Ambuj; Magazin, Anja; Schroen, Anneke T.; Soares, Heloisa; Hozo, Iztok; Clarke, Mike; Sargent, Daniel; Schell, Michael J.

2010-01-01

Objective Optimism bias refers to unwarranted belief in the efficacy of new therapies. We assessed the impact of optimism bias on a proportion of trials that did not answer their research question successfully, and explored whether poor accrual or optimism bias is responsible for inconclusive results. Study Design Systematic review Setting Retrospective analysis of a consecutive series phase III randomized controlled trials (RCTs) performed under the aegis of National Cancer Institute Cooperative groups. Results 359 trials (374 comparisons) enrolling 150,232 patients were analyzed. 70% (262/374) of the trials generated conclusive results according to the statistical criteria. Investigators made definitive statements related to the treatment preference in 73% (273/374) of studies. Investigators’ judgments and statistical inferences were concordant in 75% (279/374) of trials. Investigators consistently overestimated their expected treatment effects, but to a significantly larger extent for inconclusive trials. The median ratio of expected over observed hazard ratio or odds ratio was 1.34 (range 0.19 – 15.40) in conclusive trials compared to 1.86 (range 1.09 – 12.00) in inconclusive studies (p<0.0001). Only 17% of the trials had treatment effects that matched original researchers’ expectations. Conclusion Formal statistical inference is sufficient to answer the research question in 75% of RCTs. The answers to the other 25% depend mostly on subjective judgments, which at times are in conflict with statistical inference. Optimism bias significantly contributes to inconclusive results. PMID:21163620

Optimism bias leads to inconclusive results-an empirical study.

PubMed

Djulbegovic, Benjamin; Kumar, Ambuj; Magazin, Anja; Schroen, Anneke T; Soares, Heloisa; Hozo, Iztok; Clarke, Mike; Sargent, Daniel; Schell, Michael J

2011-06-01

Optimism bias refers to unwarranted belief in the efficacy of new therapies. We assessed the impact of optimism bias on a proportion of trials that did not answer their research question successfully and explored whether poor accrual or optimism bias is responsible for inconclusive results. Systematic review. Retrospective analysis of a consecutive-series phase III randomized controlled trials (RCTs) performed under the aegis of National Cancer Institute Cooperative groups. Three hundred fifty-nine trials (374 comparisons) enrolling 150,232 patients were analyzed. Seventy percent (262 of 374) of the trials generated conclusive results according to the statistical criteria. Investigators made definitive statements related to the treatment preference in 73% (273 of 374) of studies. Investigators' judgments and statistical inferences were concordant in 75% (279 of 374) of trials. Investigators consistently overestimated their expected treatment effects but to a significantly larger extent for inconclusive trials. The median ratio of expected and observed hazard ratio or odds ratio was 1.34 (range: 0.19-15.40) in conclusive trials compared with 1.86 (range: 1.09-12.00) in inconclusive studies (P<0.0001). Only 17% of the trials had treatment effects that matched original researchers' expectations. Formal statistical inference is sufficient to answer the research question in 75% of RCTs. The answers to the other 25% depend mostly on subjective judgments, which at times are in conflict with statistical inference. Optimism bias significantly contributes to inconclusive results. Copyright © 2011 Elsevier Inc. All rights reserved.

Forward and backward inference in spatial cognition.

PubMed

Penny, Will D; Zeidman, Peter; Burgess, Neil

2013-01-01

This paper shows that the various computations underlying spatial cognition can be implemented using statistical inference in a single probabilistic model. Inference is implemented using a common set of 'lower-level' computations involving forward and backward inference over time. For example, to estimate where you are in a known environment, forward inference is used to optimally combine location estimates from path integration with those from sensory input. To decide which way to turn to reach a goal, forward inference is used to compute the likelihood of reaching that goal under each option. To work out which environment you are in, forward inference is used to compute the likelihood of sensory observations under the different hypotheses. For reaching sensory goals that require a chaining together of decisions, forward inference can be used to compute a state trajectory that will lead to that goal, and backward inference to refine the route and estimate control signals that produce the required trajectory. We propose that these computations are reflected in recent findings of pattern replay in the mammalian brain. Specifically, that theta sequences reflect decision making, theta flickering reflects model selection, and remote replay reflects route and motor planning. We also propose a mapping of the above computational processes onto lateral and medial entorhinal cortex and hippocampus.

Forward and Backward Inference in Spatial Cognition

PubMed Central

Penny, Will D.; Zeidman, Peter; Burgess, Neil

2013-01-01

This paper shows that the various computations underlying spatial cognition can be implemented using statistical inference in a single probabilistic model. Inference is implemented using a common set of ‘lower-level’ computations involving forward and backward inference over time. For example, to estimate where you are in a known environment, forward inference is used to optimally combine location estimates from path integration with those from sensory input. To decide which way to turn to reach a goal, forward inference is used to compute the likelihood of reaching that goal under each option. To work out which environment you are in, forward inference is used to compute the likelihood of sensory observations under the different hypotheses. For reaching sensory goals that require a chaining together of decisions, forward inference can be used to compute a state trajectory that will lead to that goal, and backward inference to refine the route and estimate control signals that produce the required trajectory. We propose that these computations are reflected in recent findings of pattern replay in the mammalian brain. Specifically, that theta sequences reflect decision making, theta flickering reflects model selection, and remote replay reflects route and motor planning. We also propose a mapping of the above computational processes onto lateral and medial entorhinal cortex and hippocampus. PMID:24348230

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 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.

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.

PREFACE: ELC International Meeting on Inference, Computation, and Spin Glasses (ICSG2013)

NASA Astrophysics Data System (ADS)

Kabashima, Yoshiyuki; Hukushima, Koji; Inoue, Jun-ichi; Tanaka, Toshiyuki; Watanabe, Osamu

2013-12-01

The close relationship between probability-based inference and statistical mechanics of disordered systems has been noted for some time. This relationship has provided researchers with a theoretical foundation in various fields of information processing for analytical performance evaluation and construction of efficient algorithms based on message-passing or Monte Carlo sampling schemes. The ELC International Meeting on 'Inference, Computation, and Spin Glasses (ICSG2013)', was held in Sapporo 28-30 July 2013. The meeting was organized as a satellite meeting of STATPHYS25 in order to offer a forum where concerned researchers can assemble and exchange information on the latest results and newly established methodologies, and discuss future directions of the interdisciplinary studies between statistical mechanics and information sciences. Financial support from Grant-in-Aid for Scientific Research on Innovative Areas, MEXT, Japan 'Exploring the Limits of Computation (ELC)' is gratefully acknowledged. We are pleased to publish 23 papers contributed by invited speakers of ICSG2013 in this volume of Journal of Physics: Conference Series. We hope that this volume will promote further development of this highly vigorous interdisciplinary field between statistical mechanics and information/computer science. Editors and ICSG2013 Organizing Committee: Koji Hukushima Jun-ichi Inoue (Local Chair of ICSG2013) Yoshiyuki Kabashima (Editor-in-Chief) Toshiyuki Tanaka Osamu Watanabe (General Chair of ICSG2013)

Measuring the Number of M Dwarfs per M Dwarf Using Kepler Eclipsing Binaries

NASA Astrophysics Data System (ADS)

Shan, Yutong; Johnson, John A.; Morton, Timothy D.

2015-11-01

We measure the binarity of detached M dwarfs in the Kepler field with orbital periods in the range of 1-90 days. Kepler’s photometric precision and nearly continuous monitoring of stellar targets over time baselines ranging from 3 months to 4 years make its detection efficiency for eclipsing binaries nearly complete over this period range and for all radius ratios. Our investigation employs a statistical framework akin to that used for inferring planetary occurrence rates from planetary transits. The obvious simplification is that eclipsing binaries have a vastly improved detection efficiency that is limited chiefly by their geometric probabilities to eclipse. For the M-dwarf sample observed by the Kepler Mission, the fractional incidence of eclipsing binaries implies that there are {0.11}-0.04+0.02 close stellar companions per apparently single M dwarf. Our measured binarity is higher than previous inferences of the occurrence rate of close binaries via radial velocity techniques, at roughly the 2σ level. This study represents the first use of eclipsing binary detections from a high quality transiting planet mission to infer binary statistics. Application of this statistical framework to the eclipsing binaries discovered by future transit surveys will establish better constraints on short-period M+M binary rate, as well as binarity measurements for stars of other spectral types.

Lifetime Prediction for Degradation of Solar Mirrors using Step-Stress Accelerated Testing (Presentation)

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

Lee, J.; Elmore, R.; Kennedy, C.

This research is to illustrate the use of statistical inference techniques in order to quantify the uncertainty surrounding reliability estimates in a step-stress accelerated degradation testing (SSADT) scenario. SSADT can be used when a researcher is faced with a resource-constrained environment, e.g., limits on chamber time or on the number of units to test. We apply the SSADT methodology to a degradation experiment involving concentrated solar power (CSP) mirrors and compare the results to a more traditional multiple accelerated testing paradigm. Specifically, our work includes: (1) designing a durability testing plan for solar mirrors (3M's new improved silvered acrylic "Solarmore » Reflector Film (SFM) 1100") through the ultra-accelerated weathering system (UAWS), (2) defining degradation paths of optical performance based on the SSADT model which is accelerated by high UV-radiant exposure, and (3) developing service lifetime prediction models for solar mirrors using advanced statistical inference. We use the method of least squares to estimate the model parameters and this serves as the basis for the statistical inference in SSADT. Several quantities of interest can be estimated from this procedure, e.g., mean-time-to-failure (MTTF) and warranty time. The methods allow for the estimation of quantities that may be of interest to the domain scientists.« less

Cancer Survival Estimates Due to Non-Uniform Loss to Follow-Up and Non-Proportional Hazards

PubMed

K M, Jagathnath Krishna; Mathew, Aleyamma; Sara George, Preethi

2017-06-25

Background: Cancer survival depends on loss to follow-up (LFU) and non-proportional hazards (non-PH). If LFU is high, survival will be over-estimated. If hazard is non-PH, rank tests will provide biased inference and Cox-model will provide biased hazard-ratio. We assessed the bias due to LFU and non-PH factor in cancer survival and provided alternate methods for unbiased inference and hazard-ratio. Materials and Methods: Kaplan-Meier survival were plotted using a realistic breast cancer (BC) data-set, with >40%, 5-year LFU and compared it using another BC data-set with <15%, 5-year LFU to assess the bias in survival due to high LFU. Age at diagnosis of the latter data set was used to illustrate the bias due to a non-PH factor. Log-rank test was employed to assess the bias in p-value and Cox-model was used to assess the bias in hazard-ratio for the non-PH factor. Schoenfeld statistic was used to test the non-PH of age. For the non-PH factor, we employed Renyi statistic for inference and time dependent Cox-model for hazard-ratio. Results: Five-year BC survival was 69% (SE: 1.1%) vs. 90% (SE: 0.7%) for data with low vs. high LFU respectively. Age (<45, 46-54 & >54 years) was a non-PH factor (p-value: 0.036). However, survival by age was significant (log-rank p-value: 0.026), but not significant using Renyi statistic (p=0.067). Hazard ratio (HR) for age using Cox-model was 1.012 (95%CI: 1.004 -1.019) and the same using time-dependent Cox-model was in the other direction (HR: 0.997; 95% CI: 0.997- 0.998). Conclusion: Over-estimated survival was observed for cancer with high LFU. Log-rank statistic and Cox-model provided biased results for non-PH factor. For data with non-PH factors, Renyi statistic and time dependent Cox-model can be used as alternate methods to obtain unbiased inference and estimates. Creative Commons Attribution License

Final Report, DOE Early Career Award: Predictive modeling of complex physical systems: new tools for statistical inference, uncertainty quantification, and experimental design

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

Marzouk, Youssef

Predictive simulation of complex physical systems increasingly rests on the interplay of experimental observations with computational models. Key inputs, parameters, or structural aspects of models may be incomplete or unknown, and must be developed from indirect and limited observations. At the same time, quantified uncertainties are needed to qualify computational predictions in the support of design and decision-making. In this context, Bayesian statistics provides a foundation for inference from noisy and limited data, but at prohibitive computional expense. This project intends to make rigorous predictive modeling *feasible* in complex physical systems, via accelerated and scalable tools for uncertainty quantification, Bayesianmore » inference, and experimental design. Specific objectives are as follows: 1. Develop adaptive posterior approximations and dimensionality reduction approaches for Bayesian inference in high-dimensional nonlinear systems. 2. Extend accelerated Bayesian methodologies to large-scale {\\em sequential} data assimilation, fully treating nonlinear models and non-Gaussian state and parameter distributions. 3. Devise efficient surrogate-based methods for Bayesian model selection and the learning of model structure. 4. Develop scalable simulation/optimization approaches to nonlinear Bayesian experimental design, for both parameter inference and model selection. 5. Demonstrate these inferential tools on chemical kinetic models in reacting flow, constructing and refining thermochemical and electrochemical models from limited data. Demonstrate Bayesian filtering on canonical stochastic PDEs and in the dynamic estimation of inhomogeneous subsurface properties and flow fields.« less

Unraveling multiple changes in complex climate time series using Bayesian inference

NASA Astrophysics Data System (ADS)

Berner, Nadine; Trauth, Martin H.; Holschneider, Matthias

2016-04-01

Change points in time series are perceived as heterogeneities in the statistical or dynamical characteristics of observations. Unraveling such transitions yields essential information for the understanding of the observed system. The precise detection and basic characterization of underlying changes is therefore of particular importance in environmental sciences. We present a kernel-based Bayesian inference approach to investigate direct as well as indirect climate observations for multiple generic transition events. In order to develop a diagnostic approach designed to capture a variety of natural processes, the basic statistical features of central tendency and dispersion are used to locally approximate a complex time series by a generic transition model. A Bayesian inversion approach is developed to robustly infer on the location and the generic patterns of such a transition. To systematically investigate time series for multiple changes occurring at different temporal scales, the Bayesian inversion is extended to a kernel-based inference approach. By introducing basic kernel measures, the kernel inference results are composed into a proxy probability to a posterior distribution of multiple transitions. Thus, based on a generic transition model a probability expression is derived that is capable to indicate multiple changes within a complex time series. We discuss the method's performance by investigating direct and indirect climate observations. The approach is applied to environmental time series (about 100 a), from the weather station in Tuscaloosa, Alabama, and confirms documented instrumentation changes. Moreover, the approach is used to investigate a set of complex terrigenous dust records from the ODP sites 659, 721/722 and 967 interpreted as climate indicators of the African region of the Plio-Pleistocene period (about 5 Ma). The detailed inference unravels multiple transitions underlying the indirect climate observations coinciding with established global climate events.

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

Application of maximum entropy to statistical inference for inversion of data from a single track segment.

PubMed

Stotts, Steven A; Koch, Robert A

2017-08-01

In this paper an approach is presented to estimate the constraint required to apply maximum entropy (ME) for statistical inference with underwater acoustic data from a single track segment. Previous algorithms for estimating the ME constraint require multiple source track segments to determine the constraint. The approach is relevant for addressing model mismatch effects, i.e., inaccuracies in parameter values determined from inversions because the propagation model does not account for all acoustic processes that contribute to the measured data. One effect of model mismatch is that the lowest cost inversion solution may be well outside a relatively well-known parameter value's uncertainty interval (prior), e.g., source speed from track reconstruction or towed source levels. The approach requires, for some particular parameter value, the ME constraint to produce an inferred uncertainty interval that encompasses the prior. Motivating this approach is the hypothesis that the proposed constraint determination procedure would produce a posterior probability density that accounts for the effect of model mismatch on inferred values of other inversion parameters for which the priors might be quite broad. Applications to both measured and simulated data are presented for model mismatch that produces minimum cost solutions either inside or outside some priors.

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.

Ionospheric and Birkeland current distributions inferred from the MAGSAT magnetometer data

NASA Technical Reports Server (NTRS)

Zanetti, L. J.; Potemra, T. A.; Baumjohann, W.

1983-01-01

Ionospheric and field-aligned sheet current density distributions are presently inferred by means of MAGSAT vector magnetometer data, together with an accurate magnetic field model. By comparing Hall current densities inferred from the MAGSAT data and those inferred from simultaneously recorded ground based data acquired by the Scandinavian magnetometer array, it is determined that the former have previously been underestimated due to high damping of magnetic variations with high spatial wave numbers between the ionosphere and the MAGSAT orbit. Among important results of this study is noted the fact that the Birkeland and electrojet current systems are colocated. The analyses have shown a tendency for triangular rather than constant electrojet current distributions as a function of latitude, consistent with the statistical, uniform regions 1 and 2 Birkeland current patterns.

Inferring Markov chains: Bayesian estimation, model comparison, entropy rate, and out-of-class modeling.

PubMed

Strelioff, Christopher C; Crutchfield, James P; Hübler, Alfred W

2007-07-01

Markov chains are a natural and well understood tool for describing one-dimensional patterns in time or space. We show how to infer kth order Markov chains, for arbitrary k , from finite data by applying Bayesian methods to both parameter estimation and model-order selection. Extending existing results for multinomial models of discrete data, we connect inference to statistical mechanics through information-theoretic (type theory) techniques. We establish a direct relationship between Bayesian evidence and the partition function which allows for straightforward calculation of the expectation and variance of the conditional relative entropy and the source entropy rate. Finally, we introduce a method that uses finite data-size scaling with model-order comparison to infer the structure of out-of-class processes.

[Confidence interval or p-value--similarities and differences between two important methods of statistical inference of quantitative studies].

PubMed

Harari, Gil

2014-01-01

Statistic significance, also known as p-value, and CI (Confidence Interval) are common statistics measures and are essential for the statistical analysis of studies in medicine and life sciences. These measures provide complementary information about the statistical probability and conclusions regarding the clinical significance of study findings. This article is intended to describe the methodologies, compare between the methods, assert their suitability for the different needs of study results analysis and to explain situations in which each method should be used.

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

Comparative analysis on the selection of number of clusters in community detection

NASA Astrophysics Data System (ADS)

Kawamoto, Tatsuro; Kabashima, Yoshiyuki

2018-02-01

We conduct a comparative analysis on various estimates of the number of clusters in community detection. An exhaustive comparison requires testing of all possible combinations of frameworks, algorithms, and assessment criteria. In this paper we focus on the framework based on a stochastic block model, and investigate the performance of greedy algorithms, statistical inference, and spectral methods. For the assessment criteria, we consider modularity, map equation, Bethe free energy, prediction errors, and isolated eigenvalues. From the analysis, the tendency of overfit and underfit that the assessment criteria and algorithms have becomes apparent. In addition, we propose that the alluvial diagram is a suitable tool to visualize statistical inference results and can be useful to determine the number of clusters.

Distributed Sensing and Processing for Multi-Camera Networks

NASA Astrophysics Data System (ADS)

Sankaranarayanan, Aswin C.; Chellappa, Rama; Baraniuk, Richard G.

Sensor networks with large numbers of cameras are becoming increasingly prevalent in a wide range of applications, including video conferencing, motion capture, surveillance, and clinical diagnostics. In this chapter, we identify some of the fundamental challenges in designing such systems: robust statistical inference, computationally efficiency, and opportunistic and parsimonious sensing. We show that the geometric constraints induced by the imaging process are extremely useful for identifying and designing optimal estimators for object detection and tracking tasks. We also derive pipelined and parallelized implementations of popular tools used for statistical inference in non-linear systems, of which multi-camera systems are examples. Finally, we highlight the use of the emerging theory of compressive sensing in reducing the amount of data sensed and communicated by a camera network.

General intelligence does not help us understand cognitive evolution.

PubMed

Shuker, David M; Barrett, Louise; Dickins, Thomas E; Scott-Phillips, Thom C; Barton, Robert A

2017-01-01

Burkart et al. conflate the domain-specificity of cognitive processes with the statistical pattern of variance in behavioural measures that partly reflect those processes. General intelligence is a statistical abstraction, not a cognitive trait, and we argue that the former does not warrant inferences about the nature or evolution of the latter.

Exploring Tree Age & Diameter to Illustrate Sample Design & Inference in Observational Ecology

ERIC Educational Resources Information Center

Casady, Grant M.

2015-01-01

Undergraduate biology labs often explore the techniques of data collection but neglect the statistical framework necessary to express findings. Students can be confused about how to use their statistical knowledge to address specific biological questions. Growth in the area of observational ecology requires that students gain experience in…

Computer-Based Instruction in Statistical Inference; Final Report. Technical Memorandum (TM Series).

ERIC Educational Resources Information Center

Rosenbaum, J.; And Others

A two-year investigation into the development of computer-assisted instruction (CAI) for the improvement of undergraduate training in statistics was undertaken. The first year was largely devoted to designing PLANIT (Programming LANguage for Interactive Teaching) which reduces, or completely eliminates, the need an author of CAI lessons would…

Causal Inference for Statistics, Social, and Biomedical Sciences: An Introduction

ERIC Educational Resources Information Center

Imbens, Guido W.; Rubin, Donald B.

2015-01-01

Most questions in social and biomedical sciences are causal in nature: what would happen to individuals, or to groups, if part of their environment were changed? In this groundbreaking text, two world-renowned experts present statistical methods for studying such questions. This book starts with the notion of potential outcomes, each corresponding…

The Co-Emergence of Aggregate and Modelling Reasoning

ERIC Educational Resources Information Center

Aridor, Keren; Ben-Zvi, Dani

2017-01-01

This article examines how two processes--reasoning with statistical modelling of a real phenomenon and aggregate reasoning--can co-emerge. We focus in this case study on the emergent reasoning of two fifth graders (aged 10) involved in statistical data analysis, informal inference, and modelling activities using TinkerPlots™. We describe nine…

Can Being Scared Cause Tummy Aches? Naive Theories, Ambiguous Evidence, and Preschoolers' Causal Inferences

ERIC Educational Resources Information Center

Schulz, Laura E.; Bonawitz, Elizabeth Baraff; Griffiths, Thomas L.

2007-01-01

Causal learning requires integrating constraints provided by domain-specific theories with domain-general statistical learning. In order to investigate the interaction between these factors, the authors presented preschoolers with stories pitting their existing theories against statistical evidence. Each child heard 2 stories in which 2 candidate…

Using Informal Inferential Reasoning to Develop Formal Concepts: Analyzing an Activity

ERIC Educational Resources Information Center

Weinberg, Aaron; Wiesner, Emilie; Pfaff, Thomas J.

2010-01-01

Inferential reasoning is a central component of statistics. Researchers have suggested that students should develop an informal understanding of the ideas that underlie inference before learning the concepts formally. This paper presents a hands-on activity that is designed to help students in an introductory statistics course draw informal…

A Modeling Approach to the Development of Students' Informal Inferential Reasoning

ERIC Educational Resources Information Center

Doerr, Helen M.; Delmas, Robert; Makar, Katie

2017-01-01

Teaching from an informal statistical inference perspective can address the challenge of teaching statistics in a coherent way. We argue that activities that promote model-based reasoning address two additional challenges: providing a coherent sequence of topics and promoting the application of knowledge to novel situations. We take a models and…

Statistical inference of selection and divergence of rice blast resistance gene Pi-ta

USDA-ARS?s Scientific Manuscript database

The resistance gene Pi-ta has been effectively used to control rice blast disease worldwide. A few recent studies have described the possible evolution of Pi-ta in cultivated and weedy rice. However, evolutionary statistics used for the studies are too limited to precisely understand selection and d...

A Scalable Approach to Probabilistic Latent Space Inference of Large-Scale Networks

PubMed Central

Yin, Junming; Ho, Qirong; Xing, Eric P.

2014-01-01

We propose a scalable approach for making inference about latent spaces of large networks. With a succinct representation of networks as a bag of triangular motifs, a parsimonious statistical model, and an efficient stochastic variational inference algorithm, we are able to analyze real networks with over a million vertices and hundreds of latent roles on a single machine in a matter of hours, a setting that is out of reach for many existing methods. When compared to the state-of-the-art probabilistic approaches, our method is several orders of magnitude faster, with competitive or improved accuracy for latent space recovery and link prediction. PMID:25400487

The influence of social information on children's statistical and causal inferences.

PubMed

Sobel, David M; Kirkham, Natasha Z

2012-01-01

Constructivist accounts of learning posit that causal inference is a child-driven process. Recent interpretations of such accounts also suggest that the process children use for causal learning is rational: Children interpret and learn from new evidence in light of their existing beliefs. We argue that such mechanisms are also driven by informative social cues and suggest ways in which such information influences both preschoolers' and infants' inferences. In doing so, we argue that a rational constructivist account should not only focus on describing the child's internal cognitive mechanisms for learning but also on how social information affects the process of learning.

IMAGINE: Interstellar MAGnetic field INference Engine

NASA Astrophysics Data System (ADS)

Steininger, Theo

2018-03-01

IMAGINE (Interstellar MAGnetic field INference Engine) performs inference on generic parametric models of the Galaxy. The modular open source framework uses highly optimized tools and technology such as the MultiNest sampler (ascl:1109.006) and the information field theory framework NIFTy (ascl:1302.013) to create an instance of the Milky Way based on a set of parameters for physical observables, using Bayesian statistics to judge the mismatch between measured data and model prediction. The flexibility of the IMAGINE framework allows for simple refitting for newly available data sets and makes state-of-the-art Bayesian methods easily accessible particularly for random components of the Galactic magnetic field.

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.

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

Inferring epidemiological parameters from phylogenies using regression-ABC: A comparative study

PubMed Central

Gascuel, Olivier

2017-01-01

Inferring epidemiological parameters such as the R0 from time-scaled phylogenies is a timely challenge. Most current approaches rely on likelihood functions, which raise specific issues that range from computing these functions to finding their maxima numerically. Here, we present a new regression-based Approximate Bayesian Computation (ABC) approach, which we base on a large variety of summary statistics intended to capture the information contained in the phylogeny and its corresponding lineage-through-time plot. The regression step involves the Least Absolute Shrinkage and Selection Operator (LASSO) method, which is a robust machine learning technique. It allows us to readily deal with the large number of summary statistics, while avoiding resorting to Markov Chain Monte Carlo (MCMC) techniques. To compare our approach to existing ones, we simulated target trees under a variety of epidemiological models and settings, and inferred parameters of interest using the same priors. We found that, for large phylogenies, the accuracy of our regression-ABC is comparable to that of likelihood-based approaches involving birth-death processes implemented in BEAST2. Our approach even outperformed these when inferring the host population size with a Susceptible-Infected-Removed epidemiological model. It also clearly outperformed a recent kernel-ABC approach when assuming a Susceptible-Infected epidemiological model with two host types. Lastly, by re-analyzing data from the early stages of the recent Ebola epidemic in Sierra Leone, we showed that regression-ABC provides more realistic estimates for the duration parameters (latency and infectiousness) than the likelihood-based method. Overall, ABC based on a large variety of summary statistics and a regression method able to perform variable selection and avoid overfitting is a promising approach to analyze large phylogenies. PMID:28263987

Mathematics of Sensing, Exploitation, and Execution (MSEE) Hierarchical Representations for the Evaluation of Sensed Data

DTIC Science & Technology

2016-06-01

theories of the mammalian visual system, and exploiting descriptive text that may accompany a still image for improved inference. The focus of the Brown...test, computer vision, semantic description , street scenes, belief propagation, generative models, nonlinear filtering, sufficient statistics 16...visual system, and exploiting descriptive text that may accompany a still image for improved inference. The focus of the Brown team was on single images

STATISTICAL RELATIONAL LEARNING AND SCRIPT INDUCTION FOR TEXTUAL INFERENCE

DTIC Science & Technology

2017-12-01

E 23rd St Austin , TX 78712 8. PERFORMING ORGANIZATION REPORT NUMBER 9. SPONSORING/MONITORING AGENCY NAME(S) AND ADDRESS(ES) Air Force Research ...Processing (EMNLP), Austin , TX , 2016. 
 Pichotta, K. and Mooney, R.J., “Using Sentence-Level LSTM Language Models for Script Inference,” Proceedings of the...on Uphill Battles in Language Processing, Austin , TX , 2016. 
 Rajani, N., and Mooney, R. J., “Stacked Ensembles of Information Extractors for

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.

CADDIS Volume 3. Examples and Applications: Analytical Examples

EPA Pesticide Factsheets

Examples illustrating the use of statistical analysis to support different types of evidence, stream temperature, temperature inferred from macroinverterbate, macroinvertebrate responses, zinc concentrations, observed trait characteristics.

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 Relational Learning (SRL) as an Enabling Technology for Data Acquisition and Data Fusion in Video

DTIC Science & Technology

2013-05-02

REPORT Statistical Relational Learning ( SRL ) as an Enabling Technology for Data Acquisition and Data Fusion in Video 14. ABSTRACT 16. SECURITY...particular, it is important to reason about which portions of video require expensive analysis and storage. This project aims to make these...inferences using new and existing tools from Statistical Relational Learning ( SRL ). SRL is a recently emerging technology that enables the effective 1

Statistical Inference on Memory Structure of Processes and Its Applications to Information Theory

DTIC Science & Technology

2016-05-12

valued times series from a sample. (A practical algorithm to compute the estimator is a work in progress.) Third, finitely-valued spatial processes...ES) U.S. Army Research Office P.O. Box 12211 Research Triangle Park, NC 27709-2211 mathematical statistics; time series ; Markov chains; random...proved. Second, a statistical method is developed to estimate the memory depth of discrete- time and continuously-valued times series from a sample. (A

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.

Nonparametric predictive inference for combining diagnostic tests with parametric copula

NASA Astrophysics Data System (ADS)

Muhammad, Noryanti; Coolen, F. P. A.; Coolen-Maturi, T.

2017-09-01

Measuring the accuracy of diagnostic tests is crucial in many application areas including medicine and health care. The Receiver Operating Characteristic (ROC) curve is a popular statistical tool for describing the performance of diagnostic tests. The area under the ROC curve (AUC) is often used as a measure of the overall performance of the diagnostic test. In this paper, we interest in developing strategies for combining test results in order to increase the diagnostic accuracy. We introduce nonparametric predictive inference (NPI) for combining two diagnostic test results with considering dependence structure using parametric copula. NPI is a frequentist statistical framework for inference on a future observation based on past data observations. NPI uses lower and upper probabilities to quantify uncertainty and is based on only a few modelling assumptions. While copula is a well-known statistical concept for modelling dependence of random variables. A copula is a joint distribution function whose marginals are all uniformly distributed and it can be used to model the dependence separately from the marginal distributions. In this research, we estimate the copula density using a parametric method which is maximum likelihood estimator (MLE). We investigate the performance of this proposed method via data sets from the literature and discuss results to show how our method performs for different family of copulas. Finally, we briefly outline related challenges and opportunities for future research.

Analysis of a genetically structured variance heterogeneity model using the Box-Cox transformation.

PubMed

Yang, Ye; Christensen, Ole F; Sorensen, Daniel

2011-02-01

Over recent years, statistical support for the presence of genetic factors operating at the level of the environmental variance has come from fitting a genetically structured heterogeneous variance model to field or experimental data in various species. Misleading results may arise due to skewness of the marginal distribution of the data. To investigate how the scale of measurement affects inferences, the genetically structured heterogeneous variance model is extended to accommodate the family of Box-Cox transformations. Litter size data in rabbits and pigs that had previously been analysed in the untransformed scale were reanalysed in a scale equal to the mode of the marginal posterior distribution of the Box-Cox parameter. In the rabbit data, the statistical evidence for a genetic component at the level of the environmental variance is considerably weaker than that resulting from an analysis in the original metric. In the pig data, the statistical evidence is stronger, but the coefficient of correlation between additive genetic effects affecting mean and variance changes sign, compared to the results in the untransformed scale. The study confirms that inferences on variances can be strongly affected by the presence of asymmetry in the distribution of data. We recommend that to avoid one important source of spurious inferences, future work seeking support for a genetic component acting on environmental variation using a parametric approach based on normality assumptions confirms that these are met.

From multisensory integration in peripersonal space to bodily self-consciousness: from statistical regularities to statistical inference.

PubMed

Noel, Jean-Paul; Blanke, Olaf; Serino, Andrea

2018-06-06

Integrating information across sensory systems is a critical step toward building a cohesive representation of the environment and one's body, and as illustrated by numerous illusions, scaffolds subjective experience of the world and self. In the last years, classic principles of multisensory integration elucidated in the subcortex have been translated into the language of statistical inference understood by the neocortical mantle. Most importantly, a mechanistic systems-level description of multisensory computations via probabilistic population coding and divisive normalization is actively being put forward. In parallel, by describing and understanding bodily illusions, researchers have suggested multisensory integration of bodily inputs within the peripersonal space as a key mechanism in bodily self-consciousness. Importantly, certain aspects of bodily self-consciousness, although still very much a minority, have been recently casted under the light of modern computational understandings of multisensory integration. In doing so, we argue, the field of bodily self-consciousness may borrow mechanistic descriptions regarding the neural implementation of inference computations outlined by the multisensory field. This computational approach, leveraged on the understanding of multisensory processes generally, promises to advance scientific comprehension regarding one of the most mysterious questions puzzling humankind, that is, how our brain creates the experience of a self in interaction with the environment. © 2018 The Authors. Annals of the New York Academy of Sciences published by Wiley Periodicals, Inc. on behalf of New York Academy of Sciences.

Citizen surveillance for environmental monitoring: combining the efforts of citizen science and crowdsourcing in a quantitative data framework.

PubMed

Welvaert, Marijke; Caley, Peter

2016-01-01

Citizen science and crowdsourcing have been emerging as methods to collect data for surveillance and/or monitoring activities. They could be gathered under the overarching term citizen surveillance . The discipline, however, still struggles to be widely accepted in the scientific community, mainly because these activities are not embedded in a quantitative framework. This results in an ongoing discussion on how to analyze and make useful inference from these data. When considering the data collection process, we illustrate how citizen surveillance can be classified according to the nature of the underlying observation process measured in two dimensions-the degree of observer reporting intention and the control in observer detection effort. By classifying the observation process in these dimensions we distinguish between crowdsourcing, unstructured citizen science and structured citizen science. This classification helps the determine data processing and statistical treatment of these data for making inference. Using our framework, it is apparent that published studies are overwhelmingly associated with structured citizen science, and there are well developed statistical methods for the resulting data. In contrast, methods for making useful inference from purely crowd-sourced data remain under development, with the challenges of accounting for the unknown observation process considerable. Our quantitative framework for citizen surveillance calls for an integration of citizen science and crowdsourcing and provides a way forward to solve the statistical challenges inherent to citizen-sourced data.

Statistical Inference and Simulation with StatKey

ERIC Educational Resources Information Center

Quinn, Anne

2016-01-01

While looking for an inexpensive technology package to help students in statistics classes, the author found StatKey, a free Web-based app. Not only is StatKey useful for students' year-end projects, but it is also valuable for helping students learn fundamental content such as the central limit theorem. Using StatKey, students can engage in…

Assessing the Lexico-Grammatical Characteristics of a Corpus of College-Level Statistics Textbooks: Implications for Instruction and Practice

ERIC Educational Resources Information Center

Wagler, Amy E.; Lesser, Lawrence M.; González, Ariel I.; Leal, Luis

2015-01-01

A corpus of current editions of statistics textbooks was assessed to compare aspects and levels of readability for the topics of "measures of center," "line of fit," "regression analysis," and "regression inference." Analysis with lexical software of these text selections revealed that the large corpus can…

Counting statistics of many-particle quantum walks

NASA Astrophysics Data System (ADS)

Mayer, Klaus; Tichy, Malte C.; Mintert, Florian; Konrad, Thomas; Buchleitner, Andreas

2011-06-01

We study quantum walks of many noninteracting particles on a beam splitter array as a paradigmatic testing ground for the competition of single- and many-particle interference in a multimode system. We derive a general expression for multimode particle-number correlation functions, valid for bosons and fermions, and infer pronounced signatures of many-particle interferences in the counting statistics.

Opera Selecta Boxi. Technical Report No. 453.

ERIC Educational Resources Information Center

Geisser, Seymour

This document reviews "The Collected Works of George E. P. Box," edited by G. C. Tiao. The two-volume collection is divided into five parts. Each part is prefaced with an introduction by a statistical researcher giving his view of the motivation and highlights of the papers presented. The 16 papers in Part 1 on statistical inference,…

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.

Statistical inference to advance network models in epidemiology.

PubMed

Welch, David; Bansal, Shweta; Hunter, David R

2011-03-01

Contact networks are playing an increasingly important role in the study of epidemiology. Most of the existing work in this area has focused on considering the effect of underlying network structure on epidemic dynamics by using tools from probability theory and computer simulation. This work has provided much insight on the role that heterogeneity in host contact patterns plays on infectious disease dynamics. Despite the important understanding afforded by the probability and simulation paradigm, this approach does not directly address important questions about the structure of contact networks such as what is the best network model for a particular mode of disease transmission, how parameter values of a given model should be estimated, or how precisely the data allow us to estimate these parameter values. We argue that these questions are best answered within a statistical framework and discuss the role of statistical inference in estimating contact networks from epidemiological data. Copyright © 2011 Elsevier B.V. All rights reserved.

The potential for increased power from combining P-values testing the same hypothesis.

PubMed

Ganju, Jitendra; Julie Ma, Guoguang

2017-02-01

The conventional approach to hypothesis testing for formal inference is to prespecify a single test statistic thought to be optimal. However, we usually have more than one test statistic in mind for testing the null hypothesis of no treatment effect but we do not know which one is the most powerful. Rather than relying on a single p-value, combining p-values from prespecified multiple test statistics can be used for inference. Combining functions include Fisher's combination test and the minimum p-value. Using randomization-based tests, the increase in power can be remarkable when compared with a single test and Simes's method. The versatility of the method is that it also applies when the number of covariates exceeds the number of observations. The increase in power is large enough to prefer combined p-values over a single p-value. The limitation is that the method does not provide an unbiased estimator of the treatment effect and does not apply to situations when the model includes treatment by covariate interaction.

Additive hazards regression and partial likelihood estimation for ecological monitoring data across space.

PubMed

Lin, Feng-Chang; Zhu, Jun

2012-01-01

We develop continuous-time models for the analysis of environmental or ecological monitoring data such that subjects are observed at multiple monitoring time points across space. Of particular interest are additive hazards regression models where the baseline hazard function can take on flexible forms. We consider time-varying covariates and take into account spatial dependence via autoregression in space and time. We develop statistical inference for the regression coefficients via partial likelihood. Asymptotic properties, including consistency and asymptotic normality, are established for parameter estimates under suitable regularity conditions. Feasible algorithms utilizing existing statistical software packages are developed for computation. We also consider a simpler additive hazards model with homogeneous baseline hazard and develop hypothesis testing for homogeneity. A simulation study demonstrates that the statistical inference using partial likelihood has sound finite-sample properties and offers a viable alternative to maximum likelihood estimation. For illustration, we analyze data from an ecological study that monitors bark beetle colonization of red pines in a plantation of Wisconsin.

Statistical fluctuations of an ocean surface inferred from shoes and ships

NASA Astrophysics Data System (ADS)

Lerche, Ian; Maubeuge, Frédéric

1995-12-01

This paper shows that it is possible to roughly estimate some ocean properties using simple time-dependent statistical models of ocean fluctuations. Based on a real incident, the loss by a vessel of a Nike shoes container in the North Pacific Ocean, a statistical model was tested on data sets consisting of the Nike shoes found by beachcombers a few months later. This statistical treatment of the shoes' motion allows one to infer velocity trends of the Pacific Ocean, together with their fluctuation strengths. The idea is to suppose that there is a mean bulk flow speed that can depend on location on the ocean surface and time. The fluctuations of the surface flow speed are then treated as statistically random. The distribution of shoes is described in space and time using Markov probability processes related to the mean and fluctuating ocean properties. The aim of the exercise is to provide some of the properties of the Pacific Ocean that are otherwise calculated using a sophisticated numerical model, OSCURS, where numerous data are needed. Relevant quantities are sharply estimated, which can be useful to (1) constrain output results from OSCURS computations, and (2) elucidate the behavior patterns of ocean flow characteristics on long time scales.

Statistical Irreversible Thermodynamics in the Framework of Zubarev's Nonequilibrium Statistical Operator Method

NASA Astrophysics Data System (ADS)

Luzzi, R.; Vasconcellos, A. R.; Ramos, J. G.; Rodrigues, C. G.

2018-01-01

We describe the formalism of statistical irreversible thermodynamics constructed based on Zubarev's nonequilibrium statistical operator (NSO) method, which is a powerful and universal tool for investigating the most varied physical phenomena. We present brief overviews of the statistical ensemble formalism and statistical irreversible thermodynamics. The first can be constructed either based on a heuristic approach or in the framework of information theory in the Jeffreys-Jaynes scheme of scientific inference; Zubarev and his school used both approaches in formulating the NSO method. We describe the main characteristics of statistical irreversible thermodynamics and discuss some particular considerations of several authors. We briefly describe how Rosenfeld, Bohr, and Prigogine proposed to derive a thermodynamic uncertainty principle.

Abnormal agency experiences in schizophrenia patients: Examining the role of psychotic symptoms and familial risk.

PubMed

Prikken, Merel; van der Weiden, Anouk; Renes, Robert A; Koevoets, Martijn G J C; Heering, Henriette D; Kahn, René S; Aarts, Henk; van Haren, Neeltje E M

2017-04-01

Experiencing self-agency over one's own action outcomes is essential for social functioning. Recent research revealed that patients with schizophrenia do not use implicitly available information about their action-outcomes (i.e., prime-based agency inference) to arrive at self-agency experiences. Here, we examined whether this is related to symptoms and/or familial risk to develop the disease. Fifty-four patients, 54 controls, and 19 unaffected (and unrelated) siblings performed an agency inference task, in which experienced agency was measured over action-outcomes that matched or mismatched outcome-primes that were presented before action performance. The Positive and Negative Syndrome Scale (PANSS) and Comprehensive Assessment of Symptoms and History (CASH) were administered to assess psychopathology. Impairments in prime-based inferences did not differ between patients with symptoms of over- and underattribution. However, patients with agency underattribution symptoms reported significantly lower overall self-agency experiences. Siblings displayed stronger prime-based agency inferences than patients, but weaker prime-based inferences than healthy controls. However, these differences were not statistically significant. Findings suggest that impairments in prime-based agency inferences may be a trait characteristic of schizophrenia. Moreover, this study may stimulate further research on the familial basis and the clinical relevance of impairments in implicit agency inferences. Copyright © 2017 Elsevier Ireland Ltd. All rights reserved.

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).

Inferring time derivatives including cell growth rates using Gaussian processes

NASA Astrophysics Data System (ADS)

Swain, Peter S.; Stevenson, Keiran; Leary, Allen; Montano-Gutierrez, Luis F.; Clark, Ivan B. N.; Vogel, Jackie; Pilizota, Teuta

2016-12-01

Often the time derivative of a measured variable is of as much interest as the variable itself. For a growing population of biological cells, for example, the population's growth rate is typically more important than its size. Here we introduce a non-parametric method to infer first and second time derivatives as a function of time from time-series data. Our approach is based on Gaussian processes and applies to a wide range of data. In tests, the method is at least as accurate as others, but has several advantages: it estimates errors both in the inference and in any summary statistics, such as lag times, and allows interpolation with the corresponding error estimation. As illustrations, we infer growth rates of microbial cells, the rate of assembly of an amyloid fibril and both the speed and acceleration of two separating spindle pole bodies. Our algorithm should thus be broadly applicable.

Remembrance of inferences past: Amortization in human hypothesis generation.

PubMed

Dasgupta, Ishita; Schulz, Eric; Goodman, Noah D; Gershman, Samuel J

2018-05-21

Bayesian models of cognition assume that people compute probability distributions over hypotheses. However, the required computations are frequently intractable or prohibitively expensive. Since people often encounter many closely related distributions, selective reuse of computations (amortized inference) is a computationally efficient use of the brain's limited resources. We present three experiments that provide evidence for amortization in human probabilistic reasoning. When sequentially answering two related queries about natural scenes, participants' responses to the second query systematically depend on the structure of the first query. This influence is sensitive to the content of the queries, only appearing when the queries are related. Using a cognitive load manipulation, we find evidence that people amortize summary statistics of previous inferences, rather than storing the entire distribution. These findings support the view that the brain trades off accuracy and computational cost, to make efficient use of its limited cognitive resources to approximate probabilistic inference. Copyright © 2018 Elsevier B.V. All rights reserved.

Confidence Intervals for the Between-Study Variance in Random Effects Meta-Analysis Using Generalised Cochran Heterogeneity Statistics

ERIC Educational Resources Information Center

Jackson, Dan

2013-01-01

Statistical inference is problematic in the common situation in meta-analysis where the random effects model is fitted to just a handful of studies. In particular, the asymptotic theory of maximum likelihood provides a poor approximation, and Bayesian methods are sensitive to the prior specification. Hence, less efficient, but easily computed and…

Statistical Theory for the "RCT-YES" Software: Design-Based Causal Inference for RCTs. NCEE 2015-4011

ERIC Educational Resources Information Center

Schochet, Peter Z.

2015-01-01

This report presents the statistical theory underlying the "RCT-YES" software that estimates and reports impacts for RCTs for a wide range of designs used in social policy research. The report discusses a unified, non-parametric design-based approach for impact estimation using the building blocks of the Neyman-Rubin-Holland causal…

Managing heteroscedasticity in general linear models.

PubMed

Rosopa, Patrick J; Schaffer, Meline M; Schroeder, Amber N

2013-09-01

Heteroscedasticity refers to a phenomenon where data violate a statistical assumption. This assumption is known as homoscedasticity. When the homoscedasticity assumption is violated, this can lead to increased Type I error rates or decreased statistical power. Because this can adversely affect substantive conclusions, the failure to detect and manage heteroscedasticity could have serious implications for theory, research, and practice. In addition, heteroscedasticity is not uncommon in the behavioral and social sciences. Thus, in the current article, we synthesize extant literature in applied psychology, econometrics, quantitative psychology, and statistics, and we offer recommendations for researchers and practitioners regarding available procedures for detecting heteroscedasticity and mitigating its effects. In addition to discussing the strengths and weaknesses of various procedures and comparing them in terms of existing simulation results, we describe a 3-step data-analytic process for detecting and managing heteroscedasticity: (a) fitting a model based on theory and saving residuals, (b) the analysis of residuals, and (c) statistical inferences (e.g., hypothesis tests and confidence intervals) involving parameter estimates. We also demonstrate this data-analytic process using an illustrative example. Overall, detecting violations of the homoscedasticity assumption and mitigating its biasing effects can strengthen the validity of inferences from behavioral and social science data.

Biological Parametric Mapping: A Statistical Toolbox for Multi-Modality Brain Image Analysis

PubMed Central

Casanova, Ramon; Ryali, Srikanth; Baer, Aaron; Laurienti, Paul J.; Burdette, Jonathan H.; Hayasaka, Satoru; Flowers, Lynn; Wood, Frank; Maldjian, Joseph A.

2006-01-01

In recent years multiple brain MR imaging modalities have emerged; however, analysis methodologies have mainly remained modality specific. In addition, when comparing across imaging modalities, most researchers have been forced to rely on simple region-of-interest type analyses, which do not allow the voxel-by-voxel comparisons necessary to answer more sophisticated neuroscience questions. To overcome these limitations, we developed a toolbox for multimodal image analysis called biological parametric mapping (BPM), based on a voxel-wise use of the general linear model. The BPM toolbox incorporates information obtained from other modalities as regressors in a voxel-wise analysis, thereby permitting investigation of more sophisticated hypotheses. The BPM toolbox has been developed in MATLAB with a user friendly interface for performing analyses, including voxel-wise multimodal correlation, ANCOVA, and multiple regression. It has a high degree of integration with the SPM (statistical parametric mapping) software relying on it for visualization and statistical inference. Furthermore, statistical inference for a correlation field, rather than a widely-used T-field, has been implemented in the correlation analysis for more accurate results. An example with in-vivo data is presented demonstrating the potential of the BPM methodology as a tool for multimodal image analysis. PMID:17070709

Redshift data and statistical inference

NASA Technical Reports Server (NTRS)

Newman, William I.; Haynes, Martha P.; Terzian, Yervant

1994-01-01

Frequency histograms and the 'power spectrum analysis' (PSA) method, the latter developed by Yu & Peebles (1969), have been widely employed as techniques for establishing the existence of periodicities. We provide a formal analysis of these two classes of methods, including controlled numerical experiments, to better understand their proper use and application. In particular, we note that typical published applications of frequency histograms commonly employ far greater numbers of class intervals or bins than is advisable by statistical theory sometimes giving rise to the appearance of spurious patterns. The PSA method generates a sequence of random numbers from observational data which, it is claimed, is exponentially distributed with unit mean and variance, essentially independent of the distribution of the original data. We show that the derived random processes is nonstationary and produces a small but systematic bias in the usual estimate of the mean and variance. Although the derived variable may be reasonably described by an exponential distribution, the tail of the distribution is far removed from that of an exponential, thereby rendering statistical inference and confidence testing based on the tail of the distribution completely unreliable. Finally, we examine a number of astronomical examples wherein these methods have been used giving rise to widespread acceptance of statistically unconfirmed conclusions.

Quantitative studies of bird movement: A methodological review

USGS Publications Warehouse

Nichols, J.D.; Kaiser, A.

1999-01-01

The past several years have seen the development of a number of statistical models and methods for drawing inferences about bird movement using data from marked individuals. It can be difficult to keep up with this rapid development of new methods, so our purpose here is to categorize and review methods for drawing inferences about avian movement. We also outline recommendations about future work, dealing both with methodological developments and with studies directed at hypotheses about bird movement of interest from conservation, management, or ecological perspectives.

Quantitative studies of bird movement: a methodological review

USGS Publications Warehouse

Nichols, J.D.; Kaiser, A.

1999-01-01

The past several years have seen development of a number of statistical models and methods for drawing inferences about bird movement using data from marked individuals. It can be difficult to keep up with this rapid development of new methods, so our purpose here is to categorize and review methods for drawing inferences about avian movement. We also outline recommendations about future work dealing both with methods development and actual studies directed at hypotheses about bird movement of interest from conservation, management, or ecological perspectives.

From Neutron Star Observables to the Equation of State. II. Bayesian Inference of Equation of State Pressures

NASA Astrophysics Data System (ADS)

Raithel, Carolyn A.; Özel, Feryal; Psaltis, Dimitrios

2017-08-01

One of the key goals of observing neutron stars is to infer the equation of state (EoS) of the cold, ultradense matter in their interiors. Here, we present a Bayesian statistical method of inferring the pressures at five fixed densities, from a sample of mock neutron star masses and radii. We show that while five polytropic segments are needed for maximum flexibility in the absence of any prior knowledge of the EoS, regularizers are also necessary to ensure that simple underlying EoS are not over-parameterized. For ideal data with small measurement uncertainties, we show that the pressure at roughly twice the nuclear saturation density, {ρ }{sat}, can be inferred to within 0.3 dex for many realizations of potential sources of uncertainties. The pressures of more complicated EoS with significant phase transitions can also be inferred to within ˜30%. We also find that marginalizing the multi-dimensional parameter space of pressure to infer a mass-radius relation can lead to biases of nearly 1 km in radius, toward larger radii. Using the full, five-dimensional posterior likelihoods avoids this bias.

Insight From the Statistics of Nothing: Estimating Limits of Change Detection Using Inferred No-Change Areas in DEM Difference Maps and Application to Landslide Hazard Studies

NASA Astrophysics Data System (ADS)

Haneberg, W. C.

2017-12-01

Remote characterization of new landslides or areas of ongoing movement using differences in high resolution digital elevation models (DEMs) created through time, for example before and after major rains or earthquakes, is an attractive proposition. In the case of large catastrophic landslides, changes may be apparent enough that simple subtraction suffices. In other cases, statistical noise can obscure landslide signatures and place practical limits on detection. In ideal cases on land, GPS surveys of representative areas at the time of DEM creation can quantify the inherent errors. In less-than-ideal terrestrial cases and virtually all submarine cases, it may be impractical or impossible to independently estimate the DEM errors. Examining DEM difference statistics for areas reasonably inferred to have no change, however, can provide insight into the limits of detectability. Data from inferred no-change areas of airborne LiDAR DEM difference maps of the 2014 Oso, Washington landslide and landslide-prone colluvium slopes along the Ohio River valley in northern Kentucky, show that DEM difference maps can have non-zero mean and slope dependent error components consistent with published studies of DEM errors. Statistical thresholds derived from DEM difference error and slope data can help to distinguish between DEM differences that are likely real—and which may indicate landsliding—from those that are likely spurious or irrelevant. This presentation describes and compares two different approaches, one based upon a heuristic assumption about the proportion of the study area likely covered by new landslides and another based upon the amount of change necessary to ensure difference at a specified level of probability.

Fast maximum likelihood estimation using continuous-time neural point process models.

PubMed

Lepage, Kyle Q; MacDonald, Christopher J

2015-06-01

A recent report estimates that the number of simultaneously recorded neurons is growing exponentially. A commonly employed statistical paradigm using discrete-time point process models of neural activity involves the computation of a maximum-likelihood estimate. The time to computate this estimate, per neuron, is proportional to the number of bins in a finely spaced discretization of time. By using continuous-time models of neural activity and the optimally efficient Gaussian quadrature, memory requirements and computation times are dramatically decreased in the commonly encountered situation where the number of parameters p is much less than the number of time-bins n. In this regime, with q equal to the quadrature order, memory requirements are decreased from O(np) to O(qp), and the number of floating-point operations are decreased from O(np(2)) to O(qp(2)). Accuracy of the proposed estimates is assessed based upon physiological consideration, error bounds, and mathematical results describing the relation between numerical integration error and numerical error affecting both parameter estimates and the observed Fisher information. A check is provided which is used to adapt the order of numerical integration. The procedure is verified in simulation and for hippocampal recordings. It is found that in 95 % of hippocampal recordings a q of 60 yields numerical error negligible with respect to parameter estimate standard error. Statistical inference using the proposed methodology is a fast and convenient alternative to statistical inference performed using a discrete-time point process model of neural activity. It enables the employment of the statistical methodology available with discrete-time inference, but is faster, uses less memory, and avoids any error due to discretization.

On statistical inference in time series analysis of the evolution of road safety.

PubMed

Commandeur, Jacques J F; Bijleveld, Frits D; Bergel-Hayat, Ruth; Antoniou, Constantinos; Yannis, George; Papadimitriou, Eleonora

2013-11-01

Data collected for building a road safety observatory usually include observations made sequentially through time. Examples of such data, called time series data, include annual (or monthly) number of road traffic accidents, traffic fatalities or vehicle kilometers driven in a country, as well as the corresponding values of safety performance indicators (e.g., data on speeding, seat belt use, alcohol use, etc.). Some commonly used statistical techniques imply assumptions that are often violated by the special properties of time series data, namely serial dependency among disturbances associated with the observations. The first objective of this paper is to demonstrate the impact of such violations to the applicability of standard methods of statistical inference, which leads to an under or overestimation of the standard error and consequently may produce erroneous inferences. Moreover, having established the adverse consequences of ignoring serial dependency issues, the paper aims to describe rigorous statistical techniques used to overcome them. In particular, appropriate time series analysis techniques of varying complexity are employed to describe the development over time, relating the accident-occurrences to explanatory factors such as exposure measures or safety performance indicators, and forecasting the development into the near future. Traditional regression models (whether they are linear, generalized linear or nonlinear) are shown not to naturally capture the inherent dependencies in time series data. Dedicated time series analysis techniques, such as the ARMA-type and DRAG approaches are discussed next, followed by structural time series models, which are a subclass of state space methods. The paper concludes with general recommendations and practice guidelines for the use of time series models in road safety research. Copyright © 2012 Elsevier Ltd. All rights reserved.

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.

Approximation of epidemic models by diffusion processes and their statistical inference.

PubMed

Guy, Romain; Larédo, Catherine; Vergu, Elisabeta

2015-02-01

Multidimensional continuous-time Markov jump processes [Formula: see text] on [Formula: see text] form a usual set-up for modeling [Formula: see text]-like epidemics. However, when facing incomplete epidemic data, inference based on [Formula: see text] is not easy to be achieved. Here, we start building a new framework for the estimation of key parameters of epidemic models based on statistics of diffusion processes approximating [Formula: see text]. First, previous results on the approximation of density-dependent [Formula: see text]-like models by diffusion processes with small diffusion coefficient [Formula: see text], where [Formula: see text] is the population size, are generalized to non-autonomous systems. Second, our previous inference results on discretely observed diffusion processes with small diffusion coefficient are extended to time-dependent diffusions. Consistent and asymptotically Gaussian estimates are obtained for a fixed number [Formula: see text] of observations, which corresponds to the epidemic context, and for [Formula: see text]. A correction term, which yields better estimates non asymptotically, is also included. Finally, performances and robustness of our estimators with respect to various parameters such as [Formula: see text] (the basic reproduction number), [Formula: see text], [Formula: see text] are investigated on simulations. Two models, [Formula: see text] and [Formula: see text], corresponding to single and recurrent outbreaks, respectively, are used to simulate data. The findings indicate that our estimators have good asymptotic properties and behave noticeably well for realistic numbers of observations and population sizes. This study lays the foundations of a generic inference method currently under extension to incompletely observed epidemic data. Indeed, contrary to the majority of current inference techniques for partially observed processes, which necessitates computer intensive simulations, our method being mostly an analytical approach requires only the classical optimization steps.

How to infer relative fitness from a sample of genomic sequences.

PubMed

Dayarian, Adel; Shraiman, Boris I

2014-07-01

Mounting evidence suggests that natural populations can harbor extensive fitness diversity with numerous genomic loci under selection. It is also known that genealogical trees for populations under selection are quantifiably different from those expected under neutral evolution and described statistically by Kingman's coalescent. While differences in the statistical structure of genealogies have long been used as a test for the presence of selection, the full extent of the information that they contain has not been exploited. Here we demonstrate that the shape of the reconstructed genealogical tree for a moderately large number of random genomic samples taken from a fitness diverse, but otherwise unstructured, asexual population can be used to predict the relative fitness of individuals within the sample. To achieve this we define a heuristic algorithm, which we test in silico, using simulations of a Wright-Fisher model for a realistic range of mutation rates and selection strength. Our inferred fitness ranking is based on a linear discriminator that identifies rapidly coalescing lineages in the reconstructed tree. Inferred fitness ranking correlates strongly with actual fitness, with a genome in the top 10% ranked being in the top 20% fittest with false discovery rate of 0.1-0.3, depending on the mutation/selection parameters. The ranking also enables us to predict the genotypes that future populations inherit from the present one. While the inference accuracy increases monotonically with sample size, samples of 200 nearly saturate the performance. We propose that our approach can be used for inferring relative fitness of genomes obtained in single-cell sequencing of tumors and in monitoring viral outbreaks. Copyright © 2014 by the Genetics Society of America.

Successful Reconstruction of a Physiological Circuit with Known Connectivity from Spiking Activity Alone

PubMed Central

Gerhard, Felipe; Kispersky, Tilman; Gutierrez, Gabrielle J.; Marder, Eve; Kramer, Mark; Eden, Uri

2013-01-01

Identifying the structure and dynamics of synaptic interactions between neurons is the first step to understanding neural network dynamics. The presence of synaptic connections is traditionally inferred through the use of targeted stimulation and paired recordings or by post-hoc histology. More recently, causal network inference algorithms have been proposed to deduce connectivity directly from electrophysiological signals, such as extracellularly recorded spiking activity. Usually, these algorithms have not been validated on a neurophysiological data set for which the actual circuitry is known. Recent work has shown that traditional network inference algorithms based on linear models typically fail to identify the correct coupling of a small central pattern generating circuit in the stomatogastric ganglion of the crab Cancer borealis. In this work, we show that point process models of observed spike trains can guide inference of relative connectivity estimates that match the known physiological connectivity of the central pattern generator up to a choice of threshold. We elucidate the necessary steps to derive faithful connectivity estimates from a model that incorporates the spike train nature of the data. We then apply the model to measure changes in the effective connectivity pattern in response to two pharmacological interventions, which affect both intrinsic neural dynamics and synaptic transmission. Our results provide the first successful application of a network inference algorithm to a circuit for which the actual physiological synapses between neurons are known. The point process methodology presented here generalizes well to larger networks and can describe the statistics of neural populations. In general we show that advanced statistical models allow for the characterization of effective network structure, deciphering underlying network dynamics and estimating information-processing capabilities. PMID:23874181

Reconstructing temperatures from lake sediments in northern Europe: what do the biological proxies really tell us?

NASA Astrophysics Data System (ADS)

Cunningham, Laura; Holmes, Naomi; Bigler, Christian; Dadal, Anna; Bergman, Jonas; Eriksson, Lars; Brooks, Stephen; Langdon, Pete; Caseldine, Chris

2010-05-01

Over the past two decades considerable effort has been devoted to quantitatively reconstructing temperatures from biological proxies preserved in lake sediments, via transfer functions. Such transfer functions typically consist of modern sediment samples, collected over a broad environmental gradient. Correlations between the biological communities and environmental parameters observed over these broad gradients are assumed to be equally valid temporally. The predictive ability of such spatially based transfer functions has traditionally been assessed by comparisons of measured and inferred temperatures within the calibration sets, with little validation against historical data. Although statistical techniques such as bootstrapping may improve error estimation, this approach remains partly a circular argument. This raises the question of how reliable such reconstructions are for inferring past changes in temperature? In order to address this question, we used transfer functions to reconstruct July temperatures from diatoms and chironomids from several locations across northern Europe. The transfer functions used showed good internal calibration statistics (r2 = 0.66 - 0.91). The diatom and chironomid inferred July air temperatures were compared to local observational records. As the sediment records were non-annual, all data were first smoothed using a 15 yr moving average filter. None of the five biologically-inferred temperature records were correlated with the local meteorological records. Furthermore, diatom inferred temperatures did not agree with chironomid inferred temperatures from the same cores from the same sites. In an attempt to understand this poor performance the biological proxy data was compressed using principal component analysis (PCA), and the PCA axes compared to the local meteorological data. These analyses clearly demonstrated that July temperatures were not correlated with the biological data at these locations. Some correlations were observed between the biological proxies and autumn and spring temperatures, although this varied slightly between sites and proxies. For example, chironomid data from Iceland was most strongly correlated with temperatures in February, March and April whilst in northern Sweden, the chironomid data was most strongly correlated with temperatures in March, April and May. It is suggested that the biological data at these sites may be responding to changes in the length of the ice-free period or hydrological regimes (including snow melt), rather than temperature per se. Our findings demonstrate the need to validate inferred temperatures against local meteorological data. Where such validation cannot be undertaken, inferred temperature reconstructions should be treated cautiously.

After p Values: The New Statistics for Undergraduate Neuroscience Education.

PubMed

Calin-Jageman, Robert J

2017-01-01

Statistical inference is a methodological cornerstone for neuroscience education. For many years this has meant inculcating neuroscience majors into null hypothesis significance testing with p values. There is increasing concern, however, about the pervasive misuse of p values. It is time to start planning statistics curricula for neuroscience majors that replaces or de-emphasizes p values. One promising alternative approach is what Cumming has dubbed the "New Statistics", an approach that emphasizes effect sizes, confidence intervals, meta-analysis, and open science. I give an example of the New Statistics in action and describe some of the key benefits of adopting this approach in neuroscience education.

PROUCL 4.0 SOFTWARE

EPA Science Inventory

Statistical inference, including both estimation and hypotheses testing approaches, is routinely used to: estimate environmental parameters of interest, such as exposure point concentration (EPC) terms, not-to-exceed values, and background level threshold values (BTVs) for contam...

Reproducing a Prospective Clinical Study as a Computational Retrospective Study in MIMIC-II.

PubMed

Kury, Fabrício S P; Huser, Vojtech; Cimino, James J

2015-01-01

In this paper we sought to reproduce, as a computational retrospective study in an EHR database (MIMIC-II), a recent large prospective clinical study: the 2013 publication, by the Japanese Association for Acute Medicine (JAAM), about disseminated intravascular coagulation, in the journal Critical Care (PMID: 23787004). We designed in SQL and Java a set of electronic phenotypes that reproduced the study's data sampling, and used R to perform the same statistical inference procedures. All produced source code is available online at https://github.com/fabkury/paamia2015. Our program identified 2,257 eligible patients in MIMIC-II, and the results remarkably agreed with the prospective study. A minority of the needed data elements was not found in MIMIC-II, and statistically significant inferences were possible in the majority of the cases.

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.

Assessing dynamics, spatial scale, and uncertainty in task-related brain network analyses

PubMed Central

Stephen, Emily P.; Lepage, Kyle Q.; Eden, Uri T.; Brunner, Peter; Schalk, Gerwin; Brumberg, Jonathan S.; Guenther, Frank H.; Kramer, Mark A.

2014-01-01

The brain is a complex network of interconnected elements, whose interactions evolve dynamically in time to cooperatively perform specific functions. A common technique to probe these interactions involves multi-sensor recordings of brain activity during a repeated task. Many techniques exist to characterize the resulting task-related activity, including establishing functional networks, which represent the statistical associations between brain areas. Although functional network inference is commonly employed to analyze neural time series data, techniques to assess the uncertainty—both in the functional network edges and the corresponding aggregate measures of network topology—are lacking. To address this, we describe a statistically principled approach for computing uncertainty in functional networks and aggregate network measures in task-related data. The approach is based on a resampling procedure that utilizes the trial structure common in experimental recordings. We show in simulations that this approach successfully identifies functional networks and associated measures of confidence emergent during a task in a variety of scenarios, including dynamically evolving networks. In addition, we describe a principled technique for establishing functional networks based on predetermined regions of interest using canonical correlation. Doing so provides additional robustness to the functional network inference. Finally, we illustrate the use of these methods on example invasive brain voltage recordings collected during an overt speech task. The general strategy described here—appropriate for static and dynamic network inference and different statistical measures of coupling—permits the evaluation of confidence in network measures in a variety of settings common to neuroscience. PMID:24678295

Slowdowns in diversification rates from real phylogenies may not be real.

PubMed

Cusimano, Natalie; Renner, Susanne S

2010-07-01

Studies of diversification patterns often find a slowing in lineage accumulation toward the present. This seemingly pervasive pattern of rate downturns has been taken as evidence for adaptive radiations, density-dependent regulation, and metacommunity species interactions. The significance of rate downturns is evaluated with statistical tests (the gamma statistic and Monte Carlo constant rates (MCCR) test; birth-death likelihood models and Akaike Information Criterion [AIC] scores) that rely on null distributions, which assume that the included species are a random sample of the entire clade. Sampling in real phylogenies, however, often is nonrandom because systematists try to include early-diverging species or representatives of previous intrataxon classifications. We studied the effects of biased sampling, structured sampling, and random sampling by experimentally pruning simulated trees (60 and 150 species) as well as a completely sampled empirical tree (58 species) and then applying the gamma statistic/MCCR test and birth-death likelihood models/AIC scores to assess rate changes. For trees with random species sampling, the true model (i.e., the one fitting the complete phylogenies) could be inferred in most cases. Oversampling deep nodes, however, strongly biases inferences toward downturns, with simulations of structured and biased sampling suggesting that this occurs when sampling percentages drop below 80%. The magnitude of the effect and the sensitivity of diversification rate models is such that a useful rule of thumb may be not to infer rate downturns from real trees unless they have >80% species sampling.

Assessing dynamics, spatial scale, and uncertainty in task-related brain network analyses.

PubMed

Stephen, Emily P; Lepage, Kyle Q; Eden, Uri T; Brunner, Peter; Schalk, Gerwin; Brumberg, Jonathan S; Guenther, Frank H; Kramer, Mark A

2014-01-01

The brain is a complex network of interconnected elements, whose interactions evolve dynamically in time to cooperatively perform specific functions. A common technique to probe these interactions involves multi-sensor recordings of brain activity during a repeated task. Many techniques exist to characterize the resulting task-related activity, including establishing functional networks, which represent the statistical associations between brain areas. Although functional network inference is commonly employed to analyze neural time series data, techniques to assess the uncertainty-both in the functional network edges and the corresponding aggregate measures of network topology-are lacking. To address this, we describe a statistically principled approach for computing uncertainty in functional networks and aggregate network measures in task-related data. The approach is based on a resampling procedure that utilizes the trial structure common in experimental recordings. We show in simulations that this approach successfully identifies functional networks and associated measures of confidence emergent during a task in a variety of scenarios, including dynamically evolving networks. In addition, we describe a principled technique for establishing functional networks based on predetermined regions of interest using canonical correlation. Doing so provides additional robustness to the functional network inference. Finally, we illustrate the use of these methods on example invasive brain voltage recordings collected during an overt speech task. The general strategy described here-appropriate for static and dynamic network inference and different statistical measures of coupling-permits the evaluation of confidence in network measures in a variety of settings common to neuroscience.

Pilot points method for conditioning multiple-point statistical facies simulation on flow data

NASA Astrophysics Data System (ADS)

Ma, Wei; Jafarpour, Behnam

2018-05-01

We propose a new pilot points method for conditioning discrete multiple-point statistical (MPS) facies simulation on dynamic flow data. While conditioning MPS simulation on static hard data is straightforward, their calibration against nonlinear flow data is nontrivial. The proposed method generates conditional models from a conceptual model of geologic connectivity, known as a training image (TI), by strategically placing and estimating pilot points. To place pilot points, a score map is generated based on three sources of information: (i) the uncertainty in facies distribution, (ii) the model response sensitivity information, and (iii) the observed flow data. Once the pilot points are placed, the facies values at these points are inferred from production data and then are used, along with available hard data at well locations, to simulate a new set of conditional facies realizations. While facies estimation at the pilot points can be performed using different inversion algorithms, in this study the ensemble smoother (ES) is adopted to update permeability maps from production data, which are then used to statistically infer facies types at the pilot point locations. The developed method combines the information in the flow data and the TI by using the former to infer facies values at selected locations away from the wells and the latter to ensure consistent facies structure and connectivity where away from measurement locations. Several numerical experiments are used to evaluate the performance of the developed method and to discuss its important properties.

Assimilating Flow Data into Complex Multiple-Point Statistical Facies Models Using Pilot Points Method

NASA Astrophysics Data System (ADS)

Ma, W.; Jafarpour, B.

2017-12-01

We develop a new pilot points method for conditioning discrete multiple-point statistical (MPS) facies simulation on dynamic flow data. While conditioning MPS simulation on static hard data is straightforward, their calibration against nonlinear flow data is nontrivial. The proposed method generates conditional models from a conceptual model of geologic connectivity, known as a training image (TI), by strategically placing and estimating pilot points. To place pilot points, a score map is generated based on three sources of information:: (i) the uncertainty in facies distribution, (ii) the model response sensitivity information, and (iii) the observed flow data. Once the pilot points are placed, the facies values at these points are inferred from production data and are used, along with available hard data at well locations, to simulate a new set of conditional facies realizations. While facies estimation at the pilot points can be performed using different inversion algorithms, in this study the ensemble smoother (ES) and its multiple data assimilation variant (ES-MDA) are adopted to update permeability maps from production data, which are then used to statistically infer facies types at the pilot point locations. The developed method combines the information in the flow data and the TI by using the former to infer facies values at select locations away from the wells and the latter to ensure consistent facies structure and connectivity where away from measurement locations. Several numerical experiments are used to evaluate the performance of the developed method and to discuss its important properties.

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.

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.

SIG-VISA: Signal-based Vertically Integrated Seismic Monitoring

NASA Astrophysics Data System (ADS)

Moore, D.; Mayeda, K. M.; Myers, S. C.; Russell, S.

2013-12-01

Traditional seismic monitoring systems rely on discrete detections produced by station processing software; however, while such detections may constitute a useful summary of station activity, they discard large amounts of information present in the original recorded signal. We present SIG-VISA (Signal-based Vertically Integrated Seismic Analysis), a system for seismic monitoring through Bayesian inference on seismic signals. By directly modeling the recorded signal, our approach incorporates additional information unavailable to detection-based methods, enabling higher sensitivity and more accurate localization using techniques such as waveform matching. SIG-VISA's Bayesian forward model of seismic signal envelopes includes physically-derived models of travel times and source characteristics as well as Gaussian process (kriging) statistical models of signal properties that combine interpolation of historical data with extrapolation of learned physical trends. Applying Bayesian inference, we evaluate the model on earthquakes as well as the 2009 DPRK test event, demonstrating a waveform matching effect as part of the probabilistic inference, along with results on event localization and sensitivity. In particular, we demonstrate increased sensitivity from signal-based modeling, in which the SIGVISA signal model finds statistical evidence for arrivals even at stations for which the IMS station processing failed to register any detection.

Impact of Bayesian Priors on the Characterization of Binary Black Hole Coalescences

NASA Astrophysics Data System (ADS)

Vitale, Salvatore; Gerosa, Davide; Haster, Carl-Johan; Chatziioannou, Katerina; Zimmerman, Aaron

2017-12-01

In a regime where data are only mildly informative, prior choices can play a significant role in Bayesian statistical inference, potentially affecting the inferred physics. We show this is indeed the case for some of the parameters inferred from current gravitational-wave measurements of binary black hole coalescences. We reanalyze the first detections performed by the twin LIGO interferometers using alternative (and astrophysically motivated) prior assumptions. We find different prior distributions can introduce deviations in the resulting posteriors that impact the physical interpretation of these systems. For instance, (i) limits on the 90% credible interval on the effective black hole spin χeff are subject to variations of ˜10 % if a prior with black hole spins mostly aligned to the binary's angular momentum is considered instead of the standard choice of isotropic spin directions, and (ii) under priors motivated by the initial stellar mass function, we infer tighter constraints on the black hole masses, and in particular, we find no support for any of the inferred masses within the putative mass gap M ≲5 M⊙.

Impact of Bayesian Priors on the Characterization of Binary Black Hole Coalescences.

PubMed

Vitale, Salvatore; Gerosa, Davide; Haster, Carl-Johan; Chatziioannou, Katerina; Zimmerman, Aaron

2017-12-22

In a regime where data are only mildly informative, prior choices can play a significant role in Bayesian statistical inference, potentially affecting the inferred physics. We show this is indeed the case for some of the parameters inferred from current gravitational-wave measurements of binary black hole coalescences. We reanalyze the first detections performed by the twin LIGO interferometers using alternative (and astrophysically motivated) prior assumptions. We find different prior distributions can introduce deviations in the resulting posteriors that impact the physical interpretation of these systems. For instance, (i) limits on the 90% credible interval on the effective black hole spin χ_{eff} are subject to variations of ∼10% if a prior with black hole spins mostly aligned to the binary's angular momentum is considered instead of the standard choice of isotropic spin directions, and (ii) under priors motivated by the initial stellar mass function, we infer tighter constraints on the black hole masses, and in particular, we find no support for any of the inferred masses within the putative mass gap M≲5  M_{⊙}.

Inferred Lunar Boulder Distributions at Decimeter Scales

NASA Technical Reports Server (NTRS)

Baloga, S. M.; Glaze, L. S.; Spudis, P. D.

2012-01-01

Block size distributions of impact deposits on the Moon are diagnostic of the impact process and environmental effects, such as target lithology and weathering. Block size distributions are also important factors in trafficability, habitability, and possibly the identification of indigenous resources. Lunar block sizes have been investigated for many years for many purposes [e.g., 1-3]. An unresolved issue is the extent to which lunar block size distributions can be extrapolated to scales smaller than limits of resolution of direct measurement. This would seem to be a straightforward statistical application, but it is complicated by two issues. First, the cumulative size frequency distribution of observable boulders rolls over due to resolution limitations at the small end. Second, statistical regression provides the best fit only around the centroid of the data [4]. Confidence and prediction limits splay away from the best fit at the endpoints resulting in inferences in the boulder density at the CPR scale that can differ by many orders of magnitude [4]. These issues were originally investigated by Cintala and McBride [2] using Surveyor data. The objective of this study was to determine whether the measured block size distributions from Lunar Reconnaissance Orbiter Camera - Narrow Angle Camera (LROC-NAC) images (m-scale resolution) can be used to infer the block size distribution at length scales comparable to Mini-RF Circular Polarization Ratio (CPR) scales, nominally taken as 10 cm. This would set the stage for assessing correlations of inferred block size distributions with CPR returns [6].

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.

Map LineUps: Effects of spatial structure on graphical inference.

PubMed

Beecham, Roger; Dykes, Jason; Meulemans, Wouter; Slingsby, Aidan; Turkay, Cagatay; Wood, Jo

2017-01-01

Fundamental to the effective use of visualization as an analytic and descriptive tool is the assurance that presenting data visually provides the capability of making inferences from what we see. This paper explores two related approaches to quantifying the confidence we may have in making visual inferences from mapped geospatial data. We adapt Wickham et al.'s 'Visual Line-up' method as a direct analogy with Null Hypothesis Significance Testing (NHST) and propose a new approach for generating more credible spatial null hypotheses. Rather than using as a spatial null hypothesis the unrealistic assumption of complete spatial randomness, we propose spatially autocorrelated simulations as alternative nulls. We conduct a set of crowdsourced experiments (n=361) to determine the just noticeable difference (JND) between pairs of choropleth maps of geographic units controlling for spatial autocorrelation (Moran's I statistic) and geometric configuration (variance in spatial unit area). Results indicate that people's abilities to perceive differences in spatial autocorrelation vary with baseline autocorrelation structure and the geometric configuration of geographic units. These results allow us, for the first time, to construct a visual equivalent of statistical power for geospatial data. Our JND results add to those provided in recent years by Klippel et al. (2011), Harrison et al. (2014) and Kay & Heer (2015) for correlation visualization. Importantly, they provide an empirical basis for an improved construction of visual line-ups for maps and the development of theory to inform geospatial tests of graphical inference.

Analysis of Sensitivity Experiments - An Expanded Primer

DTIC Science & Technology

2017-03-08

diehard practitioners. The difficulty associated with mastering statistical inference presents a true dilemma. Statistics is an extremely applied...lost, perhaps forever. In other words, when on this safari, you need a guide. This report is designed to be a guide, of sorts. It focuses on analytical...estimated accurately if our analysis is to have real meaning. For this reason, the sensitivity test procedure is designed to concentrate measurements

Interpretation of correlations in clinical research.

PubMed

Hung, Man; Bounsanga, Jerry; Voss, Maren Wright

2017-11-01

Critically analyzing research is a key skill in evidence-based practice and requires knowledge of research methods, results interpretation, and applications, all of which rely on a foundation based in statistics. Evidence-based practice makes high demands on trained medical professionals to interpret an ever-expanding array of research evidence. As clinical training emphasizes medical care rather than statistics, it is useful to review the basics of statistical methods and what they mean for interpreting clinical studies. We reviewed the basic concepts of correlational associations, violations of normality, unobserved variable bias, sample size, and alpha inflation. The foundations of causal inference were discussed and sound statistical analyses were examined. We discuss four ways in which correlational analysis is misused, including causal inference overreach, over-reliance on significance, alpha inflation, and sample size bias. Recent published studies in the medical field provide evidence of causal assertion overreach drawn from correlational findings. The findings present a primer on the assumptions and nature of correlational methods of analysis and urge clinicians to exercise appropriate caution as they critically analyze the evidence before them and evaluate evidence that supports practice. Critically analyzing new evidence requires statistical knowledge in addition to clinical knowledge. Studies can overstate relationships, expressing causal assertions when only correlational evidence is available. Failure to account for the effect of sample size in the analyses tends to overstate the importance of predictive variables. It is important not to overemphasize the statistical significance without consideration of effect size and whether differences could be considered clinically meaningful.

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

Equivalent statistics and data interpretation.

PubMed

Francis, Gregory

2017-08-01

Recent reform efforts in psychological science have led to a plethora of choices for scientists to analyze their data. A scientist making an inference about their data must now decide whether to report a p value, summarize the data with a standardized effect size and its confidence interval, report a Bayes Factor, or use other model comparison methods. To make good choices among these options, it is necessary for researchers to understand the characteristics of the various statistics used by the different analysis frameworks. Toward that end, this paper makes two contributions. First, it shows that for the case of a two-sample t test with known sample sizes, many different summary statistics are mathematically equivalent in the sense that they are based on the very same information in the data set. When the sample sizes are known, the p value provides as much information about a data set as the confidence interval of Cohen's d or a JZS Bayes factor. Second, this equivalence means that different analysis methods differ only in their interpretation of the empirical data. At first glance, it might seem that mathematical equivalence of the statistics suggests that it does not matter much which statistic is reported, but the opposite is true because the appropriateness of a reported statistic is relative to the inference it promotes. Accordingly, scientists should choose an analysis method appropriate for their scientific investigation. A direct comparison of the different inferential frameworks provides some guidance for scientists to make good choices and improve scientific practice.

Statistical Inference for Cultural Consensus Theory

DTIC Science & Technology

2014-02-24

Social Network Conference XXXII , Redondo Beach, California, March 2012. Agrawal, K. (Presenter), and Batchelder, W. H. Cultural Consensus Theory...Aggregating Complete Signed Graphs Under a Balance Constraint -- Part 2. International Sunbelt Social Network Conference XXXII , Redondo Beach

Automatic physical inference with information maximizing neural networks

NASA Astrophysics Data System (ADS)

Charnock, Tom; Lavaux, Guilhem; Wandelt, Benjamin D.

2018-04-01

Compressing large data sets to a manageable number of summaries that are informative about the underlying parameters vastly simplifies both frequentist and Bayesian inference. When only simulations are available, these summaries are typically chosen heuristically, so they may inadvertently miss important information. We introduce a simulation-based machine learning technique that trains artificial neural networks to find nonlinear functionals of data that maximize Fisher information: information maximizing neural networks (IMNNs). In test cases where the posterior can be derived exactly, likelihood-free inference based on automatically derived IMNN summaries produces nearly exact posteriors, showing that these summaries are good approximations to sufficient statistics. In a series of numerical examples of increasing complexity and astrophysical relevance we show that IMNNs are robustly capable of automatically finding optimal, nonlinear summaries of the data even in cases where linear compression fails: inferring the variance of Gaussian signal in the presence of noise, inferring cosmological parameters from mock simulations of the Lyman-α forest in quasar spectra, and inferring frequency-domain parameters from LISA-like detections of gravitational waveforms. In this final case, the IMNN summary outperforms linear data compression by avoiding the introduction of spurious likelihood maxima. We anticipate that the automatic physical inference method described in this paper will be essential to obtain both accurate and precise cosmological parameter estimates from complex and large astronomical data sets, including those from LSST and Euclid.

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.

Inference of median difference based on the Box-Cox model in randomized clinical trials.

PubMed

Maruo, K; Isogawa, N; Gosho, M

2015-05-10

In randomized clinical trials, many medical and biological measurements are not normally distributed and are often skewed. The Box-Cox transformation is a powerful procedure for comparing two treatment groups for skewed continuous variables in terms of a statistical test. However, it is difficult to directly estimate and interpret the location difference between the two groups on the original scale of the measurement. We propose a helpful method that infers the difference of the treatment effect on the original scale in a more easily interpretable form. We also provide statistical analysis packages that consistently include an estimate of the treatment effect, covariance adjustments, standard errors, and statistical hypothesis tests. The simulation study that focuses on randomized parallel group clinical trials with two treatment groups indicates that the performance of the proposed method is equivalent to or better than that of the existing non-parametric approaches in terms of the type-I error rate and power. We illustrate our method with cluster of differentiation 4 data in an acquired immune deficiency syndrome clinical trial. Copyright © 2015 John Wiley & Sons, Ltd.

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.

Valid statistical inference methods for a case-control study with missing data.

PubMed

Tian, Guo-Liang; Zhang, Chi; Jiang, Xuejun

2018-04-01

The main objective of this paper is to derive the valid sampling distribution of the observed counts in a case-control study with missing data under the assumption of missing at random by employing the conditional sampling method and the mechanism augmentation method. The proposed sampling distribution, called the case-control sampling distribution, can be used to calculate the standard errors of the maximum likelihood estimates of parameters via the Fisher information matrix and to generate independent samples for constructing small-sample bootstrap confidence intervals. Theoretical comparisons of the new case-control sampling distribution with two existing sampling distributions exhibit a large difference. Simulations are conducted to investigate the influence of the three different sampling distributions on statistical inferences. One finding is that the conclusion by the Wald test for testing independency under the two existing sampling distributions could be completely different (even contradictory) from the Wald test for testing the equality of the success probabilities in control/case groups under the proposed distribution. A real cervical cancer data set is used to illustrate the proposed statistical methods.

A Dasymetric-Based Monte Carlo Simulation Approach to the Probabilistic Analysis of Spatial Variables

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

Morton, April M; Piburn, Jesse O; McManamay, Ryan A

2017-01-01

Monte Carlo simulation is a popular numerical experimentation technique used in a range of scientific fields to obtain the statistics of unknown random output variables. Despite its widespread applicability, it can be difficult to infer required input probability distributions when they are related to population counts unknown at desired spatial resolutions. To overcome this challenge, we propose a framework that uses a dasymetric model to infer the probability distributions needed for a specific class of Monte Carlo simulations which depend on population counts.

ProUCL Version 4.0 Technical Guide

EPA Science Inventory

Statistical inference, including both estimation and hypotheses testing approaches, is routinely used to: estimate environmental parameters of interest, such as exposure point concentration (EPC) terms, not-to-exceed values, and background level threshold values (BTVs) for contam...

Discovering Shifts to Suicidal Ideation from Mental Health Content in Social Media

PubMed Central

De Choudhury, Munmun; Kiciman, Emre; Dredze, Mark; Coppersmith, Glen; Kumar, Mrinal

2017-01-01

History of mental illness is a major factor behind suicide risk and ideation. However research efforts toward characterizing and forecasting this risk is limited due to the paucity of information regarding suicide ideation, exacerbated by the stigma of mental illness. This paper fills gaps in the literature by developing a statistical methodology to infer which individuals could undergo transitions from mental health discourse to suicidal ideation. We utilize semi-anonymous support communities on Reddit as unobtrusive data sources to infer the likelihood of these shifts. We develop language and interactional measures for this purpose, as well as a propensity score matching based statistical approach. Our approach allows us to derive distinct markers of shifts to suicidal ideation. These markers can be modeled in a prediction framework to identify individuals likely to engage in suicidal ideation in the future. We discuss societal and ethical implications of this research. PMID:29082385

The search for causal inferences: using propensity scores post hoc to reduce estimation error with nonexperimental research.

PubMed

Tumlinson, Samuel E; Sass, Daniel A; Cano, Stephanie M

2014-03-01

While experimental designs are regarded as the gold standard for establishing causal relationships, such designs are usually impractical owing to common methodological limitations. The objective of this article is to illustrate how propensity score matching (PSM) and using propensity scores (PS) as a covariate are viable alternatives to reduce estimation error when experimental designs cannot be implemented. To mimic common pediatric research practices, data from 140 simulated participants were used to resemble an experimental and nonexperimental design that assessed the effect of treatment status on participant weight loss for diabetes. Pretreatment participant characteristics (age, gender, physical activity, etc.) were then used to generate PS for use in the various statistical approaches. Results demonstrate how PSM and using the PS as a covariate can be used to reduce estimation error and improve statistical inferences. References for issues related to the implementation of these procedures are provided to assist researchers.

A novelty detection diagnostic methodology for gearboxes operating under fluctuating operating conditions using probabilistic techniques

NASA Astrophysics Data System (ADS)

Schmidt, S.; Heyns, P. S.; de Villiers, J. P.

2018-02-01

In this paper, a fault diagnostic methodology is developed which is able to detect, locate and trend gear faults under fluctuating operating conditions when only vibration data from a single transducer, measured on a healthy gearbox are available. A two-phase feature extraction and modelling process is proposed to infer the operating condition and based on the operating condition, to detect changes in the machine condition. Information from optimised machine and operating condition hidden Markov models are statistically combined to generate a discrepancy signal which is post-processed to infer the condition of the gearbox. The discrepancy signal is processed and combined with statistical methods for automatic fault detection and localisation and to perform fault trending over time. The proposed methodology is validated on experimental data and a tacholess order tracking methodology is used to enhance the cost-effectiveness of the diagnostic methodology.

Testing manifest monotonicity using order-constrained statistical inference.

PubMed

Tijmstra, Jesper; Hessen, David J; van der Heijden, Peter G M; Sijtsma, Klaas

2013-01-01

Most dichotomous item response models share the assumption of latent monotonicity, which states that the probability of a positive response to an item is a nondecreasing function of a latent variable intended to be measured. Latent monotonicity cannot be evaluated directly, but it implies manifest monotonicity across a variety of observed scores, such as the restscore, a single item score, and in some cases the total score. In this study, we show that manifest monotonicity can be tested by means of the order-constrained statistical inference framework. We propose a procedure that uses this framework to determine whether manifest monotonicity should be rejected for specific items. This approach provides a likelihood ratio test for which the p-value can be approximated through simulation. A simulation study is presented that evaluates the Type I error rate and power of the test, and the procedure is applied to empirical data.

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.

Discovering Shifts to Suicidal Ideation from Mental Health Content in Social Media.

PubMed

De Choudhury, Munmun; Kiciman, Emre; Dredze, Mark; Coppersmith, Glen; Kumar, Mrinal

2016-05-01

History of mental illness is a major factor behind suicide risk and ideation. However research efforts toward characterizing and forecasting this risk is limited due to the paucity of information regarding suicide ideation, exacerbated by the stigma of mental illness. This paper fills gaps in the literature by developing a statistical methodology to infer which individuals could undergo transitions from mental health discourse to suicidal ideation. We utilize semi-anonymous support communities on Reddit as unobtrusive data sources to infer the likelihood of these shifts. We develop language and interactional measures for this purpose, as well as a propensity score matching based statistical approach. Our approach allows us to derive distinct markers of shifts to suicidal ideation. These markers can be modeled in a prediction framework to identify individuals likely to engage in suicidal ideation in the future. We discuss societal and ethical implications of this research.

Cardinal rules: Visual orientation perception reflects knowledge of environmental statistics

PubMed Central

Girshick, Ahna R.; Landy, Michael S.; Simoncelli, Eero P.

2011-01-01

Humans are remarkably good at performing visual tasks, but experimental measurements reveal substantial biases in the perception of basic visual attributes. An appealing hypothesis is that these biases arise through a process of statistical inference, in which information from noisy measurements is fused with a probabilistic model of the environment. But such inference is optimal only if the observer’s internal model matches the environment. Here, we provide evidence that this is the case. We measured performance in an orientation-estimation task, demonstrating the well-known fact that orientation judgements are more accurate at cardinal (horizontal and vertical) orientations, along with a new observation that judgements made under conditions of uncertainty are strongly biased toward cardinal orientations. We estimate observers’ internal models for orientation and find that they match the local orientation distribution measured in photographs. We also show how a neural population could embed probabilistic information responsible for such biases. PMID:21642976

Linear models: permutation methods

USGS Publications Warehouse

Cade, B.S.; Everitt, B.S.; Howell, D.C.

2005-01-01

Permutation tests (see Permutation Based Inference) for the linear model have applications in behavioral studies when traditional parametric assumptions about the error term in a linear model are not tenable. Improved validity of Type I error rates can be achieved with properly constructed permutation tests. Perhaps more importantly, increased statistical power, improved robustness to effects of outliers, and detection of alternative distributional differences can be achieved by coupling permutation inference with alternative linear model estimators. For example, it is well-known that estimates of the mean in linear model are extremely sensitive to even a single outlying value of the dependent variable compared to estimates of the median [7, 19]. Traditionally, linear modeling focused on estimating changes in the center of distributions (means or medians). However, quantile regression allows distributional changes to be estimated in all or any selected part of a distribution or responses, providing a more complete statistical picture that has relevance to many biological questions [6]...

Perils of correlating CUSUM-transformed variables to infer ecological relationships (Breton et al. 2006; Glibert 2010)

USGS Publications Warehouse

Cloern, James E.; Jassby, Alan D.; Carstensen, Jacob; Bennett, William A.; Kimmerer, Wim; Mac Nally, Ralph; Schoellhamer, David H.; Winder, Monika

2012-01-01

We comment on a nonstandard statistical treatment of time-series data first published by Breton et al. (2006) in Limnology and Oceanography and, more recently, used by Glibert (2010) in Reviews in Fisheries Science. In both papers, the authors make strong inferences about the underlying causes of population variability based on correlations between cumulative sum (CUSUM) transformations of organism abundances and environmental variables. Breton et al. (2006) reported correlations between CUSUM-transformed values of diatom biomass in Belgian coastal waters and the North Atlantic Oscillation, and between meteorological and hydrological variables. Each correlation of CUSUM-transformed variables was judged to be statistically significant. On the basis of these correlations, Breton et al. (2006) developed "the first evidence of synergy between climate and human-induced river-based nitrate inputs with respect to their effects on the magnitude of spring Phaeocystis colony blooms and their dominance over diatoms."

Simulation and statistics: Like rhythm and song

NASA Astrophysics Data System (ADS)

Othman, Abdul Rahman

2013-04-01

Simulation has been introduced to solve problems in the form of systems. By using this technique the following two problems can be overcome. First, a problem that has an analytical solution but the cost of running an experiment to solve is high in terms of money and lives. Second, a problem exists but has no analytical solution. In the field of statistical inference the second problem is often encountered. With the advent of high-speed computing devices, a statistician can now use resampling techniques such as the bootstrap and permutations to form pseudo sampling distribution that will lead to the solution of the problem that cannot be solved analytically. This paper discusses how a Monte Carlo simulation was and still being used to verify the analytical solution in inference. This paper also discusses the resampling techniques as simulation techniques. The misunderstandings about these two techniques are examined. The successful usages of both techniques are also explained.

Extreme between-study homogeneity in meta-analyses could offer useful insights.

PubMed

Ioannidis, John P A; Trikalinos, Thomas A; Zintzaras, Elias

2006-10-01

Meta-analyses are routinely evaluated for the presence of large between-study heterogeneity. We examined whether it is also important to probe whether there is extreme between-study homogeneity. We used heterogeneity tests with left-sided statistical significance for inference and developed a Monte Carlo simulation test for testing extreme homogeneity in risk ratios across studies, using the empiric distribution of the summary risk ratio and heterogeneity statistic. A left-sided P=0.01 threshold was set for claiming extreme homogeneity to minimize type I error. Among 11,803 meta-analyses with binary contrasts from the Cochrane Library, 143 (1.21%) had left-sided P-value <0.01 for the asymptotic Q statistic and 1,004 (8.50%) had left-sided P-value <0.10. The frequency of extreme between-study homogeneity did not depend on the number of studies in the meta-analyses. We identified examples where extreme between-study homogeneity (left-sided P-value <0.01) could result from various possibilities beyond chance. These included inappropriate statistical inference (asymptotic vs. Monte Carlo), use of a specific effect metric, correlated data or stratification using strong predictors of outcome, and biases and potential fraud. Extreme between-study homogeneity may provide useful insights about a meta-analysis and its constituent studies.

Advances in computer simulation of genome evolution: toward more realistic evolutionary genomics analysis by approximate bayesian computation.

PubMed

Arenas, Miguel

2015-04-01

NGS technologies present a fast and cheap generation of genomic data. Nevertheless, ancestral genome inference is not so straightforward due to complex evolutionary processes acting on this material such as inversions, translocations, and other genome rearrangements that, in addition to their implicit complexity, can co-occur and confound ancestral inferences. Recently, models of genome evolution that accommodate such complex genomic events are emerging. This letter explores these novel evolutionary models and proposes their incorporation into robust statistical approaches based on computer simulations, such as approximate Bayesian computation, that may produce a more realistic evolutionary analysis of genomic data. Advantages and pitfalls in using these analytical methods are discussed. Potential applications of these ancestral genomic inferences are also pointed out.

Outcome-Dependent Sampling Design and Inference for Cox's Proportional Hazards Model.

PubMed

Yu, Jichang; Liu, Yanyan; Cai, Jianwen; Sandler, Dale P; Zhou, Haibo

2016-11-01

We propose a cost-effective outcome-dependent sampling design for the failure time data and develop an efficient inference procedure for data collected with this design. To account for the biased sampling scheme, we derive estimators from a weighted partial likelihood estimating equation. The proposed estimators for regression parameters are shown to be consistent and asymptotically normally distributed. A criteria that can be used to optimally implement the ODS design in practice is proposed and studied. The small sample performance of the proposed method is evaluated by simulation studies. The proposed design and inference procedure is shown to be statistically more powerful than existing alternative designs with the same sample sizes. We illustrate the proposed method with an existing real data from the Cancer Incidence and Mortality of Uranium Miners Study.

The visual system’s internal model of the world

PubMed Central

Lee, Tai Sing

2015-01-01

The Bayesian paradigm has provided a useful conceptual theory for understanding perceptual computation in the brain. While the detailed neural mechanisms of Bayesian inference are not fully understood, recent computational and neurophysiological works have illuminated the underlying computational principles and representational architecture. The fundamental insights are that the visual system is organized as a modular hierarchy to encode an internal model of the world, and that perception is realized by statistical inference based on such internal model. In this paper, I will discuss and analyze the varieties of representational schemes of these internal models and how they might be used to perform learning and inference. I will argue for a unified theoretical framework for relating the internal models to the observed neural phenomena and mechanisms in the visual cortex. PMID:26566294

Demographic inference under the coalescent in a spatial continuum.

PubMed

Guindon, Stéphane; Guo, Hongbin; Welch, David

2016-10-01

Understanding population dynamics from the analysis of molecular and spatial data requires sound statistical modeling. Current approaches assume that populations are naturally partitioned into discrete demes, thereby failing to be relevant in cases where individuals are scattered on a spatial continuum. Other models predict the formation of increasingly tight clusters of individuals in space, which, again, conflicts with biological evidence. Building on recent theoretical work, we introduce a new genealogy-based inference framework that alleviates these issues. This approach effectively implements a stochastic model in which the distribution of individuals is homogeneous and stationary, thereby providing a relevant null model for the fluctuation of genetic diversity in time and space. Importantly, the spatial density of individuals in a population and their range of dispersal during the course of evolution are two parameters that can be inferred separately with this method. The validity of the new inference framework is confirmed with extensive simulations and the analysis of influenza sequences collected over five seasons in the USA. Copyright © 2016 Elsevier Inc. All rights reserved.

Biostatistics primer: part I.

PubMed

Overholser, Brian R; Sowinski, Kevin M

2007-12-01

Biostatistics is the application of statistics to biologic data. The field of statistics can be broken down into 2 fundamental parts: descriptive and inferential. Descriptive statistics are commonly used to categorize, display, and summarize data. Inferential statistics can be used to make predictions based on a sample obtained from a population or some large body of information. It is these inferences that are used to test specific research hypotheses. This 2-part review will outline important features of descriptive and inferential statistics as they apply to commonly conducted research studies in the biomedical literature. Part 1 in this issue will discuss fundamental topics of statistics and data analysis. Additionally, some of the most commonly used statistical tests found in the biomedical literature will be reviewed in Part 2 in the February 2008 issue.

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

Bayesian structural inference for hidden processes.

PubMed

Strelioff, Christopher C; Crutchfield, James P

2014-04-01

We introduce a Bayesian approach to discovering patterns in structurally complex processes. The proposed method of Bayesian structural inference (BSI) relies on a set of candidate unifilar hidden Markov model (uHMM) topologies for inference of process structure from a data series. We employ a recently developed exact enumeration of topological ε-machines. (A sequel then removes the topological restriction.) This subset of the uHMM topologies has the added benefit that inferred models are guaranteed to be ε-machines, irrespective of estimated transition probabilities. Properties of ε-machines and uHMMs allow for the derivation of analytic expressions for estimating transition probabilities, inferring start states, and comparing the posterior probability of candidate model topologies, despite process internal structure being only indirectly present in data. We demonstrate BSI's effectiveness in estimating a process's randomness, as reflected by the Shannon entropy rate, and its structure, as quantified by the statistical complexity. We also compare using the posterior distribution over candidate models and the single, maximum a posteriori model for point estimation and show that the former more accurately reflects uncertainty in estimated values. We apply BSI to in-class examples of finite- and infinite-order Markov processes, as well to an out-of-class, infinite-state hidden process.

Bayesian structural inference for hidden processes

NASA Astrophysics Data System (ADS)

Strelioff, Christopher C.; Crutchfield, James P.

2014-04-01

We introduce a Bayesian approach to discovering patterns in structurally complex processes. The proposed method of Bayesian structural inference (BSI) relies on a set of candidate unifilar hidden Markov model (uHMM) topologies for inference of process structure from a data series. We employ a recently developed exact enumeration of topological ɛ-machines. (A sequel then removes the topological restriction.) This subset of the uHMM topologies has the added benefit that inferred models are guaranteed to be ɛ-machines, irrespective of estimated transition probabilities. Properties of ɛ-machines and uHMMs allow for the derivation of analytic expressions for estimating transition probabilities, inferring start states, and comparing the posterior probability of candidate model topologies, despite process internal structure being only indirectly present in data. We demonstrate BSI's effectiveness in estimating a process's randomness, as reflected by the Shannon entropy rate, and its structure, as quantified by the statistical complexity. We also compare using the posterior distribution over candidate models and the single, maximum a posteriori model for point estimation and show that the former more accurately reflects uncertainty in estimated values. We apply BSI to in-class examples of finite- and infinite-order Markov processes, as well to an out-of-class, infinite-state hidden process.

Permutation inference for the general linear model

PubMed Central

Winkler, Anderson M.; Ridgway, Gerard R.; Webster, Matthew A.; Smith, Stephen M.; Nichols, Thomas E.

2014-01-01

Permutation methods can provide exact control of false positives and allow the use of non-standard statistics, making only weak assumptions about the data. With the availability of fast and inexpensive computing, their main limitation would be some lack of flexibility to work with arbitrary experimental designs. In this paper we report on results on approximate permutation methods that are more flexible with respect to the experimental design and nuisance variables, and conduct detailed simulations to identify the best method for settings that are typical for imaging research scenarios. We present a generic framework for permutation inference for complex general linear models (glms) when the errors are exchangeable and/or have a symmetric distribution, and show that, even in the presence of nuisance effects, these permutation inferences are powerful while providing excellent control of false positives in a wide range of common and relevant imaging research scenarios. We also demonstrate how the inference on glm parameters, originally intended for independent data, can be used in certain special but useful cases in which independence is violated. Detailed examples of common neuroimaging applications are provided, as well as a complete algorithm – the “randomise” algorithm – for permutation inference with the glm. PMID:24530839

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.

Constraints on the Progenitor System of SN 2016gkg from a Comprehensive Statistical Analysis

NASA Astrophysics Data System (ADS)

Sravan, Niharika; Marchant, Pablo; Kalogera, Vassiliki; Margutti, Raffaella

2018-01-01

Type IIb supernovae (SNe) present a unique opportunity for understanding the progenitors of stripped-envelope SNe because the stellar progenitor of several SNe IIb have been identified in pre-explosion images. In this paper, we use Bayesian inference and a large grid of non-rotating solar-metallicity single and binary stellar models to derive the associated probability distributions of single and binary progenitors of the SN IIb 2016gkg using existing observational constraints. We find that potential binary star progenitors have smaller pre-SN hydrogen-envelope and helium-core masses than potential single-star progenitors typically by 0.1 M ⊙ and 2 M ⊙, respectively. We find that, a binary companion, if present, is a main-sequence or red-giant star. Apart from this, we do not find strong constraints on the nature of the companion star. We demonstrate that the range of progenitor helium-core mass inferred from observations could help improve constraints on the progenitor. We find that the probability that the progenitor of SN 2016gkg was a binary is 22% when we use constraints only on the progenitor luminosity and effective temperature. Imposing the range of pre-SN progenitor hydrogen-envelope mass and radius inferred from SN light curves, the probability that the progenitor is a binary increases to 44%. However, there is no clear preference for a binary progenitor. This is in contrast to binaries being the currently favored formation channel for SNe IIb. Our analysis demonstrates the importance of statistical inference methods to constrain progenitor channels.

A statistical approach for inferring the 3D structure of the genome.

PubMed

Varoquaux, Nelle; Ay, Ferhat; Noble, William Stafford; Vert, Jean-Philippe

2014-06-15

Recent technological advances allow the measurement, in a single Hi-C experiment, of the frequencies of physical contacts among pairs of genomic loci at a genome-wide scale. The next challenge is to infer, from the resulting DNA-DNA contact maps, accurate 3D models of how chromosomes fold and fit into the nucleus. Many existing inference methods rely on multidimensional scaling (MDS), in which the pairwise distances of the inferred model are optimized to resemble pairwise distances derived directly from the contact counts. These approaches, however, often optimize a heuristic objective function and require strong assumptions about the biophysics of DNA to transform interaction frequencies to spatial distance, and thereby may lead to incorrect structure reconstruction. We propose a novel approach to infer a consensus 3D structure of a genome from Hi-C data. The method incorporates a statistical model of the contact counts, assuming that the counts between two loci follow a Poisson distribution whose intensity decreases with the physical distances between the loci. The method can automatically adjust the transfer function relating the spatial distance to the Poisson intensity and infer a genome structure that best explains the observed data. We compare two variants of our Poisson method, with or without optimization of the transfer function, to four different MDS-based algorithms-two metric MDS methods using different stress functions, a non-metric version of MDS and ChromSDE, a recently described, advanced MDS method-on a wide range of simulated datasets. We demonstrate that the Poisson models reconstruct better structures than all MDS-based methods, particularly at low coverage and high resolution, and we highlight the importance of optimizing the transfer function. On publicly available Hi-C data from mouse embryonic stem cells, we show that the Poisson methods lead to more reproducible structures than MDS-based methods when we use data generated using different restriction enzymes, and when we reconstruct structures at different resolutions. A Python implementation of the proposed method is available at http://cbio.ensmp.fr/pastis. © The Author 2014. Published by Oxford University Press.

Influence function for robust phylogenetic reconstructions.

PubMed

Bar-Hen, Avner; Mariadassou, Mahendra; Poursat, Marie-Anne; Vandenkoornhuyse, Philippe

2008-05-01

Based on the computation of the influence function, a tool to measure the impact of each piece of sampled data on the statistical inference of a parameter, we propose to analyze the support of the maximum-likelihood (ML) tree for each site. We provide a new tool for filtering data sets (nucleotides, amino acids, and others) in the context of ML phylogenetic reconstructions. Because different sites support different phylogenic topologies in different ways, outlier sites, that is, sites with a very negative influence value, are important: they can drastically change the topology resulting from the statistical inference. Therefore, these outlier sites must be clearly identified and their effects accounted for before drawing biological conclusions from the inferred tree. A matrix containing 158 fungal terminals all belonging to Chytridiomycota, Zygomycota, and Glomeromycota is analyzed. We show that removing the strongest outlier from the analysis strikingly modifies the ML topology, with a loss of as many as 20% of the internal nodes. As a result, estimating the topology on the filtered data set results in a topology with enhanced bootstrap support. From this analysis, the polyphyletic status of the fungal phyla Chytridiomycota and Zygomycota is reinforced, suggesting the necessity of revisiting the systematics of these fungal groups. We show the ability of influence function to produce new evolution hypotheses.

Efficient Moment-Based Inference of Admixture Parameters and Sources of Gene Flow

PubMed Central

Levin, Alex; Reich, David; Patterson, Nick; Berger, Bonnie

2013-01-01

The recent explosion in available genetic data has led to significant advances in understanding the demographic histories of and relationships among human populations. It is still a challenge, however, to infer reliable parameter values for complicated models involving many populations. Here, we present MixMapper, an efficient, interactive method for constructing phylogenetic trees including admixture events using single nucleotide polymorphism (SNP) genotype data. MixMapper implements a novel two-phase approach to admixture inference using moment statistics, first building an unadmixed scaffold tree and then adding admixed populations by solving systems of equations that express allele frequency divergences in terms of mixture parameters. Importantly, all features of the model, including topology, sources of gene flow, branch lengths, and mixture proportions, are optimized automatically from the data and include estimates of statistical uncertainty. MixMapper also uses a new method to express branch lengths in easily interpretable drift units. We apply MixMapper to recently published data for Human Genome Diversity Cell Line Panel individuals genotyped on a SNP array designed especially for use in population genetics studies, obtaining confident results for 30 populations, 20 of them admixed. Notably, we confirm a signal of ancient admixture in European populations—including previously undetected admixture in Sardinians and Basques—involving a proportion of 20–40% ancient northern Eurasian ancestry. PMID:23709261

Inference of population splits and mixtures from genome-wide allele frequency data.

PubMed

Pickrell, Joseph K; Pritchard, Jonathan K

2012-01-01

Many aspects of the historical relationships between populations in a species are reflected in genetic data. Inferring these relationships from genetic data, however, remains a challenging task. In this paper, we present a statistical model for inferring the patterns of population splits and mixtures in multiple populations. In our model, the sampled populations in a species are related to their common ancestor through a graph of ancestral populations. Using genome-wide allele frequency data and a Gaussian approximation to genetic drift, we infer the structure of this graph. We applied this method to a set of 55 human populations and a set of 82 dog breeds and wild canids. In both species, we show that a simple bifurcating tree does not fully describe the data; in contrast, we infer many migration events. While some of the migration events that we find have been detected previously, many have not. For example, in the human data, we infer that Cambodians trace approximately 16% of their ancestry to a population ancestral to other extant East Asian populations. In the dog data, we infer that both the boxer and basenji trace a considerable fraction of their ancestry (9% and 25%, respectively) to wolves subsequent to domestication and that East Asian toy breeds (the Shih Tzu and the Pekingese) result from admixture between modern toy breeds and "ancient" Asian breeds. Software implementing the model described here, called TreeMix, is available at http://treemix.googlecode.com.

Some challenges with statistical inference in adaptive designs.

PubMed

Hung, H M James; Wang, Sue-Jane; Yang, Peiling

2014-01-01

Adaptive designs have generated a great deal of attention to clinical trial communities. The literature contains many statistical methods to deal with added statistical uncertainties concerning the adaptations. Increasingly encountered in regulatory applications are adaptive statistical information designs that allow modification of sample size or related statistical information and adaptive selection designs that allow selection of doses or patient populations during the course of a clinical trial. For adaptive statistical information designs, a few statistical testing methods are mathematically equivalent, as a number of articles have stipulated, but arguably there are large differences in their practical ramifications. We pinpoint some undesirable features of these methods in this work. For adaptive selection designs, the selection based on biomarker data for testing the correlated clinical endpoints may increase statistical uncertainty in terms of type I error probability, and most importantly the increased statistical uncertainty may be impossible to assess.

Refining the Use of Linkage Disequilibrium as a Robust Signature of Selective Sweeps.

PubMed

Jacobs, Guy S; Sluckin, Tim J; Kivisild, Toomas

2016-08-01

During a selective sweep, characteristic patterns of linkage disequilibrium can arise in the genomic region surrounding a selected locus. These have been used to infer past selective sweeps. However, the recombination rate is known to vary substantially along the genome for many species. We here investigate the effectiveness of current (Kelly's [Formula: see text] and [Formula: see text]) and novel statistics at inferring hard selective sweeps based on linkage disequilibrium distortions under different conditions, including a human-realistic demographic model and recombination rate variation. When the recombination rate is constant, Kelly's [Formula: see text] offers high power, but is outperformed by a novel statistic that we test, which we call [Formula: see text] We also find this statistic to be effective at detecting sweeps from standing variation. When recombination rate fluctuations are included, there is a considerable reduction in power for all linkage disequilibrium-based statistics. However, this can largely be reversed by appropriately controlling for expected linkage disequilibrium using a genetic map. To further test these different methods, we perform selection scans on well-characterized HapMap data, finding that all three statistics-[Formula: see text] Kelly's [Formula: see text] and [Formula: see text]-are able to replicate signals at regions previously identified as selection candidates based on population differentiation or the site frequency spectrum. While [Formula: see text] replicates most candidates when recombination map data are not available, the [Formula: see text] and [Formula: see text] statistics are more successful when recombination rate variation is controlled for. Given both this and their higher power in simulations of selective sweeps, these statistics are preferred when information on local recombination rate variation is available. Copyright © 2016 by the Genetics Society of America.

Information Extraction from Large-Multi-Layer Social Networks

DTIC Science & Technology

2015-08-06

mization [4]. Methods that fall into this category include spec- tral algorithms, modularity methods, and methods that rely on statistical inference...Snijders and Chris Baerveldt, “A multilevel network study of the effects of delinquent behavior on friendship evolution,” Journal of mathematical sociol- ogy...1970. [10] Ulrike Luxburg, “A tutorial on spectral clustering,” Statistics and Computing, vol. 17, no. 4, pp. 395–416, Dec. 2007. [11] R. A. Fisher, “On

Bayes in biological anthropology.

PubMed

Konigsberg, Lyle W; Frankenberg, Susan R

2013-12-01

In this article, we both contend and illustrate that biological anthropologists, particularly in the Americas, often think like Bayesians but act like frequentists when it comes to analyzing a wide variety of data. In other words, while our research goals and perspectives are rooted in probabilistic thinking and rest on prior knowledge, we often proceed to use statistical hypothesis tests and confidence interval methods unrelated (or tenuously related) to the research questions of interest. We advocate for applying Bayesian analyses to a number of different bioanthropological questions, especially since many of the programming and computational challenges to doing so have been overcome in the past two decades. To facilitate such applications, this article explains Bayesian principles and concepts, and provides concrete examples of Bayesian computer simulations and statistics that address questions relevant to biological anthropology, focusing particularly on bioarchaeology and forensic anthropology. It also simultaneously reviews the use of Bayesian methods and inference within the discipline to date. This article is intended to act as primer to Bayesian methods and inference in biological anthropology, explaining the relationships of various methods to likelihoods or probabilities and to classical statistical models. Our contention is not that traditional frequentist statistics should be rejected outright, but that there are many situations where biological anthropology is better served by taking a Bayesian approach. To this end it is hoped that the examples provided in this article will assist researchers in choosing from among the broad array of statistical methods currently available. Copyright © 2013 Wiley Periodicals, Inc.

Inference of Gene Regulatory Networks Incorporating Multi-Source Biological Knowledge via a State Space Model with L1 Regularization

PubMed Central

Hasegawa, Takanori; Yamaguchi, Rui; Nagasaki, Masao; Miyano, Satoru; Imoto, Seiya

2014-01-01

Comprehensive understanding of gene regulatory networks (GRNs) is a major challenge in the field of systems biology. Currently, there are two main approaches in GRN analysis using time-course observation data, namely an ordinary differential equation (ODE)-based approach and a statistical model-based approach. The ODE-based approach can generate complex dynamics of GRNs according to biologically validated nonlinear models. However, it cannot be applied to ten or more genes to simultaneously estimate system dynamics and regulatory relationships due to the computational difficulties. The statistical model-based approach uses highly abstract models to simply describe biological systems and to infer relationships among several hundreds of genes from the data. However, the high abstraction generates false regulations that are not permitted biologically. Thus, when dealing with several tens of genes of which the relationships are partially known, a method that can infer regulatory relationships based on a model with low abstraction and that can emulate the dynamics of ODE-based models while incorporating prior knowledge is urgently required. To accomplish this, we propose a method for inference of GRNs using a state space representation of a vector auto-regressive (VAR) model with L1 regularization. This method can estimate the dynamic behavior of genes based on linear time-series modeling constructed from an ODE-based model and can infer the regulatory structure among several tens of genes maximizing prediction ability for the observational data. Furthermore, the method is capable of incorporating various types of existing biological knowledge, e.g., drug kinetics and literature-recorded pathways. The effectiveness of the proposed method is shown through a comparison of simulation studies with several previous methods. For an application example, we evaluated mRNA expression profiles over time upon corticosteroid stimulation in rats, thus incorporating corticosteroid kinetics/dynamics, literature-recorded pathways and transcription factor (TF) information. PMID:25162401

On the Relationship Between Global Land-Ocean Temperature and Various Descriptors of Solar-Geomagnetic Activity and Climate

NASA Technical Reports Server (NTRS)

Wilson, Robert M.

2014-01-01

Examined are sunspot cycle- (SC-) length averages of the annual January-December values of the Global Land-Ocean Temperature Index () in relation to SC-length averages of annual values of various descriptors of solar-geomagnetic activity and climate, incorporating lags of 0-5 yr. For the overall interval SC12-SC23, the is inferred to correlate best against the parameter incorporating lag = 5 yr, where the parameter refers to the resultant aa value having removed that portion of the annual aa average value due to the yearly variation of sunspot number (SSN). The inferred correlation between the and is statistically important at confidence level cl > 99.9%, having a coefficient of linear correlation r = 0.865 and standard error of estimate se = 0.149 degC. Excluding the most recent cycles SC22 and SC23, the inferred correlation is stronger, having r = 0.969 and se = 0.048 degC. With respect to the overall trend in the , which has been upwards towards warmer temperatures since SC12 (1878-1888), solar-geomagnetic activity parameters are now trending downwards (since SC19). For SC20-SC23, in contrast, comparison of the against SC-length averages of the annual value of the Mauna Loa carbon dioxide () index is found to be highly statistically important (cl >> 99.9%), having r = 0.9994 and se = 0.012 degC for lag = 2 yr. On the basis of the inferred preferential linear correlation between the and , the current ongoing SC24 is inferred to have warmer than was seen in SC23 (i.e., >0.526 degC), probably in excess of 0.68 degC (relative to the 1951-1980 base period).

Weigh-in-Motion Sensor and Controller Operation and Performance Comparison

DOT National Transportation Integrated Search

2018-01-01

This research project utilized statistical inference and comparison techniques to compare the performance of different Weigh-in-Motion (WIM) sensors. First, we analyzed test-vehicle data to perform an accuracy check of the results reported by the sen...

Multilevel Model Prediction

ERIC Educational Resources Information Center

Frees, Edward W.; Kim, Jee-Seon

2006-01-01

Multilevel models are proven tools in social research for modeling complex, hierarchical systems. In multilevel modeling, statistical inference is based largely on quantification of random variables. This paper distinguishes among three types of random variables in multilevel modeling--model disturbances, random coefficients, and future response…

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.

Inference of reaction rate parameters based on summary statistics from experiments

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

Khalil, Mohammad; Chowdhary, Kamaljit Singh; Safta, Cosmin

Here, we present the results of an application of Bayesian inference and maximum entropy methods for the estimation of the joint probability density for the Arrhenius rate para meters of the rate coefficient of the H 2/O 2-mechanism chain branching reaction H + O 2 → OH + O. Available published data is in the form of summary statistics in terms of nominal values and error bars of the rate coefficient of this reaction at a number of temperature values obtained from shock-tube experiments. Our approach relies on generating data, in this case OH concentration profiles, consistent with the givenmore » summary statistics, using Approximate Bayesian Computation methods and a Markov Chain Monte Carlo procedure. The approach permits the forward propagation of parametric uncertainty through the computational model in a manner that is consistent with the published statistics. A consensus joint posterior on the parameters is obtained by pooling the posterior parameter densities given each consistent data set. To expedite this process, we construct efficient surrogates for the OH concentration using a combination of Pad'e and polynomial approximants. These surrogate models adequately represent forward model observables and their dependence on input parameters and are computationally efficient to allow their use in the Bayesian inference procedure. We also utilize Gauss-Hermite quadrature with Gaussian proposal probability density functions for moment computation resulting in orders of magnitude speedup in data likelihood evaluation. Despite the strong non-linearity in the model, the consistent data sets all res ult in nearly Gaussian conditional parameter probability density functions. The technique also accounts for nuisance parameters in the form of Arrhenius parameters of other rate coefficients with prescribed uncertainty. The resulting pooled parameter probability density function is propagated through stoichiometric hydrogen-air auto-ignition computations to illustrate the need to account for correlation among the Arrhenius rate parameters of one reaction and across rate parameters of different reactions.« less

Inference of reaction rate parameters based on summary statistics from experiments

DOE PAGES

Khalil, Mohammad; Chowdhary, Kamaljit Singh; Safta, Cosmin; ...

2016-10-15

Here, we present the results of an application of Bayesian inference and maximum entropy methods for the estimation of the joint probability density for the Arrhenius rate para meters of the rate coefficient of the H 2/O 2-mechanism chain branching reaction H + O 2 → OH + O. Available published data is in the form of summary statistics in terms of nominal values and error bars of the rate coefficient of this reaction at a number of temperature values obtained from shock-tube experiments. Our approach relies on generating data, in this case OH concentration profiles, consistent with the givenmore » summary statistics, using Approximate Bayesian Computation methods and a Markov Chain Monte Carlo procedure. The approach permits the forward propagation of parametric uncertainty through the computational model in a manner that is consistent with the published statistics. A consensus joint posterior on the parameters is obtained by pooling the posterior parameter densities given each consistent data set. To expedite this process, we construct efficient surrogates for the OH concentration using a combination of Pad'e and polynomial approximants. These surrogate models adequately represent forward model observables and their dependence on input parameters and are computationally efficient to allow their use in the Bayesian inference procedure. We also utilize Gauss-Hermite quadrature with Gaussian proposal probability density functions for moment computation resulting in orders of magnitude speedup in data likelihood evaluation. Despite the strong non-linearity in the model, the consistent data sets all res ult in nearly Gaussian conditional parameter probability density functions. The technique also accounts for nuisance parameters in the form of Arrhenius parameters of other rate coefficients with prescribed uncertainty. The resulting pooled parameter probability density function is propagated through stoichiometric hydrogen-air auto-ignition computations to illustrate the need to account for correlation among the Arrhenius rate parameters of one reaction and across rate parameters of different reactions.« less

CAN'T MISS--conquer any number task by making important statistics simple. Part 2. Probability, populations, samples, and normal distributions.

PubMed

Hansen, John P

2003-01-01

Healthcare quality improvement professionals need to understand and use inferential statistics to interpret sample data from their organizations. In quality improvement and healthcare research studies all the data from a population often are not available, so investigators take samples and make inferences about the population by using inferential statistics. This three-part series will give readers an understanding of the concepts of inferential statistics as well as the specific tools for calculating confidence intervals for samples of data. This article, Part 2, describes probability, populations, and samples. The uses of descriptive and inferential statistics are outlined. The article also discusses the properties and probability of normal distributions, including the standard normal distribution.

INfORM: Inference of NetwOrk Response Modules.

PubMed

Marwah, Veer Singh; Kinaret, Pia Anneli Sofia; Serra, Angela; Scala, Giovanni; Lauerma, Antti; Fortino, Vittorio; Greco, Dario

2018-06-15

Detecting and interpreting responsive modules from gene expression data by using network-based approaches is a common but laborious task. It often requires the application of several computational methods implemented in different software packages, forcing biologists to compile complex analytical pipelines. Here we introduce INfORM (Inference of NetwOrk Response Modules), an R shiny application that enables non-expert users to detect, evaluate and select gene modules with high statistical and biological significance. INfORM is a comprehensive tool for the identification of biologically meaningful response modules from consensus gene networks inferred by using multiple algorithms. It is accessible through an intuitive graphical user interface allowing for a level of abstraction from the computational steps. INfORM is freely available for academic use at https://github.com/Greco-Lab/INfORM. Supplementary data are available at Bioinformatics online.

Outcome-Dependent Sampling Design and Inference for Cox’s Proportional Hazards Model

PubMed Central

Yu, Jichang; Liu, Yanyan; Cai, Jianwen; Sandler, Dale P.; Zhou, Haibo

2016-01-01

We propose a cost-effective outcome-dependent sampling design for the failure time data and develop an efficient inference procedure for data collected with this design. To account for the biased sampling scheme, we derive estimators from a weighted partial likelihood estimating equation. The proposed estimators for regression parameters are shown to be consistent and asymptotically normally distributed. A criteria that can be used to optimally implement the ODS design in practice is proposed and studied. The small sample performance of the proposed method is evaluated by simulation studies. The proposed design and inference procedure is shown to be statistically more powerful than existing alternative designs with the same sample sizes. We illustrate the proposed method with an existing real data from the Cancer Incidence and Mortality of Uranium Miners Study. PMID:28090134

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

Perceptual inference.

PubMed

Aggelopoulos, Nikolaos C

2015-08-01

Perceptual inference refers to the ability to infer sensory stimuli from predictions that result from internal neural representations built through prior experience. Methods of Bayesian statistical inference and decision theory model cognition adequately by using error sensing either in guiding action or in "generative" models that predict the sensory information. In this framework, perception can be seen as a process qualitatively distinct from sensation, a process of information evaluation using previously acquired and stored representations (memories) that is guided by sensory feedback. The stored representations can be utilised as internal models of sensory stimuli enabling long term associations, for example in operant conditioning. Evidence for perceptual inference is contributed by such phenomena as the cortical co-localisation of object perception with object memory, the response invariance in the responses of some neurons to variations in the stimulus, as well as from situations in which perception can be dissociated from sensation. In the context of perceptual inference, sensory areas of the cerebral cortex that have been facilitated by a priming signal may be regarded as comparators in a closed feedback loop, similar to the better known motor reflexes in the sensorimotor system. The adult cerebral cortex can be regarded as similar to a servomechanism, in using sensory feedback to correct internal models, producing predictions of the outside world on the basis of past experience. Copyright © 2015 Elsevier Ltd. All rights reserved.

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.

Markov Chain Monte Carlo Used in Parameter Inference of Magnetic Resonance Spectra

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

Hock, Kiel; Earle, Keith

2016-02-06

In this paper, we use Boltzmann statistics and the maximum likelihood distribution derived from Bayes’ Theorem to infer parameter values for a Pake Doublet Spectrum, a lineshape of historical significance and contemporary relevance for determining distances between interacting magnetic dipoles. A Metropolis Hastings Markov Chain Monte Carlo algorithm is implemented and designed to find the optimum parameter set and to estimate parameter uncertainties. In conclusion, the posterior distribution allows us to define a metric on parameter space that induces a geometry with negative curvature that affects the parameter uncertainty estimates, particularly for spectra with low signal to noise.

Scientific thinking in young children: theoretical advances, empirical research, and policy implications.

PubMed

Gopnik, Alison

2012-09-28

New theoretical ideas and empirical research show that very young children's learning and thinking are strikingly similar to much learning and thinking in science. Preschoolers test hypotheses against data and make causal inferences; they learn from statistics and informal experimentation, and from watching and listening to others. The mathematical framework of probabilistic models and Bayesian inference can describe this learning in precise ways. These discoveries have implications for early childhood education and policy. In particular, they suggest both that early childhood experience is extremely important and that the trend toward more structured and academic early childhood programs is misguided.

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.

Mass Conservation and Inference of Metabolic Networks from High-Throughput Mass Spectrometry Data

PubMed Central

Bandaru, Pradeep; Bansal, Mukesh

2011-01-01

Abstract We present a step towards the metabolome-wide computational inference of cellular metabolic reaction networks from metabolic profiling data, such as mass spectrometry. The reconstruction is based on identification of irreducible statistical interactions among the metabolite activities using the ARACNE reverse-engineering algorithm and on constraining possible metabolic transformations to satisfy the conservation of mass. The resulting algorithms are validated on synthetic data from an abridged computational model of Escherichia coli metabolism. Precision rates upwards of 50% are routinely observed for identification of full metabolic reactions, and recalls upwards of 20% are also seen. PMID:21314454

Extending local canonical correlation analysis to handle general linear contrasts for FMRI data.

PubMed

Jin, Mingwu; Nandy, Rajesh; Curran, Tim; Cordes, Dietmar

2012-01-01

Local canonical correlation analysis (CCA) is a multivariate method that has been proposed to more accurately determine activation patterns in fMRI data. In its conventional formulation, CCA has several drawbacks that limit its usefulness in fMRI. A major drawback is that, unlike the general linear model (GLM), a test of general linear contrasts of the temporal regressors has not been incorporated into the CCA formalism. To overcome this drawback, a novel directional test statistic was derived using the equivalence of multivariate multiple regression (MVMR) and CCA. This extension will allow CCA to be used for inference of general linear contrasts in more complicated fMRI designs without reparameterization of the design matrix and without reestimating the CCA solutions for each particular contrast of interest. With the proper constraints on the spatial coefficients of CCA, this test statistic can yield a more powerful test on the inference of evoked brain regional activations from noisy fMRI data than the conventional t-test in the GLM. The quantitative results from simulated and pseudoreal data and activation maps from fMRI data were used to demonstrate the advantage of this novel test statistic.

All individuals are not created equal; accounting for interindividual variation in fitting life-history responses to toxicants.

PubMed

Jager, Tjalling

2013-02-05

The individuals of a species are not equal. These differences frustrate experimental biologists and ecotoxicologists who wish to study the response of a species (in general) to a treatment. In the analysis of data, differences between model predictions and observations on individual animals are usually treated as random measurement error around the true response. These deviations, however, are mainly caused by real differences between the individuals (e.g., differences in physiology and in initial conditions). Understanding these intraspecies differences, and accounting for them in the data analysis, will improve our understanding of the response to the treatment we are investigating and allow for a more powerful, less biased, statistical analysis. Here, I explore a basic scheme for statistical inference to estimate parameters governing stress that allows individuals to differ in their basic physiology. This scheme is illustrated using a simple toxicokinetic-toxicodynamic model and a data set for growth of the springtail Folsomia candida exposed to cadmium in food. This article should be seen as proof of concept; a first step in bringing more realism into the statistical inference for process-based models in ecotoxicology.

DETECTING UNSPECIFIED STRUCTURE IN LOW-COUNT IMAGES

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

Stein, Nathan M.; Dyk, David A. van; Kashyap, Vinay L.

Unexpected structure in images of astronomical sources often presents itself upon visual inspection of the image, but such apparent structure may either correspond to true features in the source or be due to noise in the data. This paper presents a method for testing whether inferred structure in an image with Poisson noise represents a significant departure from a baseline (null) model of the image. To infer image structure, we conduct a Bayesian analysis of a full model that uses a multiscale component to allow flexible departures from the posited null model. As a test statistic, we use a tailmore » probability of the posterior distribution under the full model. This choice of test statistic allows us to estimate a computationally efficient upper bound on a p-value that enables us to draw strong conclusions even when there are limited computational resources that can be devoted to simulations under the null model. We demonstrate the statistical performance of our method on simulated images. Applying our method to an X-ray image of the quasar 0730+257, we find significant evidence against the null model of a single point source and uniform background, lending support to the claim of an X-ray jet.« less

Extending Local Canonical Correlation Analysis to Handle General Linear Contrasts for fMRI Data

PubMed Central

Jin, Mingwu; Nandy, Rajesh; Curran, Tim; Cordes, Dietmar

2012-01-01

Local canonical correlation analysis (CCA) is a multivariate method that has been proposed to more accurately determine activation patterns in fMRI data. In its conventional formulation, CCA has several drawbacks that limit its usefulness in fMRI. A major drawback is that, unlike the general linear model (GLM), a test of general linear contrasts of the temporal regressors has not been incorporated into the CCA formalism. To overcome this drawback, a novel directional test statistic was derived using the equivalence of multivariate multiple regression (MVMR) and CCA. This extension will allow CCA to be used for inference of general linear contrasts in more complicated fMRI designs without reparameterization of the design matrix and without reestimating the CCA solutions for each particular contrast of interest. With the proper constraints on the spatial coefficients of CCA, this test statistic can yield a more powerful test on the inference of evoked brain regional activations from noisy fMRI data than the conventional t-test in the GLM. The quantitative results from simulated and pseudoreal data and activation maps from fMRI data were used to demonstrate the advantage of this novel test statistic. PMID:22461786

Connectopic mapping with resting-state fMRI.

PubMed

Haak, Koen V; Marquand, Andre F; Beckmann, Christian F

2018-04-15

Brain regions are often topographically connected: nearby locations within one brain area connect with nearby locations in another area. Mapping these connection topographies, or 'connectopies' in short, is crucial for understanding how information is processed in the brain. Here, we propose principled, fully data-driven methods for mapping connectopies using functional magnetic resonance imaging (fMRI) data acquired at rest by combining spectral embedding of voxel-wise connectivity 'fingerprints' with a novel approach to spatial statistical inference. We apply the approach in human primary motor and visual cortex, and show that it can trace biologically plausible, overlapping connectopies in individual subjects that follow these regions' somatotopic and retinotopic maps. As a generic mechanism to perform inference over connectopies, the new spatial statistics approach enables rigorous statistical testing of hypotheses regarding the fine-grained spatial profile of functional connectivity and whether that profile is different between subjects or between experimental conditions. The combined framework offers a fundamental alternative to existing approaches to investigating functional connectivity in the brain, from voxel- or seed-pair wise characterizations of functional association, towards a full, multivariate characterization of spatial topography. Copyright © 2017 The Authors. Published by Elsevier Inc. All rights reserved.

The geographic mosaic of Ecuadorian Y-chromosome ancestry.

PubMed

Toscanini, U; Gaviria, A; Pardo-Seco, J; Gómez-Carballa, A; Moscoso, F; Vela, M; Cobos, S; Lupero, A; Zambrano, A K; Martinón-Torres, F; Carabajo-Marcillo, A; Yunga-León, R; Ugalde-Noritz, N; Ordoñez-Ugalde, A; Salas, A

2018-03-01

Ecuadorians originated from a complex mixture of Native American indigenous people with Europeans and Africans. We analyzed Y-chromosome STRs (Y-STRs) in a sample of 415 Ecuadorians (145 using the AmpFlSTR ® Yfiler™ system [Life Technologies, USA] and 270 using the PowerPlex ® Y23 system [Promega Corp., USA]; hereafter Yfiler and PPY23, respectively) representing three main ecological continental regions of the country, namely Amazon rainforest, Andes, and Pacific coast. Diversity values are high in the three regions, and the PPY23 exhibits higher discrimination power than the Yfiler set. While summary statistics, AMOVA, and R ST distances show low to moderate levels of population stratification, inferred ancestry derived from Y-STRs reveal clear patterns of geographic variation. The major ancestry in Ecuadorian males is European (61%), followed by an important Native American component (34%); whereas the African ancestry (5%) is mainly concentrated in the Northwest corner of the country. We conclude that classical procedures for measuring population stratification do not have the desirable sensitivity. Statistical inference of ancestry from Y-STRS is a satisfactory alternative for revealing patterns of spatial variation that would pass unnoticed when using popular statistical summary indices. Copyright © 2017 Elsevier B.V. All rights reserved.

Practical Advice on Calculating Confidence Intervals for Radioprotection Effects and Reducing Animal Numbers in Radiation Countermeasure Experiments

PubMed Central

Landes, Reid D.; Lensing, Shelly Y.; Kodell, Ralph L.; Hauer-Jensen, Martin

2014-01-01

The dose of a substance that causes death in P% of a population is called an LDP, where LD stands for lethal dose. In radiation research, a common LDP of interest is the radiation dose that kills 50% of the population by a specified time, i.e., lethal dose 50 or LD50. When comparing LD50 between two populations, relative potency is the parameter of interest. In radiation research, this is commonly known as the dose reduction factor (DRF). Unfortunately, statistical inference on dose reduction factor is seldom reported. We illustrate how to calculate confidence intervals for dose reduction factor, which may then be used for statistical inference. Further, most dose reduction factor experiments use hundreds, rather than tens of animals. Through better dosing strategies and the use of a recently available sample size formula, we also show how animal numbers may be reduced while maintaining high statistical power. The illustrations center on realistic examples comparing LD50 values between a radiation countermeasure group and a radiation-only control. We also provide easy-to-use spreadsheets for sample size calculations and confidence interval calculations, as well as SAS® and R code for the latter. PMID:24164553

[The research protocol VI: How to choose the appropriate statistical test. Inferential statistics].

PubMed

Flores-Ruiz, Eric; Miranda-Novales, María Guadalupe; Villasís-Keever, Miguel Ángel

2017-01-01

The statistical analysis can be divided in two main components: descriptive analysis and inferential analysis. An inference is to elaborate conclusions from the tests performed with the data obtained from a sample of a population. Statistical tests are used in order to establish the probability that a conclusion obtained from a sample is applicable to the population from which it was obtained. However, choosing the appropriate statistical test in general poses a challenge for novice researchers. To choose the statistical test it is necessary to take into account three aspects: the research design, the number of measurements and the scale of measurement of the variables. Statistical tests are divided into two sets, parametric and nonparametric. Parametric tests can only be used if the data show a normal distribution. Choosing the right statistical test will make it easier for readers to understand and apply the results.

[Bayesian statistics in medicine -- part II: main applications and inference].

PubMed

Montomoli, C; Nichelatti, M

2008-01-01

Bayesian statistics is not only used when one is dealing with 2-way tables, but it can be used for inferential purposes. Using the basic concepts presented in the first part, this paper aims to give a simple overview of Bayesian methods by introducing its foundation (Bayes' theorem) and then applying this rule to a very simple practical example; whenever possible, the elementary processes at the basis of analysis are compared to those of frequentist (classical) statistical analysis. The Bayesian reasoning is naturally connected to medical activity, since it appears to be quite similar to a diagnostic process.

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.

Demonstrating urban outdoor lighting for pedestrian safety and security : final report.

DOT National Transportation Integrated Search

2015-12-31

The goal of this project is to provide statistical inference for the communitys willingness to : pay for improvements in the resiliency to extreme events of the transportation system in : New York City.This objective seeks to provide better tools ...

Climbing Mount Probable

ERIC Educational Resources Information Center

Harper, Marc Allen

2009-01-01

This work attempts to explain the relationships between natural selection, information theory, and statistical inference. In particular, a geometric formulation of information theory known as information geometry and its deep connections to evolutionary game theory inform the role of natural selection in evolutionary processes. The goals of this…

Asymptotic Distribution of the Likelihood Ratio Test Statistic for Sphericity of Complex Multivariate Normal Distribution.

DTIC Science & Technology

1981-08-01

RATIO TEST STATISTIC FOR SPHERICITY OF COMPLEX MULTIVARIATE NORMAL DISTRIBUTION* C. Fang P. R. Krishnaiah B. N. Nagarsenker** August 1981 Technical...and their applications in time sEries, the reader is referred to Krishnaiah (1976). Motivated by the applications in the area of inference on multiple...for practical purposes. Here, we note that Krishnaiah , Lee and Chang (1976) approxi- mated the null distribution of certain power of the likeli

On the Power Functions of Test Statistics in Order Restricted Inference.

DTIC Science & Technology

1984-10-01

California-Davis Actuarial Science Davis, California 95616 The University of Iowa Iowa City, Iowa 52242 *F. T. Wright Department of Mathematics and...34 SUMMARY --We study the power functions of both the likelihood ratio and con- trast statistics for detecting a totally ordered trend in a collection...samples from normal populations, Bartholomew (1959 a,b; 1961) studied the likelihood ratio tests (LRTs) for H0 versus H -H assuming in one case that

Specificity and timescales of cortical adaptation as inferences about natural movie statistics.

PubMed

Snow, Michoel; Coen-Cagli, Ruben; Schwartz, Odelia

2016-10-01

Adaptation is a phenomenological umbrella term under which a variety of temporal contextual effects are grouped. Previous models have shown that some aspects of visual adaptation reflect optimal processing of dynamic visual inputs, suggesting that adaptation should be tuned to the properties of natural visual inputs. However, the link between natural dynamic inputs and adaptation is poorly understood. Here, we extend a previously developed Bayesian modeling framework for spatial contextual effects to the temporal domain. The model learns temporal statistical regularities of natural movies and links these statistics to adaptation in primary visual cortex via divisive normalization, a ubiquitous neural computation. In particular, the model divisively normalizes the present visual input by the past visual inputs only to the degree that these are inferred to be statistically dependent. We show that this flexible form of normalization reproduces classical findings on how brief adaptation affects neuronal selectivity. Furthermore, prior knowledge acquired by the Bayesian model from natural movies can be modified by prolonged exposure to novel visual stimuli. We show that this updating can explain classical results on contrast adaptation. We also simulate the recent finding that adaptation maintains population homeostasis, namely, a balanced level of activity across a population of neurons with different orientation preferences. Consistent with previous disparate observations, our work further clarifies the influence of stimulus-specific and neuronal-specific normalization signals in adaptation.

Specificity and timescales of cortical adaptation as inferences about natural movie statistics

PubMed Central

Snow, Michoel; Coen-Cagli, Ruben; Schwartz, Odelia

2016-01-01

Adaptation is a phenomenological umbrella term under which a variety of temporal contextual effects are grouped. Previous models have shown that some aspects of visual adaptation reflect optimal processing of dynamic visual inputs, suggesting that adaptation should be tuned to the properties of natural visual inputs. However, the link between natural dynamic inputs and adaptation is poorly understood. Here, we extend a previously developed Bayesian modeling framework for spatial contextual effects to the temporal domain. The model learns temporal statistical regularities of natural movies and links these statistics to adaptation in primary visual cortex via divisive normalization, a ubiquitous neural computation. In particular, the model divisively normalizes the present visual input by the past visual inputs only to the degree that these are inferred to be statistically dependent. We show that this flexible form of normalization reproduces classical findings on how brief adaptation affects neuronal selectivity. Furthermore, prior knowledge acquired by the Bayesian model from natural movies can be modified by prolonged exposure to novel visual stimuli. We show that this updating can explain classical results on contrast adaptation. We also simulate the recent finding that adaptation maintains population homeostasis, namely, a balanced level of activity across a population of neurons with different orientation preferences. Consistent with previous disparate observations, our work further clarifies the influence of stimulus-specific and neuronal-specific normalization signals in adaptation. PMID:27699416

Packet Randomized Experiments for Eliminating Classes of Confounders

PubMed Central

Pavela, Greg; Wiener, Howard; Fontaine, Kevin R.; Fields, David A.; Voss, Jameson D.; Allison, David B.

2014-01-01

Background Although randomization is considered essential for causal inference, it is often not possible to randomize in nutrition and obesity research. To address this, we develop a framework for an experimental design—packet randomized experiments (PREs), which improves causal inferences when randomization on a single treatment variable is not possible. This situation arises when subjects are randomly assigned to a condition (such as a new roommate) which varies in one characteristic of interest (such as weight), but also varies across many others. There has been no general discussion of this experimental design, including its strengths, limitations, and statistical properties. As such, researchers are left to develop and apply PREs on an ad hoc basis, limiting its potential to improve causal inferences among nutrition and obesity researchers. Methods We introduce PREs as an intermediary design between randomized controlled trials and observational studies. We review previous research that used the PRE design and describe its application in obesity-related research, including random roommate assignments, heterochronic parabiosis, and the quasi-random assignment of subjects to geographic areas. We then provide a statistical framework to control for potential packet-level confounders not accounted for by randomization. Results PREs have successfully been used to improve causal estimates of the effect of roommates, altitude, and breastfeeding on weight outcomes. When certain assumptions are met, PREs can asymptotically control for packet-level characteristics. This has the potential to statistically estimate the effect of a single treatment even when randomization to a single treatment did not occur. Conclusions Applying PREs to obesity-related research will improve decisions about clinical, public health, and policy actions insofar as it offers researchers new insight into cause and effect relationships among variables. PMID:25444088

Improving mass-univariate analysis of neuroimaging data by modelling important unknown covariates: Application to Epigenome-Wide Association Studies.

PubMed

Guillaume, Bryan; Wang, Changqing; Poh, Joann; Shen, Mo Jun; Ong, Mei Lyn; Tan, Pei Fang; Karnani, Neerja; Meaney, Michael; Qiu, Anqi

2018-06-01

Statistical inference on neuroimaging data is often conducted using a mass-univariate model, equivalent to fitting a linear model at every voxel with a known set of covariates. Due to the large number of linear models, it is challenging to check if the selection of covariates is appropriate and to modify this selection adequately. The use of standard diagnostics, such as residual plotting, is clearly not practical for neuroimaging data. However, the selection of covariates is crucial for linear regression to ensure valid statistical inference. In particular, the mean model of regression needs to be reasonably well specified. Unfortunately, this issue is often overlooked in the field of neuroimaging. This study aims to adopt the existing Confounder Adjusted Testing and Estimation (CATE) approach and to extend it for use with neuroimaging data. We propose a modification of CATE that can yield valid statistical inferences using Principal Component Analysis (PCA) estimators instead of Maximum Likelihood (ML) estimators. We then propose a non-parametric hypothesis testing procedure that can improve upon parametric testing. Monte Carlo simulations show that the modification of CATE allows for more accurate modelling of neuroimaging data and can in turn yield a better control of False Positive Rate (FPR) and Family-Wise Error Rate (FWER). We demonstrate its application to an Epigenome-Wide Association Study (EWAS) on neonatal brain imaging and umbilical cord DNA methylation data obtained as part of a longitudinal cohort study. Software for this CATE study is freely available at http://www.bioeng.nus.edu.sg/cfa/Imaging_Genetics2.html. Copyright © 2018 The Author(s). Published by Elsevier Inc. All rights reserved.

Modeling Pair Distribution Functions of Rare-Earth Phosphate Glasses Using Principal Component Analysis.

PubMed

Cole, Jacqueline M; Cheng, Xie; Payne, Michael C

2016-11-07

The use of principal component analysis (PCA) to statistically infer features of local structure from experimental pair distribution function (PDF) data is assessed on a case study of rare-earth phosphate glasses (REPGs). Such glasses, codoped with two rare-earth ions (R and R') of different sizes and optical properties, are of interest to the laser industry. The determination of structure-property relationships in these materials is an important aspect of their technological development. Yet, realizing the local structure of codoped REPGs presents significant challenges relative to their singly doped counterparts; specifically, R and R' are difficult to distinguish in terms of establishing relative material compositions, identifying atomic pairwise correlation profiles in a PDF that are associated with each ion, and resolving peak overlap of such profiles in PDFs. This study demonstrates that PCA can be employed to help overcome these structural complications, by statistically inferring trends in PDFs that exist for a restricted set of experimental data on REPGs, and using these as training data to predict material compositions and PDF profiles in unknown codoped REPGs. The application of these PCA methods to resolve individual atomic pairwise correlations in t(r) signatures is also presented. The training methods developed for these structural predictions are prevalidated by testing their ability to reproduce known physical phenomena, such as the lanthanide contraction, on PDF signatures of the structurally simpler singly doped REPGs. The intrinsic limitations of applying PCA to analyze PDFs relative to the quality control of source data, data processing, and sample definition, are also considered. While this case study is limited to lanthanide-doped REPGs, this type of statistical inference may easily be extended to other inorganic solid-state materials and be exploited in large-scale data-mining efforts that probe many t(r) functions.

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

Dynamics of embryonic stem cell differentiation inferred from single-cell transcriptomics show a series of transitions through discrete cell states

PubMed Central

Jang, Sumin; Choubey, Sandeep; Furchtgott, Leon; Zou, Ling-Nan; Doyle, Adele; Menon, Vilas; Loew, Ethan B; Krostag, Anne-Rachel; Martinez, Refugio A; Madisen, Linda; Levi, Boaz P; Ramanathan, Sharad

2017-01-01

The complexity of gene regulatory networks that lead multipotent cells to acquire different cell fates makes a quantitative understanding of differentiation challenging. Using a statistical framework to analyze single-cell transcriptomics data, we infer the gene expression dynamics of early mouse embryonic stem (mES) cell differentiation, uncovering discrete transitions across nine cell states. We validate the predicted transitions across discrete states using flow cytometry. Moreover, using live-cell microscopy, we show that individual cells undergo abrupt transitions from a naïve to primed pluripotent state. Using the inferred discrete cell states to build a probabilistic model for the underlying gene regulatory network, we further predict and experimentally verify that these states have unique response to perturbations, thus defining them functionally. Our study provides a framework to infer the dynamics of differentiation from single cell transcriptomics data and to build predictive models of the gene regulatory networks that drive the sequence of cell fate decisions during development. DOI: http://dx.doi.org/10.7554/eLife.20487.001 PMID:28296635

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.

Modeling Protein Expression and Protein Signaling Pathways

PubMed Central

Telesca, Donatello; Müller, Peter; Kornblau, Steven M.; Suchard, Marc A.; Ji, Yuan

2015-01-01

High-throughput functional proteomic technologies provide a way to quantify the expression of proteins of interest. Statistical inference centers on identifying the activation state of proteins and their patterns of molecular interaction formalized as dependence structure. Inference on dependence structure is particularly important when proteins are selected because they are part of a common molecular pathway. In that case, inference on dependence structure reveals properties of the underlying pathway. We propose a probability model that represents molecular interactions at the level of hidden binary latent variables that can be interpreted as indicators for active versus inactive states of the proteins. The proposed approach exploits available expert knowledge about the target pathway to define an informative prior on the hidden conditional dependence structure. An important feature of this prior is that it provides an instrument to explicitly anchor the model space to a set of interactions of interest, favoring a local search approach to model determination. We apply our model to reverse-phase protein array data from a study on acute myeloid leukemia. Our inference identifies relevant subpathways in relation to the unfolding of the biological process under study. PMID:26246646

Inference of R 0 and Transmission Heterogeneity from the Size Distribution of Stuttering Chains

PubMed Central

Blumberg, Seth; Lloyd-Smith, James O.

2013-01-01

For many infectious disease processes such as emerging zoonoses and vaccine-preventable diseases, and infections occur as self-limited stuttering transmission chains. A mechanistic understanding of transmission is essential for characterizing the risk of emerging diseases and monitoring spatio-temporal dynamics. Thus methods for inferring and the degree of heterogeneity in transmission from stuttering chain data have important applications in disease surveillance and management. Previous researchers have used chain size distributions to infer , but estimation of the degree of individual-level variation in infectiousness (as quantified by the dispersion parameter, ) has typically required contact tracing data. Utilizing branching process theory along with a negative binomial offspring distribution, we demonstrate how maximum likelihood estimation can be applied to chain size data to infer both and the dispersion parameter that characterizes heterogeneity. While the maximum likelihood value for is a simple function of the average chain size, the associated confidence intervals are dependent on the inferred degree of transmission heterogeneity. As demonstrated for monkeypox data from the Democratic Republic of Congo, this impacts when a statistically significant change in is detectable. In addition, by allowing for superspreading events, inference of shifts the threshold above which a transmission chain should be considered anomalously large for a given value of (thus reducing the probability of false alarms about pathogen adaptation). Our analysis of monkeypox also clarifies the various ways that imperfect observation can impact inference of transmission parameters, and highlights the need to quantitatively evaluate whether observation is likely to significantly bias results. PMID:23658504

Visual representation of statistical information improves diagnostic inferences in doctors and their patients.

PubMed

Garcia-Retamero, Rocio; Hoffrage, Ulrich

2013-04-01

Doctors and patients have difficulty inferring the predictive value of a medical test from information about the prevalence of a disease and the sensitivity and false-positive rate of the test. Previous research has established that communicating such information in a format the human mind is adapted to-namely natural frequencies-as compared to probabilities, boosts accuracy of diagnostic inferences. In a study, we investigated to what extent these inferences can be improved-beyond the effect of natural frequencies-by providing visual aids. Participants were 81 doctors and 81 patients who made diagnostic inferences about three medical tests on the basis of information about prevalence of a disease, and the sensitivity and false-positive rate of the tests. Half of the participants received the information in natural frequencies, while the other half received the information in probabilities. Half of the participants only received numerical information, while the other half additionally received a visual aid representing the numerical information. In addition, participants completed a numeracy scale. Our study showed three important findings: (1) doctors and patients made more accurate inferences when information was communicated in natural frequencies as compared to probabilities; (2) visual aids boosted accuracy even when the information was provided in natural frequencies; and (3) doctors were more accurate in their diagnostic inferences than patients, though differences in accuracy disappeared when differences in numerical skills were controlled for. Our findings have important implications for medical practice as they suggest suitable ways to communicate quantitative medical data. Copyright © 2013 Elsevier Ltd. All rights reserved.

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

Are great apes able to reason from multi-item samples to populations of food items?

PubMed

Eckert, Johanna; Rakoczy, Hannes; Call, Josep

2017-10-01

Inductive learning from limited observations is a cognitive capacity of fundamental importance. In humans, it is underwritten by our intuitive statistics, the ability to draw systematic inferences from populations to randomly drawn samples and vice versa. According to recent research in cognitive development, human intuitive statistics develops early in infancy. Recent work in comparative psychology has produced first evidence for analogous cognitive capacities in great apes who flexibly drew inferences from populations to samples. In the present study, we investigated whether great apes (Pongo abelii, Pan troglodytes, Pan paniscus, Gorilla gorilla) also draw inductive inferences in the opposite direction, from samples to populations. In two experiments, apes saw an experimenter randomly drawing one multi-item sample from each of two populations of food items. The populations differed in their proportion of preferred to neutral items (24:6 vs. 6:24) but apes saw only the distribution of food items in the samples that reflected the distribution of the respective populations (e.g., 4:1 vs. 1:4). Based on this observation they were then allowed to choose between the two populations. Results show that apes seemed to make inferences from samples to populations and thus chose the population from which the more favorable (4:1) sample was drawn in Experiment 1. In this experiment, the more attractive sample not only contained proportionally but also absolutely more preferred food items than the less attractive sample. Experiment 2, however, revealed that when absolute and relative frequencies were disentangled, apes performed at chance level. Whether these limitations in apes' performance reflect true limits of cognitive competence or merely performance limitations due to accessory task demands is still an open question. © 2017 Wiley Periodicals, Inc.

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.

Inference of Transmission Network Structure from HIV Phylogenetic Trees

DOE PAGES

Giardina, Federica; Romero-Severson, Ethan Obie; Albert, Jan; ...

2017-01-13

Phylogenetic inference is an attractive means to reconstruct transmission histories and epidemics. However, there is not a perfect correspondence between transmission history and virus phylogeny. Both node height and topological differences may occur, depending on the interaction between within-host evolutionary dynamics and between-host transmission patterns. To investigate these interactions, we added a within-host evolutionary model in epidemiological simulations and examined if the resulting phylogeny could recover different types of contact networks. To further improve realism, we also introduced patient-specific differences in infectivity across disease stages, and on the epidemic level we considered incomplete sampling and the age of the epidemic.more » Second, we implemented an inference method based on approximate Bayesian computation (ABC) to discriminate among three well-studied network models and jointly estimate both network parameters and key epidemiological quantities such as the infection rate. Our ABC framework used both topological and distance-based tree statistics for comparison between simulated and observed trees. Overall, our simulations showed that a virus time-scaled phylogeny (genealogy) may be substantially different from the between-host transmission tree. This has important implications for the interpretation of what a phylogeny reveals about the underlying epidemic contact network. In particular, we found that while the within-host evolutionary process obscures the transmission tree, the diversification process and infectivity dynamics also add discriminatory power to differentiate between different types of contact networks. We also found that the possibility to differentiate contact networks depends on how far an epidemic has progressed, where distance-based tree statistics have more power early in an epidemic. Finally, we applied our ABC inference on two different outbreaks from the Swedish HIV-1 epidemic.« less

Inference of Transmission Network Structure from HIV Phylogenetic Trees

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

Giardina, Federica; Romero-Severson, Ethan Obie; Albert, Jan

Phylogenetic inference is an attractive means to reconstruct transmission histories and epidemics. However, there is not a perfect correspondence between transmission history and virus phylogeny. Both node height and topological differences may occur, depending on the interaction between within-host evolutionary dynamics and between-host transmission patterns. To investigate these interactions, we added a within-host evolutionary model in epidemiological simulations and examined if the resulting phylogeny could recover different types of contact networks. To further improve realism, we also introduced patient-specific differences in infectivity across disease stages, and on the epidemic level we considered incomplete sampling and the age of the epidemic.more » Second, we implemented an inference method based on approximate Bayesian computation (ABC) to discriminate among three well-studied network models and jointly estimate both network parameters and key epidemiological quantities such as the infection rate. Our ABC framework used both topological and distance-based tree statistics for comparison between simulated and observed trees. Overall, our simulations showed that a virus time-scaled phylogeny (genealogy) may be substantially different from the between-host transmission tree. This has important implications for the interpretation of what a phylogeny reveals about the underlying epidemic contact network. In particular, we found that while the within-host evolutionary process obscures the transmission tree, the diversification process and infectivity dynamics also add discriminatory power to differentiate between different types of contact networks. We also found that the possibility to differentiate contact networks depends on how far an epidemic has progressed, where distance-based tree statistics have more power early in an epidemic. Finally, we applied our ABC inference on two different outbreaks from the Swedish HIV-1 epidemic.« less

Uses and Misuses of the Correlation Coefficient.

ERIC Educational Resources Information Center

Onwuegbuzie, Anthony J.; Daniel, Larry G.

The purpose of this paper is to provide an in-depth critical analysis of the use and misuse of correlation coefficients. Various analytical and interpretational misconceptions are reviewed, beginning with the egregious assumption that correlational statistics may be useful in inferring causality. Additional misconceptions, stemming from…

Balkanization and Unification of Probabilistic Inferences

ERIC Educational Resources Information Center

Yu, Chong-Ho

2005-01-01

Many research-related classes in social sciences present probability as a unified approach based upon mathematical axioms, but neglect the diversity of various probability theories and their associated philosophical assumptions. Although currently the dominant statistical and probabilistic approach is the Fisherian tradition, the use of Fisherian…

Estimating Classification Consistency and Accuracy for Cognitive Diagnostic Assessment

ERIC Educational Resources Information Center

Cui, Ying; Gierl, Mark J.; Chang, Hua-Hua

2012-01-01

This article introduces procedures for the computation and asymptotic statistical inference for classification consistency and accuracy indices specifically designed for cognitive diagnostic assessments. The new classification indices can be used as important indicators of the reliability and validity of classification results produced by…

Australian Curriculum Linked Lessons: Statistics

ERIC Educational Resources Information Center

Day, Lorraine

2014-01-01

Students recognise and analyse data and draw inferences. They represent, summarise and interpret data and undertake purposeful investigations involving the collection and interpretation of data… They develop an increasingly sophisticated ability to critically evaluate chance and data concepts and make reasoned judgments and decisions, as well as…

Detecting local haplotype sharing and haplotype association

USDA-ARS?s Scientific Manuscript database

A novel haplotype association method is presented, and its power is demonstrated. Relying on a statistical model for linkage disequilibrium (LD), the method first infers ancestral haplotypes and their loadings at each marker for each individual. The loadings are then used to quantify local haplotype...

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

Natural frequencies improve Bayesian reasoning in simple and complex inference tasks

PubMed Central

Hoffrage, Ulrich; Krauss, Stefan; Martignon, Laura; Gigerenzer, Gerd

2015-01-01

Representing statistical information in terms of natural frequencies rather than probabilities improves performance in Bayesian inference tasks. This beneficial effect of natural frequencies has been demonstrated in a variety of applied domains such as medicine, law, and education. Yet all the research and applications so far have been limited to situations where one dichotomous cue is used to infer which of two hypotheses is true. Real-life applications, however, often involve situations where cues (e.g., medical tests) have more than one value, where more than two hypotheses (e.g., diseases) are considered, or where more than one cue is available. In Study 1, we show that natural frequencies, compared to information stated in terms of probabilities, consistently increase the proportion of Bayesian inferences made by medical students in four conditions—three cue values, three hypotheses, two cues, or three cues—by an average of 37 percentage points. In Study 2, we show that teaching natural frequencies for simple tasks with one dichotomous cue and two hypotheses leads to a transfer of learning to complex tasks with three cue values and two cues, with a proportion of 40 and 81% correct inferences, respectively. Thus, natural frequencies facilitate Bayesian reasoning in a much broader class of situations than previously thought. PMID:26528197

CellTree: an R/bioconductor package to infer the hierarchical structure of cell populations from single-cell RNA-seq data.

PubMed

duVerle, David A; Yotsukura, Sohiya; Nomura, Seitaro; Aburatani, Hiroyuki; Tsuda, Koji

2016-09-13

Single-cell RNA sequencing is fast becoming one the standard method for gene expression measurement, providing unique insights into cellular processes. A number of methods, based on general dimensionality reduction techniques, have been suggested to help infer and visualise the underlying structure of cell populations from single-cell expression levels, yet their models generally lack proper biological grounding and struggle at identifying complex differentiation paths. Here we introduce cellTree: an R/Bioconductor package that uses a novel statistical approach, based on document analysis techniques, to produce tree structures outlining the hierarchical relationship between single-cell samples, while identifying latent groups of genes that can provide biological insights. With cellTree, we provide experimentalists with an easy-to-use tool, based on statistically and biologically-sound algorithms, to efficiently explore and visualise single-cell RNA data. The cellTree package is publicly available in the online Bionconductor repository at: http://bioconductor.org/packages/cellTree/ .

Dynamic Uncertain Causality Graph for Knowledge Representation and Reasoning: Utilization of Statistical Data and Domain Knowledge in Complex Cases.

PubMed

Zhang, Qin; Yao, Quanying

2018-05-01

The dynamic uncertain causality graph (DUCG) is a newly presented framework for uncertain causality representation and probabilistic reasoning. It has been successfully applied to online fault diagnoses of large, complex industrial systems, and decease diagnoses. This paper extends the DUCG to model more complex cases than what could be previously modeled, e.g., the case in which statistical data are in different groups with or without overlap, and some domain knowledge and actions (new variables with uncertain causalities) are introduced. In other words, this paper proposes to use -mode, -mode, and -mode of the DUCG to model such complex cases and then transform them into either the standard -mode or the standard -mode. In the former situation, if no directed cyclic graph is involved, the transformed result is simply a Bayesian network (BN), and existing inference methods for BNs can be applied. In the latter situation, an inference method based on the DUCG is proposed. Examples are provided to illustrate the methodology.

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.

Inference in the brain: Statistics flowing in redundant population codes

PubMed Central

Pitkow, Xaq; Angelaki, Dora E

2017-01-01

It is widely believed that the brain performs approximate probabilistic inference to estimate causal variables in the world from ambiguous sensory data. To understand these computations, we need to analyze how information is represented and transformed by the actions of nonlinear recurrent neural networks. We propose that these probabilistic computations function by a message-passing algorithm operating at the level of redundant neural populations. To explain this framework, we review its underlying concepts, including graphical models, sufficient statistics, and message-passing, and then describe how these concepts could be implemented by recurrently connected probabilistic population codes. The relevant information flow in these networks will be most interpretable at the population level, particularly for redundant neural codes. We therefore outline a general approach to identify the essential features of a neural message-passing algorithm. Finally, we argue that to reveal the most important aspects of these neural computations, we must study large-scale activity patterns during moderately complex, naturalistic behaviors. PMID:28595050

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.

Testing for Granger Causality in the Frequency Domain: A Phase Resampling Method.

PubMed

Liu, Siwei; Molenaar, Peter

2016-01-01

This article introduces phase resampling, an existing but rarely used surrogate data method for making statistical inferences of Granger causality in frequency domain time series analysis. Granger causality testing is essential for establishing causal relations among variables in multivariate dynamic processes. However, testing for Granger causality in the frequency domain is challenging due to the nonlinear relation between frequency domain measures (e.g., partial directed coherence, generalized partial directed coherence) and time domain data. Through a simulation study, we demonstrate that phase resampling is a general and robust method for making statistical inferences even with short time series. With Gaussian data, phase resampling yields satisfactory type I and type II error rates in all but one condition we examine: when a small effect size is combined with an insufficient number of data points. Violations of normality lead to slightly higher error rates but are mostly within acceptable ranges. We illustrate the utility of phase resampling with two empirical examples involving multivariate electroencephalography (EEG) and skin conductance data.

The HCUP SID Imputation Project: Improving Statistical Inferences for Health Disparities Research by Imputing Missing Race Data.

PubMed

Ma, Yan; Zhang, Wei; Lyman, Stephen; Huang, Yihe

2018-06-01

To identify the most appropriate imputation method for missing data in the HCUP State Inpatient Databases (SID) and assess the impact of different missing data methods on racial disparities research. HCUP SID. A novel simulation study compared four imputation methods (random draw, hot deck, joint multiple imputation [MI], conditional MI) for missing values for multiple variables, including race, gender, admission source, median household income, and total charges. The simulation was built on real data from the SID to retain their hierarchical data structures and missing data patterns. Additional predictive information from the U.S. Census and American Hospital Association (AHA) database was incorporated into the imputation. Conditional MI prediction was equivalent or superior to the best performing alternatives for all missing data structures and substantially outperformed each of the alternatives in various scenarios. Conditional MI substantially improved statistical inferences for racial health disparities research with the SID. © Health Research and Educational Trust.

How we load our data sets with theories and why we do so purposefully.

PubMed

Rochefort-Maranda, Guillaume

2016-12-01

In this paper, I compare theory-laden perceptions with imputed data sets. The similarities between the two allow me to show how the phenomenon of theory-ladenness can manifest itself in statistical analyses. More importantly, elucidating the differences between them will allow me to broaden the focus of the existing literature on theory-ladenness and to introduce some much-needed nuances. The topic of statistical imputation has received no attention in philosophy of science. Yet, imputed data sets are very similar to theory-laden perceptions, and they are now an integral part of many scientific inferences. Unlike the existence of theory-laden perceptions, that of imputed data sets cannot be challenged or reduced to a manageable source of error. In fact, imputed data sets are created purposefully in order to improve the quality of our inferences. They do not undermine the possibility of scientific knowledge; on the contrary, they are epistemically desirable. Copyright © 2016 Elsevier Ltd. All rights reserved.

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.

Using GIS to generate spatially balanced random survey designs for natural resource applications.

PubMed

Theobald, David M; Stevens, Don L; White, Denis; Urquhart, N Scott; Olsen, Anthony R; Norman, John B

2007-07-01

Sampling of a population is frequently required to understand trends and patterns in natural resource management because financial and time constraints preclude a complete census. A rigorous probability-based survey design specifies where to sample so that inferences from the sample apply to the entire population. Probability survey designs should be used in natural resource and environmental management situations because they provide the mathematical foundation for statistical inference. Development of long-term monitoring designs demand survey designs that achieve statistical rigor and are efficient but remain flexible to inevitable logistical or practical constraints during field data collection. Here we describe an approach to probability-based survey design, called the Reversed Randomized Quadrant-Recursive Raster, based on the concept of spatially balanced sampling and implemented in a geographic information system. This provides environmental managers a practical tool to generate flexible and efficient survey designs for natural resource applications. Factors commonly used to modify sampling intensity, such as categories, gradients, or accessibility, can be readily incorporated into the spatially balanced sample design.

Inferring Models of Bacterial Dynamics toward Point Sources

PubMed Central

Jashnsaz, Hossein; Nguyen, Tyler; Petrache, Horia I.; Pressé, Steve

2015-01-01

Experiments have shown that bacteria can be sensitive to small variations in chemoattractant (CA) concentrations. Motivated by these findings, our focus here is on a regime rarely studied in experiments: bacteria tracking point CA sources (such as food patches or even prey). In tracking point sources, the CA detected by bacteria may show very large spatiotemporal fluctuations which vary with distance from the source. We present a general statistical model to describe how bacteria locate point sources of food on the basis of stochastic event detection, rather than CA gradient information. We show how all model parameters can be directly inferred from single cell tracking data even in the limit of high detection noise. Once parameterized, our model recapitulates bacterial behavior around point sources such as the “volcano effect”. In addition, while the search by bacteria for point sources such as prey may appear random, our model identifies key statistical signatures of a targeted search for a point source given any arbitrary source configuration. PMID:26466373

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

The t-test: An Influential Inferential Tool in Chaplaincy and Other Healthcare Research.

PubMed

Jankowski, Katherine R B; Flannelly, Kevin J; Flannelly, Laura T

2018-01-01

The t-test developed by William S. Gosset (also known as Student's t-test and the two-sample t-test) is commonly used to compare one sample mean on a measure with another sample mean on the same measure. The outcome of the t-test is used to draw inferences about how different the samples are from each other. It is probably one of the most frequently relied upon statistics in inferential research. It is easy to use: a researcher can calculate the statistic with three simple tools: paper, pen, and a calculator. A computer program can quickly calculate the t-test for large samples. The ease of use can result in the misuse of the t-test. This article discusses the development of the original t-test, basic principles of the t-test, two additional types of t-tests (the one-sample t-test and the paired t-test), and recommendations about what to consider when using the t-test to draw inferences in research.

Two Different Views on the World Around Us: The World of Uniformity versus Diversity.

PubMed

Kwon, JaeHwan; Nayakankuppam, Dhananjay

2016-01-01

We propose that when individuals believe in fixed traits of personality (entity theorists), they are likely to expect a world of "uniformity." As such, they easily infer a population statistic from a small sample of data with confidence. In contrast, individuals who believe in malleable traits of personality (incremental theorists) are likely to presume a world of "diversity," such that they "hesitate" to infer a population statistic from a similarly sized sample. In four laboratory experiments, we found that compared to incremental theorists, entity theorists estimated a population mean from a sample with a greater level of confidence (Studies 1a and 1b), expected more homogeneity among the entities within a population (Study 2), and perceived an extreme value to be more indicative of an outlier (Study 3). These results suggest that individuals are likely to use their implicit self-theory orientations (entity theory versus incremental theory) to see a population in general as a constitution either of homogeneous or heterogeneous entities.

Basis function models for animal movement

USGS Publications Warehouse

Hooten, Mevin B.; Johnson, Devin S.

2017-01-01

Advances in satellite-based data collection techniques have served as a catalyst for new statistical methodology to analyze these data. In wildlife ecological studies, satellite-based data and methodology have provided a wealth of information about animal space use and the investigation of individual-based animal–environment relationships. With the technology for data collection improving dramatically over time, we are left with massive archives of historical animal telemetry data of varying quality. While many contemporary statistical approaches for inferring movement behavior are specified in discrete time, we develop a flexible continuous-time stochastic integral equation framework that is amenable to reduced-rank second-order covariance parameterizations. We demonstrate how the associated first-order basis functions can be constructed to mimic behavioral characteristics in realistic trajectory processes using telemetry data from mule deer and mountain lion individuals in western North America. Our approach is parallelizable and provides inference for heterogenous trajectories using nonstationary spatial modeling techniques that are feasible for large telemetry datasets. Supplementary materials for this article are available online.

Refining the Use of Linkage Disequilibrium as a Robust Signature of Selective Sweeps

PubMed Central

Jacobs, Guy S.; Sluckin, Timothy J.; Kivisild, Toomas

2016-01-01

During a selective sweep, characteristic patterns of linkage disequilibrium can arise in the genomic region surrounding a selected locus. These have been used to infer past selective sweeps. However, the recombination rate is known to vary substantially along the genome for many species. We here investigate the effectiveness of current (Kelly’s ZnS and ωmax) and novel statistics at inferring hard selective sweeps based on linkage disequilibrium distortions under different conditions, including a human-realistic demographic model and recombination rate variation. When the recombination rate is constant, Kelly’s ZnS offers high power, but is outperformed by a novel statistic that we test, which we call Zα. We also find this statistic to be effective at detecting sweeps from standing variation. When recombination rate fluctuations are included, there is a considerable reduction in power for all linkage disequilibrium-based statistics. However, this can largely be reversed by appropriately controlling for expected linkage disequilibrium using a genetic map. To further test these different methods, we perform selection scans on well-characterized HapMap data, finding that all three statistics—ωmax, Kelly’s ZnS, and Zα—are able to replicate signals at regions previously identified as selection candidates based on population differentiation or the site frequency spectrum. While ωmax replicates most candidates when recombination map data are not available, the ZnS and Zα statistics are more successful when recombination rate variation is controlled for. Given both this and their higher power in simulations of selective sweeps, these statistics are preferred when information on local recombination rate variation is available. PMID:27516617

How accurately can other people infer your thoughts-And does culture matter?

PubMed

Valanides, Constantinos; Sheppard, Elizabeth; Mitchell, Peter

2017-01-01

This research investigated how accurately people infer what others are thinking after observing a brief sample of their behaviour and whether culture/similarity is a relevant factor. Target participants (14 British and 14 Mediterraneans) were cued to think about either positive or negative events they had experienced. Subsequently, perceiver participants (16 British and 16 Mediterraneans) watched videos of the targets thinking about these things. Perceivers (both groups) were significantly accurate in judging when targets had been cued to think of something positive versus something negative, indicating notable inferential ability. Additionally, Mediterranean perceivers were better than British perceivers in making such inferences, irrespective of nationality of the targets, something that was statistically accounted for by corresponding group differences in levels of independently measured collectivism. The results point to the need for further research to investigate the possibility that being reared in a collectivist culture fosters ability in interpreting others' behaviour.

Friction Laws Derived From the Acoustic Emissions of a Laboratory Fault by Machine Learning

NASA Astrophysics Data System (ADS)

Rouet-Leduc, B.; Hulbert, C.; Ren, C. X.; Bolton, D. C.; Marone, C.; Johnson, P. A.

2017-12-01

Fault friction controls nearly all aspects of fault rupture, yet it is only possible to measure in the laboratory. Here we describe laboratory experiments where acoustic emissions are recorded from the fault. We find that by applying a machine learning approach known as "extreme gradient boosting trees" to the continuous acoustical signal, the fault friction can be directly inferred, showing that instantaneous characteristics of the acoustic signal are a fingerprint of the frictional state. This machine learning-based inference leads to a simple law that links the acoustic signal to the friction state, and holds for every stress cycle the laboratory fault goes through. The approach does not use any other measured parameter than instantaneous statistics of the acoustic signal. This finding may have importance for inferring frictional characteristics from seismic waves in Earth where fault friction cannot be measured.

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.

Stochastic inference with spiking neurons in the high-conductance state

NASA Astrophysics Data System (ADS)

Petrovici, Mihai A.; Bill, Johannes; Bytschok, Ilja; Schemmel, Johannes; Meier, Karlheinz

2016-10-01

The highly variable dynamics of neocortical circuits observed in vivo have been hypothesized to represent a signature of ongoing stochastic inference but stand in apparent contrast to the deterministic response of neurons measured in vitro. Based on a propagation of the membrane autocorrelation across spike bursts, we provide an analytical derivation of the neural activation function that holds for a large parameter space, including the high-conductance state. On this basis, we show how an ensemble of leaky integrate-and-fire neurons with conductance-based synapses embedded in a spiking environment can attain the correct firing statistics for sampling from a well-defined target distribution. For recurrent networks, we examine convergence toward stationarity in computer simulations and demonstrate sample-based Bayesian inference in a mixed graphical model. This points to a new computational role of high-conductance states and establishes a rigorous link between deterministic neuron models and functional stochastic dynamics on the network level.

Similar Associations of Tooth Microwear and Morphology Indicate Similar Diet across Marsupial and Placental Mammals

PubMed Central

Christensen, Hilary B.

2014-01-01

Low-magnification microwear techniques have been used effectively to infer diets within many unrelated mammalian orders, but the extent to which patterns are comparable among such different groups, including long extinct mammal lineages, is unknown. Microwear patterns between ecologically equivalent placental and marsupial mammals are found to be statistically indistinguishable, indicating that microwear can be used to infer diet across the mammals. Microwear data were compared to body size and molar shearing crest length in order to develop a system to distinguish the diet of mammals. Insectivores and carnivores were difficult to distinguish from herbivores using microwear alone, but combining microwear data with body size estimates and tooth morphology provides robust dietary inferences. This approach is a powerful tool for dietary assessment of fossils from extinct lineages and from museum specimens of living species where field study would be difficult owing to the animal’s behavior, habitat, or conservation status. PMID:25099537

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

Bayesian Inference on Proportional Elections

PubMed Central

Brunello, Gabriel Hideki Vatanabe; Nakano, Eduardo Yoshio

2015-01-01

Polls for majoritarian voting systems usually show estimates of the percentage of votes for each candidate. However, proportional vote systems do not necessarily guarantee the candidate with the most percentage of votes will be elected. Thus, traditional methods used in majoritarian elections cannot be applied on proportional elections. In this context, the purpose of this paper was to perform a Bayesian inference on proportional elections considering the Brazilian system of seats distribution. More specifically, a methodology to answer the probability that a given party will have representation on the chamber of deputies was developed. Inferences were made on a Bayesian scenario using the Monte Carlo simulation technique, and the developed methodology was applied on data from the Brazilian elections for Members of the Legislative Assembly and Federal Chamber of Deputies in 2010. A performance rate was also presented to evaluate the efficiency of the methodology. Calculations and simulations were carried out using the free R statistical software. PMID:25786259

Bayesian inference on proportional elections.

PubMed

Brunello, Gabriel Hideki Vatanabe; Nakano, Eduardo Yoshio

2015-01-01

Polls for majoritarian voting systems usually show estimates of the percentage of votes for each candidate. However, proportional vote systems do not necessarily guarantee the candidate with the most percentage of votes will be elected. Thus, traditional methods used in majoritarian elections cannot be applied on proportional elections. In this context, the purpose of this paper was to perform a Bayesian inference on proportional elections considering the Brazilian system of seats distribution. More specifically, a methodology to answer the probability that a given party will have representation on the chamber of deputies was developed. Inferences were made on a Bayesian scenario using the Monte Carlo simulation technique, and the developed methodology was applied on data from the Brazilian elections for Members of the Legislative Assembly and Federal Chamber of Deputies in 2010. A performance rate was also presented to evaluate the efficiency of the methodology. Calculations and simulations were carried out using the free R statistical software.

Causal inference as an emerging statistical approach in neurology: an example for epilepsy in the elderly.

PubMed

Moura, Lidia Mvr; Westover, M Brandon; Kwasnik, David; Cole, Andrew J; Hsu, John

2017-01-01

The elderly population faces an increasing number of cases of chronic neurological conditions, such as epilepsy and Alzheimer's disease. Because the elderly with epilepsy are commonly excluded from randomized controlled clinical trials, there are few rigorous studies to guide clinical practice. When the elderly are eligible for trials, they either rarely participate or frequently have poor adherence to therapy, thus limiting both generalizability and validity. In contrast, large observational data sets are increasingly available, but are susceptible to bias when using common analytic approaches. Recent developments in causal inference-analytic approaches also introduce the possibility of emulating randomized controlled trials to yield valid estimates. We provide a practical example of the application of the principles of causal inference to a large observational data set of patients with epilepsy. This review also provides a framework for comparative-effectiveness research in chronic neurological conditions.

How accurately can other people infer your thoughts—And does culture matter?

PubMed Central

Valanides, Constantinos; Sheppard, Elizabeth; Mitchell, Peter

2017-01-01

This research investigated how accurately people infer what others are thinking after observing a brief sample of their behaviour and whether culture/similarity is a relevant factor. Target participants (14 British and 14 Mediterraneans) were cued to think about either positive or negative events they had experienced. Subsequently, perceiver participants (16 British and 16 Mediterraneans) watched videos of the targets thinking about these things. Perceivers (both groups) were significantly accurate in judging when targets had been cued to think of something positive versus something negative, indicating notable inferential ability. Additionally, Mediterranean perceivers were better than British perceivers in making such inferences, irrespective of nationality of the targets, something that was statistically accounted for by corresponding group differences in levels of independently measured collectivism. The results point to the need for further research to investigate the possibility that being reared in a collectivist culture fosters ability in interpreting others’ behaviour. PMID:29112972

The influence of cognitive ability and instructional set on causal conditional inference.

PubMed

Evans, Jonathan St B T; Handley, Simon J; Neilens, Helen; Over, David

2010-05-01

We report a large study in which participants are invited to draw inferences from causal conditional sentences with varying degrees of believability. General intelligence was measured, and participants were split into groups of high and low ability. Under strict deductive-reasoning instructions, it was observed that higher ability participants were significantly less influenced by prior belief than were those of lower ability. This effect disappeared, however, when pragmatic reasoning instructions were employed in a separate group. These findings are in accord with dual-process theories of reasoning. We also took detailed measures of beliefs in the conditional sentences used for the reasoning tasks. Statistical modelling showed that it is not belief in the conditional statement per se that is the causal factor, but rather correlates of it. Two different models of belief-based reasoning were found to fit the data according to the kind of instructions and the type of inference under consideration.

Fluency heuristic: a model of how the mind exploits a by-product of information retrieval.

PubMed

Hertwig, Ralph; Herzog, Stefan M; Schooler, Lael J; Reimer, Torsten

2008-09-01

Boundedly rational heuristics for inference can be surprisingly accurate and frugal for several reasons. They can exploit environmental structures, co-opt complex capacities, and elude effortful search by exploiting information that automatically arrives on the mental stage. The fluency heuristic is a prime example of a heuristic that makes the most of an automatic by-product of retrieval from memory, namely, retrieval fluency. In 4 experiments, the authors show that retrieval fluency can be a proxy for real-world quantities, that people can discriminate between two objects' retrieval fluencies, and that people's inferences are in line with the fluency heuristic (in particular fast inferences) and with experimentally manipulated fluency. The authors conclude that the fluency heuristic may be one tool in the mind's repertoire of strategies that artfully probes memory for encapsulated frequency information that can veridically reflect statistical regularities in the world. (c) 2008 APA, all rights reserved.

Effects of Data Anonymization by Cell Suppression on Descriptive Statistics and Predictive Modeling Performance

PubMed Central

Ohno-Machado, Lucila; Vinterbo, Staal; Dreiseitl, Stephan

2002-01-01

Protecting individual data in disclosed databases is essential. Data anonymization strategies can produce table ambiguation by suppression of selected cells. Using table ambiguation, different degrees of anonymization can be achieved, depending on the number of individuals that a particular case must become indistinguishable from. This number defines the level of anonymization. Anonymization by cell suppression does not necessarily prevent inferences from being made from the disclosed data. Preventing inferences may be important to preserve confidentiality. We show that anonymized data sets can preserve descriptive characteristics of the data, but might also be used for making inferences on particular individuals, which is a feature that may not be desirable. The degradation of predictive performance is directly proportional to the degree of anonymity. As an example, we report the effect of anonymization on the predictive performance of a model constructed to estimate the probability of disease given clinical findings.

Effects of data anonymization by cell suppression on descriptive statistics and predictive modeling performance.

PubMed Central

Ohno-Machado, L.; Vinterbo, S. A.; Dreiseitl, S.

2001-01-01

Protecting individual data in disclosed databases is essential. Data anonymization strategies can produce table ambiguation by suppression of selected cells. Using table ambiguation, different degrees of anonymization can be achieved, depending on the number of individuals that a particular case must become indistinguishable from. This number defines the level of anonymization. Anonymization by cell suppression does not necessarily prevent inferences from being made from the disclosed data. Preventing inferences may be important to preserve confidentiality. We show that anonymized data sets can preserve descriptive characteristics of the data, but might also be used for making inferences on particular individuals, which is a feature that may not be desirable. The degradation of predictive performance is directly proportional to the degree of anonymity. As an example, we report the effect of anonymization on the predictive performance of a model constructed to estimate the probability of disease given clinical findings. PMID:11825239

Mistaking geography for biology: inferring processes from species distributions.

PubMed

Warren, Dan L; Cardillo, Marcel; Rosauer, Dan F; Bolnick, Daniel I

2014-10-01

Over the past few decades, there has been a rapid proliferation of statistical methods that infer evolutionary and ecological processes from data on species distributions. These methods have led to considerable new insights, but they often fail to account for the effects of historical biogeography on present-day species distributions. Because the geography of speciation can lead to patterns of spatial and temporal autocorrelation in the distributions of species within a clade, this can result in misleading inferences about the importance of deterministic processes in generating spatial patterns of biodiversity. In this opinion article, we discuss ways in which patterns of species distributions driven by historical biogeography are often interpreted as evidence of particular evolutionary or ecological processes. We focus on three areas that are especially prone to such misinterpretations: community phylogenetics, environmental niche modelling, and analyses of beta diversity (compositional turnover of biodiversity). Crown Copyright © 2014. Published by Elsevier Ltd. All rights reserved.

Modeling coverage gaps in haplotype frequencies via Bayesian inference to improve stem cell donor selection.

PubMed

Louzoun, Yoram; Alter, Idan; Gragert, Loren; Albrecht, Mark; Maiers, Martin

2018-05-01

Regardless of sampling depth, accurate genotype imputation is limited in regions of high polymorphism which often have a heavy-tailed haplotype frequency distribution. Many rare haplotypes are thus unobserved. Statistical methods to improve imputation by extending reference haplotype distributions using linkage disequilibrium patterns that relate allele and haplotype frequencies have not yet been explored. In the field of unrelated stem cell transplantation, imputation of highly polymorphic human leukocyte antigen (HLA) genes has an important application in identifying the best-matched stem cell donor when searching large registries totaling over 28,000,000 donors worldwide. Despite these large registry sizes, a significant proportion of searched patients present novel HLA haplotypes. Supporting this observation, HLA population genetic models have indicated that many extant HLA haplotypes remain unobserved. The absent haplotypes are a significant cause of error in haplotype matching. We have applied a Bayesian inference methodology for extending haplotype frequency distributions, using a model where new haplotypes are created by recombination of observed alleles. Applications of this joint probability model offer significant improvement in frequency distribution estimates over the best existing alternative methods, as we illustrate using five-locus HLA frequency data from the National Marrow Donor Program registry. Transplant matching algorithms and disease association studies involving phasing and imputation of rare variants may benefit from this statistical inference framework.

A review and comparison of Bayesian and likelihood-based inferences in beta regression and zero-or-one-inflated beta regression.

PubMed

Liu, Fang; Eugenio, Evercita C

2018-04-01

Beta regression is an increasingly popular statistical technique in medical research for modeling of outcomes that assume values in (0, 1), such as proportions and patient reported outcomes. When outcomes take values in the intervals [0,1), (0,1], or [0,1], zero-or-one-inflated beta (zoib) regression can be used. We provide a thorough review on beta regression and zoib regression in the modeling, inferential, and computational aspects via the likelihood-based and Bayesian approaches. We demonstrate the statistical and practical importance of correctly modeling the inflation at zero/one rather than ad hoc replacing them with values close to zero/one via simulation studies; the latter approach can lead to biased estimates and invalid inferences. We show via simulation studies that the likelihood-based approach is computationally faster in general than MCMC algorithms used in the Bayesian inferences, but runs the risk of non-convergence, large biases, and sensitivity to starting values in the optimization algorithm especially with clustered/correlated data, data with sparse inflation at zero and one, and data that warrant regularization of the likelihood. The disadvantages of the regular likelihood-based approach make the Bayesian approach an attractive alternative in these cases. Software packages and tools for fitting beta and zoib regressions in both the likelihood-based and Bayesian frameworks are also reviewed.

Bayesian Reconstruction of Disease Outbreaks by Combining Epidemiologic and Genomic Data

PubMed Central

Jombart, Thibaut; Cori, Anne; Didelot, Xavier; Cauchemez, Simon; Fraser, Christophe; Ferguson, Neil

2014-01-01

Recent years have seen progress in the development of statistically rigorous frameworks to infer outbreak transmission trees (“who infected whom”) from epidemiological and genetic data. Making use of pathogen genome sequences in such analyses remains a challenge, however, with a variety of heuristic approaches having been explored to date. We introduce a statistical method exploiting both pathogen sequences and collection dates to unravel the dynamics of densely sampled outbreaks. Our approach identifies likely transmission events and infers dates of infections, unobserved cases and separate introductions of the disease. It also proves useful for inferring numbers of secondary infections and identifying heterogeneous infectivity and super-spreaders. After testing our approach using simulations, we illustrate the method with the analysis of the beginning of the 2003 Singaporean outbreak of Severe Acute Respiratory Syndrome (SARS), providing new insights into the early stage of this epidemic. Our approach is the first tool for disease outbreak reconstruction from genetic data widely available as free software, the R package outbreaker. It is applicable to various densely sampled epidemics, and improves previous approaches by detecting unobserved and imported cases, as well as allowing multiple introductions of the pathogen. Because of its generality, we believe this method will become a tool of choice for the analysis of densely sampled disease outbreaks, and will form a rigorous framework for subsequent methodological developments. PMID:24465202

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.

Software for Statistical Analysis of Weibull Distributions with Application to Gear Fatigue Data: User Manual with Verification

NASA Technical Reports Server (NTRS)

Krantz, Timothy L.

2002-01-01

The Weibull distribution has been widely adopted for the statistical description and inference of fatigue data. This document provides user instructions, examples, and verification for software to analyze gear fatigue test data. The software was developed presuming the data are adequately modeled using a two-parameter Weibull distribution. The calculations are based on likelihood methods, and the approach taken is valid for data that include type 1 censoring. The software was verified by reproducing results published by others.

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.