Today's Web-enabled deluge of electronic data calls for automated methods of data analysis. Machine learning provides these, developing methods that can automatically detect patterns in data and then use the uncovered patterns to predict future data. This textbook offers a comprehensive and self-contained introduction to the field of machine learning, based on a unified, probabilistic approach. The coverage combines breadth and depth, offering necessary background material on such topics as probability, optimization, and linear algebra as well as discussion of recent developments in the field, including conditional random fields, L1 regularization, and deep learning. The book is written in an informal, accessible style, complete with pseudo-code for the most important algorithms. All topics are copiously illustrated with color images and worked examples drawn from such application domains as biology, text processing, computer vision, and robotics. Rather than providing a cookbook of different heuristic methods, the book stresses a principled model-based approach, often using the language of graphical models to specify models in a concise and intuitive way. Almost all the models described have been implemented in a MATLAB software package--PMTK (probabilistic modeling toolkit)--that is freely available online. The book is suitable for upper-level undergraduates with an introductory-level college math background and beginning graduate students.

Machine Learning : A Probabilistic Perspective

Bayesian methods have garnered huge interest in cognitive science as an approach to models of cognition and perception. On the other hand, Bayesian methods for data analysis have not yet made much headway in cognitive science against the institutionalized inertia of 20th century null hypothesis significance testing (NHST). Ironically, specific Bayesian models of cognition and perception may not long endure the ravages of empirical verification, but generic Bayesian methods for data analysis will eventually dominate. It is time that Bayesian data analysis became the norm for empirical methods in cognitive science. This article reviews a fatal flaw of NHST and introduces the reader to some benefits of Bayesian data analysis. The article presents illustrative examples of multiple comparisons in Bayesian analysis of variance and Bayesian approaches to statistical power. Copyright © 2010 John Wiley & Sons, Ltd. For further resources related to this article, please visit the WIREs website.

Bayesian data analysis.

Cobb’s concern was a long-worrisome circularity in the sociology of science based on the use of bright lines such as p< 0.05: “We teach it because it’s what we do; we do it because it’s what we teach.” This concern was brought to the attention of the ASA Board. The ASA Board was also stimulated by highly visible discussions over the last few years. For example, ScienceNews (Siegfried 2010) wrote: “It’s science’s dirtiest secret: The ‘scientific method’ of testing hypotheses by statistical analysis stands on a flimsy foundation.” A November 2013, article in Phys.org Science News Wire (2013) cited “numerous deep flaws” in null hypothesis significance testing. A ScienceNews article (Siegfried 2014) on February 7, 2014, said “statistical techniques for testing hypotheses...havemore flaws than Facebook’s privacy policies.” Aweek later, statistician and “Simply Statistics” blogger Jeff Leek responded. “The problem is not that people use P-values poorly,” Leek wrote, “it is that the vast majority of data analysis is not performed by people properly trained to perform data analysis” (Leek 2014). That same week, statistician and science writer Regina Nuzzo published an article in Nature entitled “Scientific Method: Statistical Errors” (Nuzzo 2014). That article is nowone of the most highly viewedNature articles, as reported by altmetric.com (http://www.altmetric.com/details/2115792#score). Of course, it was not simply a matter of responding to some articles in print. The statistical community has been deeply concerned about issues of reproducibility and replicability of scientific conclusions. Without getting into definitions and distinctions of these terms, we observe that much confusion and even doubt about the validity of science is arising. Such doubt can lead to radical choices, such as the one taken by the editors of Basic andApplied Social Psychology, who decided to ban p-values (null hypothesis significance testing) (Trafimow and Marks 2015). Misunderstanding or misuse of statistical inference is only one cause of the “reproducibility crisis” (Peng 2015), but to our community, it is an important one. When the ASA Board decided to take up the challenge of developing a policy statement on p-values and statistical significance, it did so recognizing this was not a lightly taken step. The ASA has not previously taken positions on specific matters of statistical practice. The closest the association has come to this is a statement on the use of value-added models (VAM) for educational assessment (Morganstein and Wasserstein 2014) and a statement on risk-limiting post-election audits (American Statistical Association 2010). However, these were truly policy-related statements. The VAM statement addressed a key educational policy issue, acknowledging the complexity of the issues involved, citing limitations of VAMs as effective performance models, and urging that they be developed and interpreted with the involvement of statisticians. The statement on election auditing was also in response to a major but specific policy issue (close elections in 2008), and said that statistically based election audits should become a routine part of election processes. By contrast, the Board envisioned that the ASA statement on p-values and statistical significance would shed light on an aspect of our field that is too often misunderstood and misused in the broader research community, and, in the process, provides the community a service. The intended audience would be researchers, practitioners, and science writers who are not primarily statisticians. Thus, this statementwould be quite different from anything previously attempted. The Board tasked Wasserstein with assembling a group of experts representing a wide variety of points of view. On behalf of the Board, he reached out to more than two dozen such people, all of whom said theywould be happy to be involved. Several expressed doubt about whether agreement could be reached, but those who did said, in effect, that if there was going to be a discussion, they wanted to be involved. Over the course of many months, group members discussed what format the statement should take, tried to more concretely visualize the audience for the statement, and began to find points of agreement. That turned out to be relatively easy to do, but it was just as easy to find points of intense disagreement. The time came for the group to sit down together to hash out these points, and so in October 2015, 20 members of the group met at the ASA Office in Alexandria, Virginia. The 2-day meeting was facilitated by Regina Nuzzo, and by the end of the meeting, a good set of points around which the statement could be built was developed. The next 3 months saw multiple drafts of the statement, reviewed by group members, by Board members (in a lengthy discussion at the November 2015 ASA Board meeting), and by members of the target audience. Finally, on January 29, 2016, the Executive Committee of the ASA approved the statement. The statement development process was lengthier and more controversial than anticipated. For example, there was considerable discussion about how best to address the issue of multiple potential comparisons (Gelman and Loken 2014). We debated at some length the issues behind the words “a p-value near 0.05 taken by itself offers only weak evidence against the null

https://www.tandfonline.com/doi/pdf/10.1080/00031305.2016.1154108

The ASA's Statement on p-Values: Context, Process, and Purpose

The analysis of medical images has been woven into the fabric of the pattern analysis and machine intelligence (PAMI) community since the earliest days of these Transactions. Initially, the efforts in this area were seen as applying pattern analysis and computer vision techniques to another interesting dataset. However, over the last two to three decades, the unique nature of the problems presented within this area of study have led to the development of a new discipline in its own right. Examples of these include: the types of image information that are acquired, the fully three-dimensional image data, the nonrigid nature of object motion and deformation, and the statistical variation of both the underlying normal and abnormal ground truth. In this paper, we look at progress in the field over the last 20 years and suggest some of the challenges that remain for the years to come.

https://hal.inria.fr/inria-00615100/document

Medical image analysis: progress over two decades and the challenges ahead

(1998). Human cognitive abilities: A survey of factor analytic studies. Gifted and Talented International: Vol. 13, No. 2, pp. 97-98.

Human cognitive abilities: A survey of factor analytic studies

Item Response Modeling

Existing Bayesian model selection procedures require the specification of prior distributions on the parameters appearing in every model in the selection set. In practice, this requirement limits the application of Bayesian model selection methodology. To overcome this limitation, we propose a new approach towards Bayesian model selection that uses classical test statistics to compute Bayes factors between possible models. In several test cases, our approach produces results that are similar to previously proposed Bayesian model selection and model averaging techniques in which prior distributions were carefully chosen. In addition to eliminating the requirement to specify complicated prior distributions, this method offers important computational and algorithmic advantages over existing simulation-based methods. Because it is easy to evaluate the operating characteristics of this procedure for a given sample size and specified number of covariates, our method facilitates the selection of hyperparameter values through prior-predictive simulation.

/pdf/bayesian-model-selection-using-test-statistics-58uvkk2hzl.pdf

Bayesian model selection using test statistics.

We propose a Bayesian model for medical image analysis that permits prior structural information to be incorporated into the estimation of image features. Although the proposed methodology can be applied to a broad spectrum of images, we restrict attention here to emission computed tomography (ECT) images, and in particular single photon emission computed tomography (SPECT) images.

Analysis and Reconstruction of Medical Images Using Prior Information

Purpose: Evaluation of count rate performance (CRP) is an integral component of gamma camera quality assurance and system deadtime (τ) may be utilized for image correction in quantitative studies. This work characterizes the CRP of three modern gamma cameras and estimates τ using two established methods (decay and dual source) under a variety of experimental conditions. Methods: For the decay method, uncollimated detectors were exposed to a Tc-99m source of relatively high activity and count rates were sampled regularly over 48 h. Input count rate at each time point was based on the lowest observed count rate data point. The input count rate was plotted against the observed count rate and fit via least-squares to the paralyzable detector model (PDM) to estimateτ (rates method). A novel expression for observed counts as a function of measurement time interval was derived, taking into account the PDM and the presence of background but making no assumption regarding input count rate. The observed counts were fit via least-squares to this novel expression to estimate τ (counts method). Correlation and Bland-Altman analyses were performed to assess agreement in estimates of τ between the rates and counts methods. The dependence of τ on energy window definition and incident energy spectrum were characterized. The dual source method was also used to estimate τ and its agreement with estimates from the decay method under identical conditions was also investigated. The dependences of τ on the total activity and the ratio of source activities were characterized. Results: The observed CRP curves for each gamma camera agreed with the PDM at low count rates but deviated substantially from it at high count rates. The estimates ofτ determined from the paralyzable portion of the CPR curve using the rates method and the counts method were found to be highly correlated (r = 0.999) but with a small (∼6%) difference. No statistically significant difference was observed between the estimates of τ using the decay or dual source methods under identical experimental conditions (p = 0.13). Estimates of τ increased as a power-law function with decreasing ratio of counts in the photopeak to the total counts. Also, estimates of τ increased linearly as spectral effective energy decreased. No significant difference was observed between the dependences of τ on energy window definition or incident spectrum between the decay and dual source methods. Estimates of τ using the dual source method varied as a quadratic on the ratio of the single source to combined source activities and linearly with total activity. Conclusions: The CRP curves for three modern gamma camera models have been characterized, demonstrating unexpected behavior that necessitates the determination of bothτ and maximum count rate to fully characterize the CRP curve. τ was estimated under a variety of experimental conditions, based on which guidelines for the performance of CRP testing in a clinical setting have been proposed.

/pdf/characterization-of-the-count-rate-performance-of-modern-2lqlw2hkqu.pdf

Characterization of the count rate performance of modern gamma cameras

In this paper we describe a statistical model for the observation of labeled points in gated cardiac single photon emission computed tomography (SPECT) images. The model has two major parts: one based on shape correspondence between the image for evaluation and a reference image, and a second based on the match in image features. While the statistical deformation model is applicable to a broad range of image objects, the addition of a contraction mechanism to the baseline model provides particularly convincing results in gated cardiac SPECT. The model is applied to clinical data and provides marked improvement in the quality of summary images for the time series. Estimates of heart deformation and contraction parameters are also obtained.

Valen E. Johnson

Papers

Item Response Modeling

Bayesian model selection using test statistics.

Analysis and Reconstruction of Medical Images Using Prior Information

Characterization of the count rate performance of modern gamma cameras

A Hierarchical Feature Based Deformation Model Applied to 4D Cardiac SPECT Data