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

This paper presents a fully Bayesian approach that simultaneously combines basic event and statistically independent higher event-level failure data in fault tree quantification. Such higher-level data could correspond to train, sub-system or system failure events. The full Bayesian approach also allows the highest-level data that are usually available for existing facilities to be automatically propagated to lower levels. A simple example illustrates the proposed approach. The optimal allocation of resources for collecting additional data from a choice of different level events is also presented. The optimization is achieved using a genetic algorithm.

/pdf/a-fully-bayesian-approach-for-combining-multilevel-failure-23j95czbst.pdf

A Fully Bayesian Approach for Combining Multilevel Failure Information in Fault Tree Quantification and Corresponding Optimal Resource Allocation

Two methods for segmenting SPECT (single photon emission computed tomography) and PET (positron emission tomography) images are introduced and evaluated These region classification schemes are intended primarily for use within Bayesian reconstruction procedures that estimate the number of regions, the region means, and the region membership and radiopharmaceutical concentration for each pixel One segmentation method utilizes the probability of the unobserved number of photons emitted from a pixel given that pixel's region membership The second technique considers directly the conditional probability of the detector data This second method is more robust and leads to better estimates of radiopharmaceutical concentration >

Image segmentation in Bayesian reconstructions for emission computed tomography

In SPECT and PET imaging, radiopharmaceutical concentration is often strongly correlated with anatomical structure A Bayesian image reconstruction procedure is presented that uses this a priori knowledge to improve the detection and quantification of an unknown number of lesions The a priori distribution employed encourages the emission tomography segmentation to stay close to the anatomical segmentation Departures from the anatomical segmentation are detected by calculating and segmenting a deviances image: Let n/sub i/ be the estimated number of photons emitted from voxel i, /spl mu//sub ri/ the estimated mean activity of the region that contains voxel i, and l(/spl lambda//sub i/;n/sub i/) the Poisson log likelihood function for /spl lambda//sub i/, where /spl lambda//sub i/ is the mean of n/sub i/ The deviances are defined as 2(l(n/sub i/;n/sub i/)-l(/spl mu//sub ri/;n/sub i/)) Parts of the image having large deviances are candidates for becoming new regions Hypothesis testing is performed to determine which of these candidates are justified by the projection data as being new regions The procedure was tested by adding hot lesions to a bitmap of the Hoffman brain phantom and then simulating noisy projection data Improvements in detection and quantification of these lesions were observed as compared to FBP and ML-EM reconstructions >

Improved lesion detection and quantification in emission tomography using anatomical and physiological prior information

To evaluate the utility of automated deformable image registration (DIR) algorithms, it is necessary to evaluate both the registration accuracy of the DIR algorithm itself, as well as the registration accuracy of the human readers from whom the ”gold standard” is obtained. We propose a Bayesian hierarchical model to evaluate the spatial accuracy of human readers and automatic DIR methods based on multiple image registration data generated by human readers and automatic DIR methods. To fully account for the locations of landmarks in all images, we treat the true locations of landmarks as latent variables and impose a hierarchical structure on the magnitude of registration errors observed across image pairs. DIR registration errors are modeled using Gaussian processes with reference prior densities on prior parameters that determine the associated covariance matrices. We develop a Gibbs sampling algorithm to efficiently fit our models to high-dimensional data, and apply the proposed method to analyze an image dataset obtained from a 4D thoracic CT study.

Evaluation of image registration spatial accuracy using a Bayesian hierarchical model

Differences between inferences obtained from Bayesian reliability models using system-level data versus component-level data have motivated a call for a 'basic restructuring of the Bayes procedure'. This paper explores the source of such differences and demonstrates that Bayesian models would be aberrant only if such differences did not exist.

Valen E. Johnson

Papers

A Fully Bayesian Approach for Combining Multilevel Failure Information in Fault Tree Quantification and Corresponding Optimal Resource Allocation

Image segmentation in Bayesian reconstructions for emission computed tomography

Improved lesion detection and quantification in emission tomography using anatomical and physiological prior information

Evaluation of image registration spatial accuracy using a Bayesian hierarchical model

Bayesian aggregation error