1
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Lu Y, Zheng Q, Henning K. An Exact Bayesian Model for Meta-Analysis of the Standardized Mean Difference with Its Simultaneous Credible Intervals. MULTIVARIATE BEHAVIORAL RESEARCH 2024:1-19. [PMID: 39042102 DOI: 10.1080/00273171.2024.2358233] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 07/24/2024]
Abstract
While Bayesian methodology is increasingly favored in behavioral research for its clear probabilistic inference and model structure, its widespread acceptance as a standard meta-analysis approach remains limited. Although some conventional Bayesian hierarchical models are frequently used for analysis, their performance has not been thoroughly examined. This study evaluates two commonly used Bayesian models for meta-analysis of standardized mean difference and identifies significant issues with these models. In response, we introduce a new Bayesian model equipped with novel features that address existing model concerns and a broader limitation of the current Bayesian meta-analysis. Furthermore, we introduce a simple computational approach to construct simultaneous credible intervals for the summary effect and between-study heterogeneity, based on their joint posterior samples. This fully captures the joint uncertainty in these parameters, a task that is challenging or impractical with frequentist models. Through simulation studies rooted in a joint Bayesian/frequentist paradigm, we compare our model's performance against existing ones under conditions that mirror realistic research scenarios. The results reveal that our new model outperforms others and shows enhanced statistical properties. We also demonstrate the practicality of our models using real-world examples, highlighting how our approach strengthens the robustness of inferences regarding the summary effect.
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Affiliation(s)
| | | | - Kevin Henning
- Sam Houston State University, Huntsville, Texas, USA
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2
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Manning TS, Alexander E, Cumming BG, DeAngelis GC, Huang X, Cooper EA. Transformations of sensory information in the brain suggest changing criteria for optimality. PLoS Comput Biol 2024; 20:e1011783. [PMID: 38206969 PMCID: PMC10807827 DOI: 10.1371/journal.pcbi.1011783] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/17/2023] [Revised: 01/24/2024] [Accepted: 12/22/2023] [Indexed: 01/13/2024] Open
Abstract
Neurons throughout the brain modulate their firing rate lawfully in response to sensory input. Theories of neural computation posit that these modulations reflect the outcome of a constrained optimization in which neurons aim to robustly and efficiently represent sensory information. Our understanding of how this optimization varies across different areas in the brain, however, is still in its infancy. Here, we show that neural sensory responses transform along the dorsal stream of the visual system in a manner consistent with a transition from optimizing for information preservation towards optimizing for perceptual discrimination. Focusing on the representation of binocular disparities-the slight differences in the retinal images of the two eyes-we re-analyze measurements characterizing neuronal tuning curves in brain areas V1, V2, and MT (middle temporal) in the macaque monkey. We compare these to measurements of the statistics of binocular disparity typically encountered during natural behaviors using a Fisher Information framework. The differences in tuning curve characteristics across areas are consistent with a shift in optimization goals: V1 and V2 population-level responses are more consistent with maximizing the information encoded about naturally occurring binocular disparities, while MT responses shift towards maximizing the ability to support disparity discrimination. We find that a change towards tuning curves preferring larger disparities is a key driver of this shift. These results provide new insight into previously-identified differences between disparity-selective areas of cortex and suggest these differences play an important role in supporting visually-guided behavior. Our findings emphasize the need to consider not just information preservation and neural resources, but also relevance to behavior, when assessing the optimality of neural codes.
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Affiliation(s)
- Tyler S. Manning
- Herbert Wertheim School of Optometry & Vision Science, University of California, Berkeley
| | - Emma Alexander
- Department of Computer Science, Northwestern University, Illinois, United States of America
| | - Bruce G. Cumming
- Laboratory of Sensorimotor Research, National Eye Institute, National Institutes of Health, Maryland, United States of America
| | - Gregory C. DeAngelis
- Department of Brain and Cognitive Sciences, University of Rochester, New York, United States of America
| | - Xin Huang
- Department of Neuroscience, University of Wisconsin, Madison
| | - Emily A. Cooper
- Herbert Wertheim School of Optometry & Vision Science, University of California, Berkeley
- Helen Wills Neuroscience Institute, University of California, Berkeley
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3
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Ali S, Waheed M, Shah I, Raza SMM. Bayesian sample size determination for coefficient of variation of normal distribution. J Appl Stat 2023; 51:1271-1286. [PMID: 38835829 PMCID: PMC11146254 DOI: 10.1080/02664763.2023.2197571] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/15/2021] [Accepted: 03/27/2023] [Indexed: 06/06/2024]
Abstract
Sample size determination is an active area of research in statistics. Generally, Bayesian methods provide relatively smaller sample sizes than the classical techniques, particularly average length criterion is more conventional and gives relatively small sample sizes under the given constraints. The objective of this study is to utilize major Bayesian sample size determination techniques for the coefficient of variation of normal distribution and assess their performance by comparing the results with the freqentist approach. To this end, we noticed that the average coverage criterion is the one that provides relatively smaller sample sizes than the worst outcome criterion. By comparing with the existing frequentist studies, we show that a smaller sample size is required in Bayesian methods to achieve the same efficiency.
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Affiliation(s)
- Sajid Ali
- Department of Statistics, Quaid-i-Azam University, Islamabad, Pakistan
| | - Mariyam Waheed
- Department of Statistics, Quaid-i-Azam University, Islamabad, Pakistan
| | - Ismail Shah
- Department of Statistics, Quaid-i-Azam University, Islamabad, Pakistan
| | - Syed Muhammad Muslim Raza
- Department of Economics and Statistics, Dr Hasan Murad School of Management Sciences, University of Management and Technology, Lahore, Pakistan
- Department of Statistics, Virtual University of Pakistan, Lahore, Pakistan
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4
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Hai Y, Shi S, Qin G. Bayesian and influence function-based empirical likelihoods for inference of sensitivity to the early diseased stage in diagnostic tests. Biom J 2023; 65:e2200021. [PMID: 36642803 PMCID: PMC10006346 DOI: 10.1002/bimj.202200021] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/21/2022] [Revised: 09/11/2022] [Accepted: 10/08/2022] [Indexed: 01/17/2023]
Abstract
In practice, a disease process might involve three ordinal diagnostic stages: the normal healthy stage, the early stage of the disease, and the stage of full development of the disease. Early detection is critical for some diseases since it often means an optimal time window for therapeutic treatments of the diseases. In this study, we propose a new influence function-based empirical likelihood method and Bayesian empirical likelihood methods to construct confidence/credible intervals for the sensitivity of a test to patients in the early diseased stage given a specificity and a sensitivity of the test to patients in the fully diseased stage. Numerical studies are performed to compare the finite sample performances of the proposed approaches with existing methods. The proposed methods are shown to outperform existing methods in terms of coverage probability. A real dataset from the Alzheimer's Disease Neuroimaging Initiative (ANDI) is used to illustrate the proposed methods.
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Affiliation(s)
- Yan Hai
- Department of Mathematics and Statistics, Georgia State University, Atlanta GA 30303, U.S.A
| | - Shuangfei Shi
- Department of Mathematics and Statistics, Georgia State University, Atlanta GA 30303, U.S.A
| | - Gengsheng Qin
- Department of Mathematics and Statistics, Georgia State University, Atlanta GA 30303, U.S.A
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5
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Williams JP, Ommen DM, Hannig J. Generalized fiducial factor: An alternative to the Bayes factor for forensic identification of source problems. Ann Appl Stat 2023. [DOI: 10.1214/22-aoas1632] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/26/2023]
Affiliation(s)
| | | | - Jan Hannig
- Department of Statistics and Operations Research, UNC at Chapel Hill and National Institute of Standards and Technology
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6
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Shemyakin A. Hellinger Information Matrix and Hellinger Priors. ENTROPY (BASEL, SWITZERLAND) 2023; 25:e25020344. [PMID: 36832710 PMCID: PMC9954804 DOI: 10.3390/e25020344] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/20/2022] [Revised: 01/16/2023] [Accepted: 02/06/2023] [Indexed: 06/01/2023]
Abstract
Hellinger information as a local characteristic of parametric distribution families was first introduced in 2011. It is related to the much older concept of the Hellinger distance between two points in a parametric set. Under certain regularity conditions, the local behavior of the Hellinger distance is closely connected to Fisher information and the geometry of Riemann manifolds. Nonregular distributions (non-differentiable distribution densities, undefined Fisher information or denisities with support depending on the parameter), including uniform, require using analogues or extensions of Fisher information. Hellinger information may serve to construct information inequalities of the Cramer-Rao type, extending the lower bounds of the Bayes risk to the nonregular case. A construction of non-informative priors based on Hellinger information was also suggested by the author in 2011. Hellinger priors extend the Jeffreys rule to nonregular cases. For many examples, they are identical or close to the reference priors or probability matching priors. Most of the paper was dedicated to the one-dimensional case, but the matrix definition of Hellinger information was also introduced for higher dimensions. Conditions of existence and the nonnegative definite property of Hellinger information matrix were not discussed. Hellinger information for the vector parameter was applied by Yin et al. to problems of optimal experimental design. A special class of parametric problems was considered, requiring the directional definition of Hellinger information, but not a full construction of Hellinger information matrix. In the present paper, a general definition, the existence and nonnegative definite property of Hellinger information matrix is considered for nonregular settings.
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Affiliation(s)
- Arkady Shemyakin
- Mathematics Department, University of St. Thomas, 2115 Summit Ave, St. Paul, MN 55105, USA
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7
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Markon KE. Reliability as Lindley Information. MULTIVARIATE BEHAVIORAL RESEARCH 2022:1-28. [PMID: 36539390 DOI: 10.1080/00273171.2022.2136613] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/17/2023]
Abstract
This paper introduces a definition of reliability based on Lindley information, which is the mutual information between an observed measure and latent attribute. This definition reduces to the traditional definition of reliability in the case of normal variables, but can be applied to any joint distribution of observed and latent variables. Importantly, unlike traditional definitions of reliability, this formulation of reliability applies to vector- or matrix-valued estimates and summaries of responses, and therefore generalizes reliability to sets of scores and estimates in addition to individual scores and estimates. This formulation also leads to new bounds for reliability, as well as newly reported relationships between reliability and the traditional Fisher information function familiar in item response theory literature. This form of reliability can be estimated using formulae, or methods used in Bayesian inference such as Markov Chain Monte Carlo (MCMC) depending on the case. Examples based on well-studied datasets are provided, as well as applications to drift-diffusion modeling and randomly-varying intraindividual covariance structures.
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8
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Fay MP, Proschan MA, Brittain EH, Tiwari R. Interpreting p-Values and Confidence Intervals Using Well-Calibrated Null Preference Priors. Stat Sci 2022. [DOI: 10.1214/21-sts833] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
Affiliation(s)
- Michael P. Fay
- Michael P. Fay is Mathematical Statisticians at the Biostatistics Research Branch, National Institute of Allergy and Infectious Diseases, 5601 Fishers Lane, Rockville, Maryland 20852 USA
| | - Michael A. Proschan
- Michael A. Proschan is Mathematical Statisticians at the Biostatistics Research Branch, National Institute of Allergy and Infectious Diseases, 5601 Fishers Lane, Rockville, Maryland 20852 USA
| | - Erica H. Brittain
- Erica H. Brittain is Mathematical Statisticians at the Biostatistics Research Branch, National Institute of Allergy and Infectious Diseases, 5601 Fishers Lane, Rockville, Maryland 20852 USA
| | - Ram Tiwari
- Ram Tiwari is Head of Statistical Methodology, Bristol Myers Squibb, Global Biometrics and Data Sciences, Bristol Myers Squibb, 3401 Princeton Pike, Lawrence Township, New Jersey, 08648 USA
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9
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Williams JP, Xie Y, Hannig J. The EAS approach for graphical selection consistency in vector autoregression models. CAN J STAT 2022. [DOI: 10.1002/cjs.11726] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/08/2022]
Affiliation(s)
- Jonathan P. Williams
- Department of Statistics, North Carolina State University Raleigh North Carolina USA
| | - Yuying Xie
- Department of Statistics and Probability, Department of Computational Mathematics, Science and Engineering, Michigan State University East Lansing Michigan USA
| | - Jan Hannig
- Department of Statistics and Operations Research, University of North Carolina Chapel Hill North Carolina USA
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10
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Oda H, Komaki F. Enriched standard conjugate priors and the right invariant prior for Wishart distributions. J MULTIVARIATE ANAL 2022. [DOI: 10.1016/j.jmva.2022.105105] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/17/2022]
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11
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Bayesian linear models for cardinal paired comparison data. Comput Stat Data Anal 2022. [DOI: 10.1016/j.csda.2022.107481] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/17/2022]
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12
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Westland JC. Information loss and bias in likert survey responses. PLoS One 2022; 17:e0271949. [PMID: 35901102 PMCID: PMC9333316 DOI: 10.1371/journal.pone.0271949] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/20/2021] [Accepted: 07/11/2022] [Indexed: 11/18/2022] Open
Abstract
Likert response surveys are widely applied in marketing, public opinion polls, epidemiological and economic disciplines. Theoretically, Likert mapping from real-world beliefs could lose significant amounts of information, as they are discrete categorical metrics. Similarly, the subjective nature of Likert-scale data capture, through questionnaires, holds the potential to inject researcher biases into the statistical analysis. Arguments and counterexamples are provided to show how this loss and bias can potentially be substantial under extreme polarization or strong beliefs held by the surveyed population, and where the survey instruments are poorly controlled. These theoretical possibilities were tested using a large survey with 14 Likert-scaled questions presented to 125,387 respondents in 442 distinct behavioral-demographic groups. Despite the potential for bias and information loss, the empirical analysis found strong support for an assumption of minimal information loss under Normal beliefs in Likert scaled surveys. Evidence from this study found that the Normal assumption is a very good fit to the majority of actual responses, the only variance from Normal being slightly platykurtic (kurtosis ~ 2) which is likely due to censoring of beliefs after the lower and upper extremes of the Likert mapping. The discussion and conclusions argue that further revisions to survey protocols can assure that information loss and bias in Likert-scaled data are minimal.
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13
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Bunouf P. An objective bayesian approach to estimation in multistage experiments. Stat Methods Med Res 2022; 31:1579-1589. [PMID: 35543014 DOI: 10.1177/09622802221099640] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/16/2022]
Abstract
This article presents a Bayesian approach to estimation in multistage experiments based on the reference prior theory. The idea of deriving design-dependent priors was first introduced using Jeffreys' criterion. A theoretical framework was then established by showing that explicit reference to the design is fully Bayesian justified and Bayesian objectivity cannot ignore such information. Extending the work to multi-parameter problems, a general form of priors was derived from the reference prior theory. In this article, I evidence the good frequentist properties of the reference posterior estimators with normally distributed data. As a notable advance, I address the issue of the point and the interval estimations upon experiment termination. The approach is applied to a data set collected in a clinical trial in schizophrenia with the possibility to stop the trial early if interim results provide sufficient evidence of efficacy or futility. Finally, I discuss the idea of using the reference posterior estimators as a default choice for objective estimation in multistage experiment.
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14
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Nishimura A, Suchard MA. Prior-preconditioned conjugate gradient method for accelerated Gibbs sampling in ‘large n & large p’ Bayesian sparse regression. J Am Stat Assoc 2022. [DOI: 10.1080/01621459.2022.2057859] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/18/2022]
Affiliation(s)
| | - Marc A. Suchard
- Department of Biomathematics, Biostatistics, and Human Genetics, University of California - Los Angeles
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15
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Affiliation(s)
- Zifei Han
- School of Statistics, University of International Business and Economics
| | - Keying Ye
- Department of Management Science and Statistics, The University of Texas at San Antonio
| | - Min Wang
- Department of Management Science and Statistics, The University of Texas at San Antonio
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16
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Jonas KG. Global Information for Multidimensional Tests. APPLIED PSYCHOLOGICAL MEASUREMENT 2021; 45:494-517. [PMID: 34866709 PMCID: PMC8640353 DOI: 10.1177/01466216211042803] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/13/2023]
Abstract
New measures of test information, termed global information, quantify test information relative to the entire range of the trait being assessed. Estimating global information relative to a non-informative prior distribution results in a measure of how much information could be gained by administering the test to an unspecified examinee. Currently, such measures have been developed only for unidimensional tests. This study introduces measures of multidimensional global test information and validates them in simulated data. Then, the utility of global test information is tested in neuropsychological data collected as part of Rush University's Memory and Aging Project. These measures allow for direct comparison of complex tests calibrated in different samples, facilitating test development and selection.
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Affiliation(s)
- Katherine G. Jonas
- Psychiatry and Behavioral Health, Stony Brook University, Stony Brook, NY, USA
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17
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Lee BR, Budzillo A, Hadley K, Miller JA, Jarsky T, Baker K, Hill D, Kim L, Mann R, Ng L, Oldre A, Rajanbabu R, Trinh J, Vargas S, Braun T, Dalley RA, Gouwens NW, Kalmbach BE, Kim TK, Smith KA, Soler-Llavina G, Sorensen S, Tasic B, Ting JT, Lein E, Zeng H, Murphy GJ, Berg J. Scaled, high fidelity electrophysiological, morphological, and transcriptomic cell characterization. eLife 2021; 10:e65482. [PMID: 34387544 PMCID: PMC8428855 DOI: 10.7554/elife.65482] [Citation(s) in RCA: 23] [Impact Index Per Article: 7.7] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/06/2020] [Accepted: 08/12/2021] [Indexed: 11/13/2022] Open
Abstract
The Patch-seq approach is a powerful variation of the patch-clamp technique that allows for the combined electrophysiological, morphological, and transcriptomic characterization of individual neurons. To generate Patch-seq datasets at scale, we identified and refined key factors that contribute to the efficient collection of high-quality data. We developed patch-clamp electrophysiology software with analysis functions specifically designed to automate acquisition with online quality control. We recognized the importance of extracting the nucleus for transcriptomic success and maximizing membrane integrity during nucleus extraction for morphology success. The protocol is generalizable to different species and brain regions, as demonstrated by capturing multimodal data from human and macaque brain slices. The protocol, analysis and acquisition software are compiled at https://githubcom/AllenInstitute/patchseqtools. This resource can be used by individual labs to generate data across diverse mammalian species and that is compatible with large publicly available Patch-seq datasets.
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Affiliation(s)
- Brian R Lee
- Allen Institute for Brain ScienceSeattleUnited States
| | | | | | | | - Tim Jarsky
- Allen Institute for Brain ScienceSeattleUnited States
| | | | - DiJon Hill
- Allen Institute for Brain ScienceSeattleUnited States
| | - Lisa Kim
- Allen Institute for Brain ScienceSeattleUnited States
| | - Rusty Mann
- Allen Institute for Brain ScienceSeattleUnited States
| | - Lindsay Ng
- Allen Institute for Brain ScienceSeattleUnited States
| | - Aaron Oldre
- Allen Institute for Brain ScienceSeattleUnited States
| | - Ram Rajanbabu
- Allen Institute for Brain ScienceSeattleUnited States
| | - Jessica Trinh
- Allen Institute for Brain ScienceSeattleUnited States
| | - Sara Vargas
- Allen Institute for Brain ScienceSeattleUnited States
| | | | | | | | - Brian E Kalmbach
- Allen Institute for Brain ScienceSeattleUnited States
- Department of Physiology and Biophysics, University of WashingtonSeattleUnited States
| | - Tae Kyung Kim
- Allen Institute for Brain ScienceSeattleUnited States
| | | | | | | | | | - Jonathan T Ting
- Allen Institute for Brain ScienceSeattleUnited States
- Department of Physiology and Biophysics, University of WashingtonSeattleUnited States
| | - Ed Lein
- Allen Institute for Brain ScienceSeattleUnited States
| | - Hongkui Zeng
- Allen Institute for Brain ScienceSeattleUnited States
| | - Gabe J Murphy
- Allen Institute for Brain ScienceSeattleUnited States
- Department of Physiology and Biophysics, University of WashingtonSeattleUnited States
| | - Jim Berg
- Allen Institute for Brain ScienceSeattleUnited States
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18
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He L. Objective Bayesian analysis of accelerated degradation models based on Wiener process with correlation. COMMUN STAT-THEOR M 2021. [DOI: 10.1080/03610926.2021.1957111] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/20/2022]
Affiliation(s)
- Lei He
- Department of Statistics, Anhui Normal University, Wuhu, China
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19
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Hashimoto S. Reference priors via α-divergence for a certain non-regular model in the presence of a nuisance parameter. J Stat Plan Inference 2021. [DOI: 10.1016/j.jspi.2020.11.007] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/22/2022]
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20
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Bullerjahn JT, Hummer G. Maximum likelihood estimates of diffusion coefficients from single-particle tracking experiments. J Chem Phys 2021; 154:234105. [PMID: 34241279 DOI: 10.1063/5.0038174] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Single-molecule localization microscopy allows practitioners to locate and track labeled molecules in biological systems. When extracting diffusion coefficients from the resulting trajectories, it is common practice to perform a linear fit on mean-squared-displacement curves. However, this strategy is suboptimal and prone to errors. Recently, it was shown that the increments between the observed positions provide a good estimate for the diffusion coefficient, and their statistics are well-suited for likelihood-based analysis methods. Here, we revisit the problem of extracting diffusion coefficients from single-particle tracking experiments subject to static noise and dynamic motion blur using the principle of maximum likelihood. Taking advantage of an efficient real-space formulation, we extend the model to mixtures of subpopulations differing in their diffusion coefficients, which we estimate with the help of the expectation-maximization algorithm. This formulation naturally leads to a probabilistic assignment of trajectories to subpopulations. We employ the theory to analyze experimental tracking data that cannot be explained with a single diffusion coefficient. We test how well a dataset conforms to the assumptions of a diffusion model and determine the optimal number of subpopulations with the help of a quality factor of known analytical distribution. To facilitate use by practitioners, we provide a fast open-source implementation of the theory for the efficient analysis of multiple trajectories in arbitrary dimensions simultaneously.
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Affiliation(s)
- Jakob Tómas Bullerjahn
- Department of Theoretical Biophysics, Max Planck Institute of Biophysics, 60438 Frankfurt am Main, Germany
| | - Gerhard Hummer
- Department of Theoretical Biophysics, Max Planck Institute of Biophysics, 60438 Frankfurt am Main, Germany
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21
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Ott M, Plummer M, Roos M. How vague is vague? How informative is informative? Reference analysis for Bayesian meta-analysis. Stat Med 2021; 40:4505-4521. [PMID: 34041768 PMCID: PMC8453582 DOI: 10.1002/sim.9076] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/16/2020] [Revised: 04/28/2021] [Accepted: 05/10/2021] [Indexed: 11/06/2022]
Abstract
Meta-analysis provides important insights for evidence-based medicine by synthesizing evidence from multiple studies which address the same research question. Within the Bayesian framework, meta-analysis is frequently expressed by a Bayesian normal-normal hierarchical model (NNHM). Recently, several publications have discussed the choice of the prior distribution for the between-study heterogeneity in the Bayesian NNHM and used several "vague" priors. However, no approach exists to quantify the informativeness of such priors, and thus, we develop a principled reference analysis framework for the Bayesian NNHM acting at the posterior level. The posterior reference analysis (post-RA) is based on two posterior benchmarks: one induced by the improper reference prior, which is minimally informative for the data, and the other induced by a highly anticonservative proper prior. This approach applies the Hellinger distance to quantify the informativeness of a heterogeneity prior of interest by comparing the corresponding marginal posteriors with both posterior benchmarks. The post-RA is implemented in the freely accessible R package ra4bayesmeta and is applied to two medical case studies. Our findings show that anticonservative heterogeneity priors produce platykurtic posteriors compared with the reference posterior, and they produce shorter 95% credible intervals (CrI) and optimistic inference compared with the reference prior. Conservative heterogeneity priors produce leptokurtic posteriors, longer 95% CrI and cautious inference. The novel post-RA framework could support numerous Bayesian meta-analyses in many research fields, as it determines how informative a heterogeneity prior is for the actual data as compared with the minimally informative reference prior.
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Affiliation(s)
- Manuela Ott
- Department of Biostatistics at Epidemiology, Biostatistics and Prevention Institute, University of Zurich, Zurich, Switzerland
| | - Martyn Plummer
- Department of Statistics, University of Warwick, Warwickshire, UK
| | - Małgorzata Roos
- Department of Biostatistics at Epidemiology, Biostatistics and Prevention Institute, University of Zurich, Zurich, Switzerland
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22
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Sharpe J, Juárez MA. Estimation of the Pareto and related distributions – A reference-intrinsic approach. COMMUN STAT-THEOR M 2021. [DOI: 10.1080/03610926.2021.1916826] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/21/2022]
Affiliation(s)
| | - Miguel A. Juárez
- School of Mathematics and Statistics, The University of Sheffield, Sheffield, UK
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23
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Reimherr M, Meng X, Nicolae DL. Prior sample size extensions for assessing prior impact and prior‐likelihood discordance. J R Stat Soc Series B Stat Methodol 2021. [DOI: 10.1111/rssb.12414] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
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24
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Evans M, Guo Y. Measuring and Controlling Bias for Some Bayesian Inferences and the Relation to Frequentist Criteria. ENTROPY 2021; 23:e23020190. [PMID: 33557320 PMCID: PMC7914689 DOI: 10.3390/e23020190] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 01/09/2021] [Revised: 01/30/2021] [Accepted: 02/01/2021] [Indexed: 11/19/2022]
Abstract
A common concern with Bayesian methodology in scientific contexts is that inferences can be heavily influenced by subjective biases. As presented here, there are two types of bias for some quantity of interest: bias against and bias in favor. Based upon the principle of evidence, it is shown how to measure and control these biases for both hypothesis assessment and estimation problems. Optimality results are established for the principle of evidence as the basis of the approach to these problems. A close relationship is established between measuring bias in Bayesian inferences and frequentist properties that hold for any proper prior. This leads to a possible resolution to an apparent conflict between these approaches to statistical reasoning. Frequentism is seen as establishing figures of merit for a statistical study, while Bayes determines the inferences based upon statistical evidence.
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25
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Druilhet P, Saint Loubert Bié E. Improper versus finitely additive distributions as limits of countably additive probabilities. ANN I STAT MATH 2021. [DOI: 10.1007/s10463-020-00779-8] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/22/2022]
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26
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He D, Liu L, Cao M. A doubly accelerated degradation model based on the inverse Gaussian process and its objective Bayesian analysis. J STAT COMPUT SIM 2020. [DOI: 10.1080/00949655.2020.1858083] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/22/2022]
Affiliation(s)
- Daojiang He
- Key Laboratory of Advanced Theory and Application in Statistics and Data Science, East China Normal University, Shanghai, People's Republic of China
- Department of Statistics, Anhui Normal University, Wuhu, People's Republic of China
| | - Lei Liu
- School of Mathematics and Physics, Anqing Normal University, Wuhu, People's Republic of China
| | - Mingxiang Cao
- Department of Statistics, Anhui Normal University, Wuhu, People's Republic of China
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27
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Gouwens NW, Sorensen SA, Baftizadeh F, Budzillo A, Lee BR, Jarsky T, Alfiler L, Baker K, Barkan E, Berry K, Bertagnolli D, Bickley K, Bomben J, Braun T, Brouner K, Casper T, Crichton K, Daigle TL, Dalley R, de Frates RA, Dee N, Desta T, Lee SD, Dotson N, Egdorf T, Ellingwood L, Enstrom R, Esposito L, Farrell C, Feng D, Fong O, Gala R, Gamlin C, Gary A, Glandon A, Goldy J, Gorham M, Graybuck L, Gu H, Hadley K, Hawrylycz MJ, Henry AM, Hill D, Hupp M, Kebede S, Kim TK, Kim L, Kroll M, Lee C, Link KE, Mallory M, Mann R, Maxwell M, McGraw M, McMillen D, Mukora A, Ng L, Ng L, Ngo K, Nicovich PR, Oldre A, Park D, Peng H, Penn O, Pham T, Pom A, Popović Z, Potekhina L, Rajanbabu R, Ransford S, Reid D, Rimorin C, Robertson M, Ronellenfitch K, Ruiz A, Sandman D, Smith K, Sulc J, Sunkin SM, Szafer A, Tieu M, Torkelson A, Trinh J, Tung H, Wakeman W, Ward K, Williams G, Zhou Z, Ting JT, Arkhipov A, Sümbül U, Lein ES, Koch C, Yao Z, Tasic B, Berg J, Murphy GJ, Zeng H. Integrated Morphoelectric and Transcriptomic Classification of Cortical GABAergic Cells. Cell 2020; 183:935-953.e19. [PMID: 33186530 PMCID: PMC7781065 DOI: 10.1016/j.cell.2020.09.057] [Citation(s) in RCA: 254] [Impact Index Per Article: 63.5] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/15/2020] [Revised: 07/06/2020] [Accepted: 09/22/2020] [Indexed: 12/20/2022]
Abstract
Neurons are frequently classified into distinct types on the basis of structural, physiological, or genetic attributes. To better constrain the definition of neuronal cell types, we characterized the transcriptomes and intrinsic physiological properties of over 4,200 mouse visual cortical GABAergic interneurons and reconstructed the local morphologies of 517 of those neurons. We find that most transcriptomic types (t-types) occupy specific laminar positions within visual cortex, and, for most types, the cells mapping to a t-type exhibit consistent electrophysiological and morphological properties. These properties display both discrete and continuous variation among t-types. Through multimodal integrated analysis, we define 28 met-types that have congruent morphological, electrophysiological, and transcriptomic properties and robust mutual predictability. We identify layer-specific axon innervation pattern as a defining feature distinguishing different met-types. These met-types represent a unified definition of cortical GABAergic interneuron types, providing a systematic framework to capture existing knowledge and bridge future analyses across different modalities.
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Affiliation(s)
| | | | | | - Agata Budzillo
- Allen Institute for Brain Science, Seattle, WA 98109, USA
| | - Brian R Lee
- Allen Institute for Brain Science, Seattle, WA 98109, USA
| | - Tim Jarsky
- Allen Institute for Brain Science, Seattle, WA 98109, USA
| | - Lauren Alfiler
- Allen Institute for Brain Science, Seattle, WA 98109, USA
| | | | - Eliza Barkan
- Allen Institute for Brain Science, Seattle, WA 98109, USA
| | - Kyla Berry
- Allen Institute for Brain Science, Seattle, WA 98109, USA
| | | | - Kris Bickley
- Allen Institute for Brain Science, Seattle, WA 98109, USA
| | - Jasmine Bomben
- Allen Institute for Brain Science, Seattle, WA 98109, USA
| | - Thomas Braun
- Byte Physics, Schwarzastraße 9, Berlin 12055, Germany
| | - Krissy Brouner
- Allen Institute for Brain Science, Seattle, WA 98109, USA
| | - Tamara Casper
- Allen Institute for Brain Science, Seattle, WA 98109, USA
| | | | - Tanya L Daigle
- Allen Institute for Brain Science, Seattle, WA 98109, USA
| | - Rachel Dalley
- Allen Institute for Brain Science, Seattle, WA 98109, USA
| | | | - Nick Dee
- Allen Institute for Brain Science, Seattle, WA 98109, USA
| | - Tsega Desta
- Allen Institute for Brain Science, Seattle, WA 98109, USA
| | | | | | - Tom Egdorf
- Allen Institute for Brain Science, Seattle, WA 98109, USA
| | | | - Rachel Enstrom
- Allen Institute for Brain Science, Seattle, WA 98109, USA
| | - Luke Esposito
- Allen Institute for Brain Science, Seattle, WA 98109, USA
| | - Colin Farrell
- Allen Institute for Brain Science, Seattle, WA 98109, USA
| | - David Feng
- Allen Institute for Brain Science, Seattle, WA 98109, USA
| | - Olivia Fong
- Allen Institute for Brain Science, Seattle, WA 98109, USA
| | - Rohan Gala
- Allen Institute for Brain Science, Seattle, WA 98109, USA
| | - Clare Gamlin
- Allen Institute for Brain Science, Seattle, WA 98109, USA
| | - Amanda Gary
- Allen Institute for Brain Science, Seattle, WA 98109, USA
| | | | - Jeff Goldy
- Allen Institute for Brain Science, Seattle, WA 98109, USA
| | - Melissa Gorham
- Allen Institute for Brain Science, Seattle, WA 98109, USA
| | - Lucas Graybuck
- Allen Institute for Brain Science, Seattle, WA 98109, USA
| | - Hong Gu
- Allen Institute for Brain Science, Seattle, WA 98109, USA
| | - Kristen Hadley
- Allen Institute for Brain Science, Seattle, WA 98109, USA
| | | | - Alex M Henry
- Allen Institute for Brain Science, Seattle, WA 98109, USA
| | - DiJon Hill
- Allen Institute for Brain Science, Seattle, WA 98109, USA
| | - Madie Hupp
- Allen Institute for Brain Science, Seattle, WA 98109, USA
| | - Sara Kebede
- Allen Institute for Brain Science, Seattle, WA 98109, USA
| | - Tae Kyung Kim
- Allen Institute for Brain Science, Seattle, WA 98109, USA
| | - Lisa Kim
- Allen Institute for Brain Science, Seattle, WA 98109, USA
| | - Matthew Kroll
- Allen Institute for Brain Science, Seattle, WA 98109, USA
| | - Changkyu Lee
- Allen Institute for Brain Science, Seattle, WA 98109, USA
| | | | | | - Rusty Mann
- Allen Institute for Brain Science, Seattle, WA 98109, USA
| | | | - Medea McGraw
- Allen Institute for Brain Science, Seattle, WA 98109, USA
| | | | - Alice Mukora
- Allen Institute for Brain Science, Seattle, WA 98109, USA
| | - Lindsay Ng
- Allen Institute for Brain Science, Seattle, WA 98109, USA
| | - Lydia Ng
- Allen Institute for Brain Science, Seattle, WA 98109, USA
| | - Kiet Ngo
- Allen Institute for Brain Science, Seattle, WA 98109, USA
| | | | - Aaron Oldre
- Allen Institute for Brain Science, Seattle, WA 98109, USA
| | - Daniel Park
- Allen Institute for Brain Science, Seattle, WA 98109, USA
| | - Hanchuan Peng
- Allen Institute for Brain Science, Seattle, WA 98109, USA
| | - Osnat Penn
- Allen Institute for Brain Science, Seattle, WA 98109, USA
| | - Thanh Pham
- Allen Institute for Brain Science, Seattle, WA 98109, USA
| | - Alice Pom
- Allen Institute for Brain Science, Seattle, WA 98109, USA
| | - Zoran Popović
- Center for Game Science, Paul G. Allen School of Computer Science and Engineering, University of Washington, Seattle, WA 98195, USA
| | | | | | - Shea Ransford
- Allen Institute for Brain Science, Seattle, WA 98109, USA
| | - David Reid
- Allen Institute for Brain Science, Seattle, WA 98109, USA
| | | | | | | | - Augustin Ruiz
- Allen Institute for Brain Science, Seattle, WA 98109, USA
| | - David Sandman
- Allen Institute for Brain Science, Seattle, WA 98109, USA
| | - Kimberly Smith
- Allen Institute for Brain Science, Seattle, WA 98109, USA
| | - Josef Sulc
- Allen Institute for Brain Science, Seattle, WA 98109, USA
| | - Susan M Sunkin
- Allen Institute for Brain Science, Seattle, WA 98109, USA
| | - Aaron Szafer
- Allen Institute for Brain Science, Seattle, WA 98109, USA
| | - Michael Tieu
- Allen Institute for Brain Science, Seattle, WA 98109, USA
| | - Amy Torkelson
- Allen Institute for Brain Science, Seattle, WA 98109, USA
| | - Jessica Trinh
- Allen Institute for Brain Science, Seattle, WA 98109, USA
| | - Herman Tung
- Allen Institute for Brain Science, Seattle, WA 98109, USA
| | - Wayne Wakeman
- Allen Institute for Brain Science, Seattle, WA 98109, USA
| | - Katelyn Ward
- Allen Institute for Brain Science, Seattle, WA 98109, USA
| | - Grace Williams
- Allen Institute for Brain Science, Seattle, WA 98109, USA
| | - Zhi Zhou
- Allen Institute for Brain Science, Seattle, WA 98109, USA
| | | | - Anton Arkhipov
- Allen Institute for Brain Science, Seattle, WA 98109, USA
| | - Uygar Sümbül
- Allen Institute for Brain Science, Seattle, WA 98109, USA
| | - Ed S Lein
- Allen Institute for Brain Science, Seattle, WA 98109, USA
| | - Christof Koch
- Allen Institute for Brain Science, Seattle, WA 98109, USA
| | - Zizhen Yao
- Allen Institute for Brain Science, Seattle, WA 98109, USA
| | - Bosiljka Tasic
- Allen Institute for Brain Science, Seattle, WA 98109, USA
| | - Jim Berg
- Allen Institute for Brain Science, Seattle, WA 98109, USA
| | - Gabe J Murphy
- Allen Institute for Brain Science, Seattle, WA 98109, USA.
| | - Hongkui Zeng
- Allen Institute for Brain Science, Seattle, WA 98109, USA
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28
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Klebanov I, Sikorski A, Schütte C, Röblitz S. Objective priors in the empirical Bayes framework. Scand Stat Theory Appl 2020. [DOI: 10.1111/sjos.12485] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
| | | | - Christof Schütte
- Zuse Institute Berlin
- Department of Mathematics and Computer Science, Free University Berlin
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29
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Hai Y, Min X, Qin G. Bayesian and influence function-based empirical likelihoods for inference of sensitivity in diagnostic tests. Stat Methods Med Res 2020; 29:3457-3491. [PMID: 32552342 DOI: 10.1177/0962280220929042] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/17/2022]
Abstract
In medical diagnostic studies, a diagnostic test can be evaluated based on its sensitivity under a desired specificity. Existing methods for inference on sensitivity include normal approximation-based approaches and empirical likelihood (EL)-based approaches. These methods generally have poor performance when the specificity is high, and some require choosing smoothing parameters. We propose a new influence function-based empirical likelihood method and Bayesian empirical likelihood methods to overcome such problems. Numerical studies are performed to compare the finite sample performance of the proposed approaches with existing methods. The proposed methods are shown to perform better in terms of both coverage probability and interval length. A real data set from Alzheimer's Disease Neuroimaging Initiative (ANDI) is analyzed.
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Affiliation(s)
- Yan Hai
- Department of Mathematics and Statistics, Georgia State University, Atlanta, GA, USA
| | - Xiaoyi Min
- Department of Mathematics and Statistics, Georgia State University, Atlanta, GA, USA
| | - Gengsheng Qin
- Department of Mathematics and Statistics, Georgia State University, Atlanta, GA, USA
| | -
- Department of Mathematics and Statistics, Georgia State University, Atlanta, GA, USA
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30
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Loss-based approach to two-piece location-scale distributions with applications to dependent data. STAT METHOD APPL-GER 2020. [DOI: 10.1007/s10260-019-00481-x] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/26/2022]
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31
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Nott DJ, Wang X, Evans M, Englert BG. Checking for Prior-Data Conflict Using Prior-to-Posterior Divergences. Stat Sci 2020. [DOI: 10.1214/19-sts731] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
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32
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Kolchinsky A, Corominas-Murtra B. Decomposing information into copying versus transformation. J R Soc Interface 2020; 17:20190623. [PMID: 31964273 DOI: 10.1098/rsif.2019.0623] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/21/2023] Open
Abstract
In many real-world systems, information can be transmitted in two qualitatively different ways: by copying or by transformation. Copying occurs when messages are transmitted without modification, e.g. when an offspring receives an unaltered copy of a gene from its parent. Transformation occurs when messages are modified systematically during transmission, e.g. when mutational biases occur during genetic replication. Standard information-theoretic measures do not distinguish these two modes of information transfer, although they may reflect different mechanisms and have different functional consequences. Starting from a few simple axioms, we derive a decomposition of mutual information into the information transmitted by copying versus the information transmitted by transformation. We begin with a decomposition that applies when the source and destination of the channel have the same set of messages and a notion of message identity exists. We then generalize our decomposition to other kinds of channels, which can involve different source and destination sets and broader notions of similarity. In addition, we show that copy information can be interpreted as the minimal work needed by a physical copying process, which is relevant for understanding the physics of replication. We use the proposed decomposition to explore a model of amino acid substitution rates. Our results apply to any system in which the fidelity of copying, rather than simple predictability, is of critical relevance.
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33
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A method for calculating the strength of evidence associated with an earwitness's claimed recognition of a familiar speaker. Sci Justice 2019; 59:585-596. [PMID: 31606096 DOI: 10.1016/j.scijus.2019.07.001] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Submit a Manuscript] [Subscribe] [Scholar Register] [Received: 04/24/2019] [Revised: 07/01/2019] [Accepted: 07/06/2019] [Indexed: 11/22/2022]
Abstract
The present paper proposes and demonstrates a method for assessing strength of evidence when an earwitness claims to recognize the voice of a speaker who is familiar to them. The method calculates a Bayes factor that answers the question: What is the probability that the earwitness would claim to recognize the offender as the suspect if the offender was the suspect versus what is the probability that the earwitness would claim to recognize the offender as the suspect if the offender was not the suspect but some other speaker from the relevant population? By "claim" we mean a claim made by a cooperative earwitness not a claim made by an earwitness who is intentionally deceptive. Relevant data are derived from naïve listeners' responses to recordings of familiar speakers presented in a speaker lineup. The method is demonstrated under recording conditions that broadly reflect those of a real case.
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34
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Wiesenfarth M, Calderazzo S. Quantification of prior impact in terms of effective current sample size. Biometrics 2019; 76:326-336. [PMID: 31364156 DOI: 10.1111/biom.13124] [Citation(s) in RCA: 15] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/03/2018] [Accepted: 07/25/2019] [Indexed: 02/06/2023]
Abstract
Bayesian methods allow borrowing of historical information through prior distributions. The concept of prior effective sample size (prior ESS) facilitates quantification and communication of such prior information by equating it to a sample size. Prior information can arise from historical observations; thus, the traditional approach identifies the ESS with such a historical sample size. However, this measure is independent of newly observed data, and thus would not capture an actual "loss of information" induced by the prior in case of prior-data conflict. We build on a recent work to relate prior impact to the number of (virtual) samples from the current data model and introduce the effective current sample size (ECSS) of a prior, tailored to the application in Bayesian clinical trial designs. Special emphasis is put on robust mixture, power, and commensurate priors. We apply the approach to an adaptive design in which the number of recruited patients is adjusted depending on the effective sample size at an interim analysis. We argue that the ECSS is the appropriate measure in this case, as the aim is to save current (as opposed to historical) patients from recruitment. Furthermore, the ECSS can help overcome lack of consensus in the ESS assessment of mixture priors and can, more broadly, provide further insights into the impact of priors. An R package accompanies the paper.
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Affiliation(s)
- Manuel Wiesenfarth
- Division of Biostatistics, German Cancer Research Center, Heidelberg, Germany
| | - Silvia Calderazzo
- Division of Biostatistics, German Cancer Research Center, Heidelberg, Germany
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35
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Cui Y, Hannig J. Nonparametric generalized fiducial inference for survival functions under censoring. Biometrika 2019. [DOI: 10.1093/biomet/asz016] [Citation(s) in RCA: 15] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Summary
Since the introduction of fiducial inference by Fisher in the 1930s, its application has been largely confined to relatively simple, parametric problems. In this paper, we present what might be the first time fiducial inference is systematically applied to estimation of a nonparametric survival function under right censoring. We find that the resulting fiducial distribution gives rise to surprisingly good statistical procedures applicable to both one-sample and two-sample problems. In particular, we use the fiducial distribution of a survival function to construct pointwise and curvewise confidence intervals for the survival function, and propose tests based on the curvewise confidence interval. We establish a functional Bernstein–von Mises theorem, and perform thorough simulation studies in scenarios with different levels of censoring. The proposed fiducial-based confidence intervals maintain coverage in situations where asymptotic methods often have substantial coverage problems. Furthermore, the average length of the proposed confidence intervals is often shorter than the length of confidence intervals for competing methods that maintain coverage. Finally, the proposed fiducial test is more powerful than various types of log-rank tests and sup log-rank tests in some scenarios. We illustrate the proposed fiducial test by comparing chemotherapy against chemotherapy combined with radiotherapy, using data from the treatment of locally unresectable gastric cancer.
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Affiliation(s)
- Y Cui
- Department of Statistics, The Wharton School, University of Pennsylvania, 3730 Walnut Street, Philadelphia, Pennsylvania 19104, USA
| | - J Hannig
- Department of Statistics and Operations Research, University of North Carolina at Chapel Hill, 318 Hanes Hall, Chapel Hill, North Carolina 27599, USA
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36
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How the Choice of Distance Measure Influences the Detection of Prior-Data Conflict. ENTROPY 2019; 21:e21050446. [PMID: 33267160 PMCID: PMC7514935 DOI: 10.3390/e21050446] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 03/28/2019] [Revised: 04/16/2019] [Accepted: 04/23/2019] [Indexed: 11/17/2022]
Abstract
The present paper contrasts two related criteria for the evaluation of prior-data conflict: the Data Agreement Criterion (DAC; Bousquet, 2008) and the criterion of Nott et al. (2016). One aspect that these criteria have in common is that they depend on a distance measure, of which dozens are available, but so far, only the Kullback-Leibler has been used. We describe and compare both criteria to determine whether a different choice of distance measure might impact the results. By means of a simulation study, we investigate how the choice of a specific distance measure influences the detection of prior-data conflict. The DAC seems more susceptible to the choice of distance measure, while the criterion of Nott et al. seems to lead to reasonably comparable conclusions of prior-data conflict, regardless of the distance measure choice. We conclude with some practical suggestions for the user of the DAC and the criterion of Nott et al.
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37
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Vexler A, Zou L, Hutson AD. The empirical likelihood prior applied to bias reduction of general estimating equations. Comput Stat Data Anal 2019; 138:96-106. [PMID: 31031458 DOI: 10.1016/j.csda.2019.04.001] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/27/2022]
Abstract
The practice of employing empirical likelihood (EL) components in place of parametric likelihood functions in the construction of Bayesian-type procedures has been well-addressed in the modern statistical literature. The EL prior, a Jeffreys-type prior, which asymptotically maximizes the Shannon mutual information between data and the parameters of interest, is rigorously derived. The focus of the proposed approach is on an integrated Kullback-Leibler distance between the EL-based posterior and prior density functions. The EL prior density is the density function for which the corresponding posterior form is asymptotically negligibly different from the EL. The proposed result can be used to develop a methodology for reducing the asymptotic bias of solutions of general estimating equations and M-estimation schemes by removing the first-order term. This technique is developed in a similar manner to methods employed to reduce the asymptotic bias of maximum likelihood estimates via penalizing the underlying parametric likelihoods by their Jeffreys invariant priors. A real data example related to a study of myocardial infarction illustrates the attractiveness of the proposed technique in practical aspects.
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Affiliation(s)
- Albert Vexler
- Department of Biostatistics, State University of New York at Buffalo, Buffalo, USA
| | - Li Zou
- Department of Statistics and Biostatistics, California State University, East Bay, CA, USA
| | - Alan D Hutson
- Department of Biostatistics and Bioinformatics, Roswell Park Cancer Institute, Buffalo, NY, USA
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38
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Feng D, Baumgartner R, Svetnik V. Bayesian Estimation of Agreement of Biomarkers in Early Drug Development. Stat Biopharm Res 2019. [DOI: 10.1080/19466315.2018.1537887] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/26/2022]
Affiliation(s)
- Dai Feng
- Biometrics Research, Merck & Co., Inc., Rahway, NJ
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39
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Boluki S, Esfahani MS, Qian X, Dougherty ER. Constructing Pathway-Based Priors within a Gaussian Mixture Model for Bayesian Regression and Classification. IEEE/ACM TRANSACTIONS ON COMPUTATIONAL BIOLOGY AND BIOINFORMATICS 2019; 16:524-537. [PMID: 29990066 DOI: 10.1109/tcbb.2017.2778715] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/08/2023]
Abstract
Gene-expression-based classification and regression are major concerns in translational genomics. If the feature-label distribution is known, then an optimal classifier can be derived. If the predictor-target distribution is known, then an optimal regression function can be derived. In practice, neither is known, data must be employed, and, for small samples, prior knowledge concerning the feature-label or predictor-target distribution can be used in the learning process. Optimal Bayesian classification and optimal Bayesian regression provide optimality under uncertainty. With optimal Bayesian classification (or regression), uncertainty is treated directly on the feature-label (or predictor-target) distribution. The fundamental engineering problem is prior construction. The Regularized Expected Mean Log-Likelihood Prior (REMLP) utilizes pathway information and provides viable priors for the feature-label distribution, assuming that the training data contain labels. In practice, the labels may not be observed. This paper extends the REMLP methodology to a Gaussian mixture model (GMM) when the labels are unknown. Prior construction bundled with prior update via Bayesian sampling results in Monte Carlo approximations to the optimal Bayesian regression function and optimal Bayesian classifier. Simulations demonstrate that the GMM REMLP prior yields better performance than the EM algorithm for small data sets. We apply it to phenotype classification when the prior knowledge consists of colon cancer pathways.
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40
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Lu Y, Westfall P. Simple and flexible Bayesian inferences for standardized regression coefficients. J Appl Stat 2019. [DOI: 10.1080/02664763.2019.1584609] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/27/2022]
Affiliation(s)
- Yonggang Lu
- Department of Information Systems and Decision Sciences, University of Alaska, Anchorage, AK, USA
| | - Peter Westfall
- Area of Information Systems and Quantitative Sciences, Texas Tech University, Lubbock, TX, USA
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41
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Abstract
When the sample size is not too small, M-estimators of regression coefficients
are approximately normal and unbiased. This leads to the familiar frequentist
inference in terms of normality-based confidence intervals and
p-values. From a Bayesian perspective, use of the
(improper) uniform prior yields matching results in the sense that posterior
quantiles agree with one-sided confidence bounds. For this, and various other
reasons, the uniform prior is often considered objective or non-informative. In
spite of this, we argue that the uniform prior is not suitable as a default
prior for inference about a regression coefficient in the context of the
bio-medical and social sciences. We propose that a more suitable default choice
is the normal distribution with mean zero and standard deviation equal to the
standard error of the M-estimator. We base this recommendation on two arguments.
First, we show that this prior is non-informative for inference about the sign
of the regression coefficient. Second, we show that this prior agrees well with
a meta-analysis of 50 articles from the MEDLINE database.
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Affiliation(s)
- Erik van Zwet
- Department of Biomedical Data Sciences, Leiden University Medical Center, Leiden, The Netherlands
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42
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Alonso A, Van der Elst W, Molenberghs G. A maximum entropy approach for the evaluation of surrogate endpoints based on causal inference. Stat Med 2018; 37:4525-4538. [DOI: 10.1002/sim.7939] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/09/2017] [Revised: 05/26/2018] [Accepted: 07/21/2018] [Indexed: 11/11/2022]
Affiliation(s)
| | - Wim Van der Elst
- Janssen Pharmaceutical Companies of Johnson & Johnson; Beerse Belgium
| | - Geert Molenberghs
- I-BioStat; KU Leuven; Leuven Belgium
- I-BioStat; Universiteit Hasselt; Hasselt Belgium
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Using the Data Agreement Criterion to Rank Experts' Beliefs. ENTROPY 2018; 20:e20080592. [PMID: 33265681 PMCID: PMC7513104 DOI: 10.3390/e20080592] [Citation(s) in RCA: 13] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 05/30/2018] [Revised: 08/07/2018] [Accepted: 08/07/2018] [Indexed: 12/02/2022]
Abstract
Experts’ beliefs embody a present state of knowledge. It is desirable to take this knowledge into account when making decisions. However, ranking experts based on the merit of their beliefs is a difficult task. In this paper, we show how experts can be ranked based on their knowledge and their level of (un)certainty. By letting experts specify their knowledge in the form of a probability distribution, we can assess how accurately they can predict new data, and how appropriate their level of (un)certainty is. The expert’s specified probability distribution can be seen as a prior in a Bayesian statistical setting. We evaluate these priors by extending an existing prior-data (dis)agreement measure, the Data Agreement Criterion, and compare this approach to using Bayes factors to assess prior specification. We compare experts with each other and the data to evaluate their appropriateness. Using this method, new research questions can be asked and answered, for instance: Which expert predicts the new data best? Is there agreement between my experts and the data? Which experts’ representation is more valid or useful? Can we reach convergence between expert judgement and data? We provided an empirical example ranking (regional) directors of a large financial institution based on their predictions of turnover.
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Fuglstad GA, Simpson D, Lindgren F, Rue H. Constructing Priors that Penalize the Complexity of Gaussian Random Fields. J Am Stat Assoc 2018. [DOI: 10.1080/01621459.2017.1415907] [Citation(s) in RCA: 53] [Impact Index Per Article: 8.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/18/2022]
Affiliation(s)
| | - Daniel Simpson
- Department of Statistical Sciences, University of Toronto, Toronto, Ontario, Canada
| | - Finn Lindgren
- School of Mathematics, University of Edinburgh, Edinburgh, Scotland, United Kingdom
| | - Håvard Rue
- CEMSE Division, King Abdullah University of Science and Technology, Thuwal, Makkah Province, Saudi Arabia
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Affiliation(s)
- Xueou Wang
- Department of Statistics and Applied Probability, National University of Singapore, Singapore, Singapore
| | - David J. Nott
- Department of Statistics and Applied Probability, National University of Singapore, Singapore, Singapore
| | | | - Kerrie Mengersen
- School of Mathematical Sciences, Queensland University of Technology, Brisbane, Australia
- ACEMS, the ARC Centre of Excellence in Mathematical and Statistical Frontiers, Victoria, Australia
| | - Michael Evans
- Department of Statistics, University of Toronto, Toronto, Ontario, Canada
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Holbrook A, Lan S, Vandenberg-Rodes A, Shahbaba B. Geodesic Lagrangian Monte Carlo over the space of positive definite matrices: with application to Bayesian spectral density estimation. J STAT COMPUT SIM 2017; 88:982-1002. [PMID: 31105358 PMCID: PMC6521973 DOI: 10.1080/00949655.2017.1416470] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/18/2022]
Abstract
We present geodesic Lagrangian Monte Carlo, an extension of Hamiltonian Monte Carlo for sampling from posterior distributions defined on general Riemannian manifolds. We apply this new algorithm to Bayesian inference on symmetric or Hermitian positive definite matrices. To do so, we exploit the Riemannian structure induced by Cartan's canonical metric. The geodesics that correspond to this metric are available in closed-form and-within the context of Lagrangian Monte Carlo-provide a principled way to travel around the space of positive definite matrices. Our method improves Bayesian inference on such matrices by allowing for a broad range of priors, so we are not limited to conjugate priors only. In the context of spectral density estimation, we use the (non-conjugate) complex reference prior as an example modeling option made available by the algorithm. Results based on simulated and real-world multivariate time series are presented in this context, and future directions are outlined.
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Affiliation(s)
- Andrew Holbrook
- University of California, Irvine, Department of Statistics, Irvine, CA, USA
| | - Shiwei Lan
- California Institute of Technology, Department of Computing and Mathematical Sciences, Pasadena, CA, USA
| | | | - Babak Shahbaba
- University of California, Irvine, Department of Statistics, Irvine, CA, USA
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Affiliation(s)
- Edward Susko
- Department of Mathematics and Statistics; Dalhousie University; Halifax, NS Canada
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Moreno E, Vázquez-Polo FJ, Negrín MA. Bayesian meta-analysis: The role of the between-sample heterogeneity. Stat Methods Med Res 2017; 27:3643-3657. [PMID: 28511616 DOI: 10.1177/0962280217709837] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022]
Abstract
The random effect approach for meta-analysis was motivated by a lack of consistent assessment of homogeneity of treatment effect before pooling. The random effect model assumes that the distribution of the treatment effect is fully heterogenous across the experiments. However, other models arising by grouping some of the experiments are plausible. We illustrate on simulated binary experiments that the fully heterogenous model gives a poor meta-inference when fully heterogeneity is not the true model and that the knowledge of the true cluster model considerably improves the inference. We propose the use of a Bayesian model selection procedure for estimating the true cluster model, and Bayesian model averaging to incorporate into the meta-analysis the clustering estimation. A well-known meta-analysis for six major multicentre trials to assess the efficacy of a given dose of aspirin in post-myocardial infarction patients is reanalysed.
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Affiliation(s)
- Elías Moreno
- 1 Department of Statistics, University of Granada, Granada, Spain
| | - Francisco-José Vázquez-Polo
- 2 Department of Quantitative Methods and TiDES Institute, University of Las Palmas de Gran Canaria, Las Palmas, Spain
| | - Miguel A Negrín
- 2 Department of Quantitative Methods and TiDES Institute, University of Las Palmas de Gran Canaria, Las Palmas, Spain
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