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Simpson MJ, Maclaren OJ. Profile-Wise Analysis: A profile likelihood-based workflow for identifiability analysis, estimation, and prediction with mechanistic mathematical models. PLoS Comput Biol 2023; 19:e1011515. [PMID: 37773942 PMCID: PMC10566698 DOI: 10.1371/journal.pcbi.1011515] [Citation(s) in RCA: 8] [Impact Index Per Article: 8.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/27/2023] [Revised: 10/11/2023] [Accepted: 09/14/2023] [Indexed: 10/01/2023] Open
Abstract
Interpreting data using mechanistic mathematical models provides a foundation for discovery and decision-making in all areas of science and engineering. Developing mechanistic insight by combining mathematical models and experimental data is especially critical in mathematical biology as new data and new types of data are collected and reported. Key steps in using mechanistic mathematical models to interpret data include: (i) identifiability analysis; (ii) parameter estimation; and (iii) model prediction. Here we present a systematic, computationally-efficient workflow we call Profile-Wise Analysis (PWA) that addresses all three steps in a unified way. Recently-developed methods for constructing 'profile-wise' prediction intervals enable this workflow and provide the central linkage between different workflow components. These methods propagate profile-likelihood-based confidence sets for model parameters to predictions in a way that isolates how different parameter combinations affect model predictions. We show how to extend these profile-wise prediction intervals to two-dimensional interest parameters. We then demonstrate how to combine profile-wise prediction confidence sets to give an overall prediction confidence set that approximates the full likelihood-based prediction confidence set well. Our three case studies illustrate practical aspects of the workflow, focusing on ordinary differential equation (ODE) mechanistic models with both Gaussian and non-Gaussian noise models. While the case studies focus on ODE-based models, the workflow applies to other classes of mathematical models, including partial differential equations and simulation-based stochastic models. Open-source software on GitHub can be used to replicate the case studies.
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Affiliation(s)
- Matthew J. Simpson
- School of Mathematical Sciences, Queensland University of Technology, Brisbane, Australia
| | - Oliver J. Maclaren
- Department of Engineering Science, University of Auckland, Auckland, New Zealand
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2
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Augustin D, Lambert B, Wang K, Walz AC, Robinson M, Gavaghan D. Filter inference: A scalable nonlinear mixed effects inference approach for snapshot time series data. PLoS Comput Biol 2023; 19:e1011135. [PMID: 37216399 DOI: 10.1371/journal.pcbi.1011135] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/01/2022] [Accepted: 04/26/2023] [Indexed: 05/24/2023] Open
Abstract
Variability is an intrinsic property of biological systems and is often at the heart of their complex behaviour. Examples range from cell-to-cell variability in cell signalling pathways to variability in the response to treatment across patients. A popular approach to model and understand this variability is nonlinear mixed effects (NLME) modelling. However, estimating the parameters of NLME models from measurements quickly becomes computationally expensive as the number of measured individuals grows, making NLME inference intractable for datasets with thousands of measured individuals. This shortcoming is particularly limiting for snapshot datasets, common e.g. in cell biology, where high-throughput measurement techniques provide large numbers of single cell measurements. We introduce a novel approach for the estimation of NLME model parameters from snapshot measurements, which we call filter inference. Filter inference uses measurements of simulated individuals to define an approximate likelihood for the model parameters, avoiding the computational limitations of traditional NLME inference approaches and making efficient inferences from snapshot measurements possible. Filter inference also scales well with the number of model parameters, using state-of-the-art gradient-based MCMC algorithms such as the No-U-Turn Sampler (NUTS). We demonstrate the properties of filter inference using examples from early cancer growth modelling and from epidermal growth factor signalling pathway modelling.
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Affiliation(s)
- David Augustin
- Department of Computer Science, University of Oxford, Oxford, United Kingdom
| | - Ben Lambert
- College of Engineering, Mathematics and Physical Sciences, University of Exeter, Exeter, United Kingdom
| | - Ken Wang
- Research and Early Development, F. Hoffmann-La Roche AG, Basel, Switzerland
| | | | - Martin Robinson
- Department of Computer Science, University of Oxford, Oxford, United Kingdom
| | - David Gavaghan
- Department of Computer Science, University of Oxford, Oxford, United Kingdom
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3
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Bon JJ, Bretherton A, Buchhorn K, Cramb S, Drovandi C, Hassan C, Jenner AL, Mayfield HJ, McGree JM, Mengersen K, Price A, Salomone R, Santos-Fernandez E, Vercelloni J, Wang X. Being Bayesian in the 2020s: opportunities and challenges in the practice of modern applied Bayesian statistics. PHILOSOPHICAL TRANSACTIONS. SERIES A, MATHEMATICAL, PHYSICAL, AND ENGINEERING SCIENCES 2023; 381:20220156. [PMID: 36970822 PMCID: PMC10041356 DOI: 10.1098/rsta.2022.0156] [Citation(s) in RCA: 2] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 08/22/2022] [Accepted: 01/06/2023] [Indexed: 06/18/2023]
Abstract
Building on a strong foundation of philosophy, theory, methods and computation over the past three decades, Bayesian approaches are now an integral part of the toolkit for most statisticians and data scientists. Whether they are dedicated Bayesians or opportunistic users, applied professionals can now reap many of the benefits afforded by the Bayesian paradigm. In this paper, we touch on six modern opportunities and challenges in applied Bayesian statistics: intelligent data collection, new data sources, federated analysis, inference for implicit models, model transfer and purposeful software products. This article is part of the theme issue 'Bayesian inference: challenges, perspectives, and prospects'.
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Affiliation(s)
- Joshua J. Bon
- Centre for Data Science, Queensland University of Technology, Brisbane, Queensland, Australia
- School of Mathematical Sciences, Queensland University of Technology, Brisbane, Queensland, Australia
| | - Adam Bretherton
- Centre for Data Science, Queensland University of Technology, Brisbane, Queensland, Australia
- School of Mathematical Sciences, Queensland University of Technology, Brisbane, Queensland, Australia
| | - Katie Buchhorn
- Centre for Data Science, Queensland University of Technology, Brisbane, Queensland, Australia
- School of Mathematical Sciences, Queensland University of Technology, Brisbane, Queensland, Australia
| | - Susanna Cramb
- Centre for Data Science, Queensland University of Technology, Brisbane, Queensland, Australia
- School of Public Health and Social Work, Queensland University of Technology, Brisbane, Queensland, Australia
| | - Christopher Drovandi
- Centre for Data Science, Queensland University of Technology, Brisbane, Queensland, Australia
- School of Mathematical Sciences, Queensland University of Technology, Brisbane, Queensland, Australia
| | - Conor Hassan
- Centre for Data Science, Queensland University of Technology, Brisbane, Queensland, Australia
- School of Mathematical Sciences, Queensland University of Technology, Brisbane, Queensland, Australia
| | - Adrianne L. Jenner
- Centre for Data Science, Queensland University of Technology, Brisbane, Queensland, Australia
- School of Mathematical Sciences, Queensland University of Technology, Brisbane, Queensland, Australia
| | - Helen J. Mayfield
- Centre for Data Science, Queensland University of Technology, Brisbane, Queensland, Australia
- School of Public Health, The University of Queensland, Saint Lucia, Queensland, Australia
| | - James M. McGree
- Centre for Data Science, Queensland University of Technology, Brisbane, Queensland, Australia
- School of Mathematical Sciences, Queensland University of Technology, Brisbane, Queensland, Australia
| | - Kerrie Mengersen
- Centre for Data Science, Queensland University of Technology, Brisbane, Queensland, Australia
- School of Mathematical Sciences, Queensland University of Technology, Brisbane, Queensland, Australia
| | - Aiden Price
- Centre for Data Science, Queensland University of Technology, Brisbane, Queensland, Australia
- School of Mathematical Sciences, Queensland University of Technology, Brisbane, Queensland, Australia
| | - Robert Salomone
- Centre for Data Science, Queensland University of Technology, Brisbane, Queensland, Australia
- School of Computer Science, Queensland University of Technology, Brisbane, Queensland, Australia
| | - Edgar Santos-Fernandez
- Centre for Data Science, Queensland University of Technology, Brisbane, Queensland, Australia
- School of Mathematical Sciences, Queensland University of Technology, Brisbane, Queensland, Australia
| | - Julie Vercelloni
- Centre for Data Science, Queensland University of Technology, Brisbane, Queensland, Australia
- School of Mathematical Sciences, Queensland University of Technology, Brisbane, Queensland, Australia
| | - Xiaoyu Wang
- Centre for Data Science, Queensland University of Technology, Brisbane, Queensland, Australia
- School of Mathematical Sciences, Queensland University of Technology, Brisbane, Queensland, Australia
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4
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Moriña D, Fernández-Fontelo A, Cabaña A, Arratia A, Puig P. Estimated Covid-19 burden in Spain: ARCH underreported non-stationary time series. BMC Med Res Methodol 2023; 23:75. [PMID: 36977977 PMCID: PMC10043853 DOI: 10.1186/s12874-023-01894-9] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/03/2022] [Accepted: 03/17/2023] [Indexed: 03/30/2023] Open
Abstract
BACKGROUND The problem of dealing with misreported data is very common in a wide range of contexts for different reasons. The current situation caused by the Covid-19 worldwide pandemic is a clear example, where the data provided by official sources were not always reliable due to data collection issues and to the high proportion of asymptomatic cases. In this work, a flexible framework is proposed, with the objective of quantifying the severity of misreporting in a time series and reconstructing the most likely evolution of the process. METHODS The performance of Bayesian Synthetic Likelihood to estimate the parameters of a model based on AutoRegressive Conditional Heteroskedastic time series capable of dealing with misreported information and to reconstruct the most likely evolution of the phenomenon is assessed through a comprehensive simulation study and illustrated by reconstructing the weekly Covid-19 incidence in each Spanish Autonomous Community. RESULTS Only around 51% of the Covid-19 cases in the period 2020/02/23-2022/02/27 were reported in Spain, showing relevant differences in the severity of underreporting across the regions. CONCLUSIONS The proposed methodology provides public health decision-makers with a valuable tool in order to improve the assessment of a disease evolution under different scenarios.
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Affiliation(s)
- David Moriña
- Department of Econometrics, Statistics and Applied Economics, Riskcenter-IREA, Universitat de Barcelona (UB), Barcelona, Spain.
| | - Amanda Fernández-Fontelo
- Departament de Matemàtiques, Universitat Autònoma de Barcelona (UAB), Cerdanyola del Vallès, Spain
| | - Alejandra Cabaña
- Departament de Matemàtiques, Universitat Autònoma de Barcelona (UAB), Cerdanyola del Vallès, Spain
| | - Argimiro Arratia
- Department of Computer Science, Universitat Politècnica de Catalunya (UPC), Barcelona, Spain
| | - Pedro Puig
- Departament de Matemàtiques, Universitat Autònoma de Barcelona (UAB), Cerdanyola del Vallès, Spain
- Centre de Recerca Matemàtica (CRM), Barcelona, Spain
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5
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Järvenpää M, Corander J. On predictive inference for intractable models via approximate Bayesian computation. STATISTICS AND COMPUTING 2023; 33:42. [PMID: 36785730 PMCID: PMC9911513 DOI: 10.1007/s11222-022-10163-6] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 03/23/2022] [Accepted: 10/02/2022] [Indexed: 06/18/2023]
Abstract
UNLABELLED Approximate Bayesian computation (ABC) is commonly used for parameter estimation and model comparison for intractable simulator-based statistical models whose likelihood function cannot be evaluated. In this paper we instead investigate the feasibility of ABC as a generic approximate method for predictive inference, in particular, for computing the posterior predictive distribution of future observations or missing data of interest. We consider three complementary ABC approaches for this goal, each based on different assumptions regarding which predictive density of the intractable model can be sampled from. The case where only simulation from the joint density of the observed and future data given the model parameters can be used for inference is given particular attention and it is shown that the ideal summary statistic in this setting is minimal predictive sufficient instead of merely minimal sufficient (in the ordinary sense). An ABC prediction approach that takes advantage of a certain latent variable representation is also investigated. We additionally show how common ABC sampling algorithms can be used in the predictive settings considered. Our main results are first illustrated by using simple time-series models that facilitate analytical treatment, and later by using two common intractable dynamic models. SUPPLEMENTARY INFORMATION The online version contains supplementary material available at 10.1007/s11222-022-10163-6.
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Affiliation(s)
- Marko Järvenpää
- Department of Biostatistics, University of Oslo, Oslo, Norway
| | - Jukka Corander
- Department of Biostatistics, University of Oslo, Oslo, Norway
- Department of Mathematics and Statistics, Helsinki Institute of Information Technology (HIIT), University of Helsinki, Helsinki, Finland
- Wellcome Sanger Institute, Hinxton, Cambridgeshire, UK
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6
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Martin GM, Frazier DT, Robert CP. Computing Bayes: From Then ‘Til Now. Stat Sci 2023. [DOI: 10.1214/22-sts876] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 03/06/2023]
Affiliation(s)
- Gael M. Martin
- Gael M. Martin is Professor, Department of Econometrics and Business Statistics, Monash University, Melbourne, Australia
| | - David T. Frazier
- David T. Frazier is Associate Professor, Department of Econometrics and Business Statistics, Monash University, Melbourne, Australia
| | - Christian P. Robert
- Christian P. Robert is Professor, Ceremade, Université Paris-Dauphine, Paris, France, and Department of Statistics, Warwick University, Coventry, UK
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7
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Martin GM, Frazier DT, Robert CP. Approximating Bayes in the 21st Century. Stat Sci 2023. [DOI: 10.1214/22-sts875] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/25/2023]
Affiliation(s)
- Gael M. Martin
- Gael M. Martin is Professor, Department of Econometrics and Business Statistics, Monash University, Melbourne, Australia
| | - David T. Frazier
- David T. Frazier is Associate Professor, Department of Econometrics and Business Statistics, Monash University, Melbourne, Australia
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8
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Pesonen H, Simola U, Köhn‐Luque A, Vuollekoski H, Lai X, Frigessi A, Kaski S, Frazier DT, Maneesoonthorn W, Martin GM, Corander J. ABC of the future. Int Stat Rev 2022. [DOI: 10.1111/insr.12522] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Affiliation(s)
- Henri Pesonen
- Oslo Centre for Biostatistics and Epidemiology University of Oslo Oslo Norway
| | - Umberto Simola
- Helsinki Institute of Information Technology, Department of Mathematics and Statistics University of Helsinki Helsinki Finland
| | - Alvaro Köhn‐Luque
- Oslo Centre for Biostatistics and Epidemiology University of Oslo Oslo Norway
| | - Henri Vuollekoski
- Helsinki Institute of Information Technology, Department of Computer Science Aalto University Helsinki Finland
| | - Xiaoran Lai
- Oslo Centre for Biostatistics and Epidemiology University of Oslo Oslo Norway
| | - Arnoldo Frigessi
- Oslo Centre for Biostatistics and Epidemiology University of Oslo Oslo Norway
- Oslo Centre for Biostatistics and Epidemiology Oslo University Hospital Oslo Norway
| | - Samuel Kaski
- Helsinki Institute of Information Technology, Department of Computer Science Aalto University Helsinki Finland
- Department of Computer Science University of Manchester Manchester UK
| | - David T. Frazier
- Department of Econometrics & Business Statistics Monash University Clayton Victoria Australia
| | | | - Gael M. Martin
- Department of Econometrics & Business Statistics Monash University Clayton Victoria Australia
| | - Jukka Corander
- Oslo Centre for Biostatistics and Epidemiology University of Oslo Oslo Norway
- Helsinki Institute of Information Technology, Department of Mathematics and Statistics University of Helsinki Helsinki Finland
- Parasites and Microbes Wellcome Sanger Institute Hinxton UK
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9
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Aushev A, Pesonen H, Heinonen M, Corander J, Kaski S. Likelihood-free inference with deep Gaussian processes. Comput Stat Data Anal 2022. [DOI: 10.1016/j.csda.2022.107529] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/03/2022]
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10
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Monsalve-Bravo GM, Lawson BAJ, Drovandi C, Burrage K, Brown KS, Baker CM, Vollert SA, Mengersen K, McDonald-Madden E, Adams MP. Analysis of sloppiness in model simulations: Unveiling parameter uncertainty when mathematical models are fitted to data. SCIENCE ADVANCES 2022; 8:eabm5952. [PMID: 36129974 PMCID: PMC9491719 DOI: 10.1126/sciadv.abm5952] [Citation(s) in RCA: 5] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 10/01/2021] [Accepted: 08/10/2022] [Indexed: 06/15/2023]
Abstract
This work introduces a comprehensive approach to assess the sensitivity of model outputs to changes in parameter values, constrained by the combination of prior beliefs and data. This approach identifies stiff parameter combinations strongly affecting the quality of the model-data fit while simultaneously revealing which of these key parameter combinations are informed primarily by the data or are also substantively influenced by the priors. We focus on the very common context in complex systems where the amount and quality of data are low compared to the number of model parameters to be collectively estimated, and showcase the benefits of this technique for applications in biochemistry, ecology, and cardiac electrophysiology. We also show how stiff parameter combinations, once identified, uncover controlling mechanisms underlying the system being modeled and inform which of the model parameters need to be prioritized in future experiments for improved parameter inference from collective model-data fitting.
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Affiliation(s)
- Gloria M. Monsalve-Bravo
- School of Earth and Environmental Sciences, The University of Queensland, St Lucia, QLD 4072, Australia
- Centre for Biodiversity and Conservation Science, The University of Queensland, St Lucia, QLD 4072, Australia
- School of Chemical Engineering, The University of Queensland, St Lucia, QLD 4072, Australia
| | - Brodie A. J. Lawson
- Centre for Data Science, Queensland University of Technology, Brisbane, QLD 4001, Australia
- ARC Centre of Excellence for Mathematical and Statistical Frontiers, Queensland University of Technology, Brisbane, QLD 4001, Australia
- School of Mathematical Sciences, Queensland University of Technology, Brisbane, QLD 4001, Australia
- ARC Centre of Excellence for Plant Success in Nature and Agriculture, Queensland University of Technology, Brisbane, QLD 4001, Australia
| | - Christopher Drovandi
- Centre for Data Science, Queensland University of Technology, Brisbane, QLD 4001, Australia
- ARC Centre of Excellence for Mathematical and Statistical Frontiers, Queensland University of Technology, Brisbane, QLD 4001, Australia
- School of Mathematical Sciences, Queensland University of Technology, Brisbane, QLD 4001, Australia
| | - Kevin Burrage
- ARC Centre of Excellence for Mathematical and Statistical Frontiers, Queensland University of Technology, Brisbane, QLD 4001, Australia
- School of Mathematical Sciences, Queensland University of Technology, Brisbane, QLD 4001, Australia
- ARC Centre of Excellence for Plant Success in Nature and Agriculture, Queensland University of Technology, Brisbane, QLD 4001, Australia
- Department of Computer Science, University of Oxford, Oxford OX1 3QD, UK
| | - Kevin S. Brown
- Department of Pharmaceutical Sciences, Oregon State University, Corvallis, OR 97331, USA
- Department of Chemical, Biological, & Environmental Engineering, Oregon State University, Corvallis, OR 97331, USA
| | - Christopher M. Baker
- School of Mathematics and Statistics, The University of Melbourne, Parkville, VIC 3010, Australia
- Melbourne Centre for Data Science, The University of Melbourne, Parkville, VIC 3010, Australia
- Centre of Excellence for Biosecurity Risk Analysis, The University of Melbourne, Parkville, VIC 3010, Australia
| | - Sarah A. Vollert
- Centre for Data Science, Queensland University of Technology, Brisbane, QLD 4001, Australia
- ARC Centre of Excellence for Mathematical and Statistical Frontiers, Queensland University of Technology, Brisbane, QLD 4001, Australia
- School of Mathematical Sciences, Queensland University of Technology, Brisbane, QLD 4001, Australia
| | - Kerrie Mengersen
- Centre for Data Science, Queensland University of Technology, Brisbane, QLD 4001, Australia
- ARC Centre of Excellence for Mathematical and Statistical Frontiers, Queensland University of Technology, Brisbane, QLD 4001, Australia
- School of Mathematical Sciences, Queensland University of Technology, Brisbane, QLD 4001, Australia
| | - Eve McDonald-Madden
- School of Earth and Environmental Sciences, The University of Queensland, St Lucia, QLD 4072, Australia
- Centre for Biodiversity and Conservation Science, The University of Queensland, St Lucia, QLD 4072, Australia
| | - Matthew P. Adams
- School of Chemical Engineering, The University of Queensland, St Lucia, QLD 4072, Australia
- Centre for Data Science, Queensland University of Technology, Brisbane, QLD 4001, Australia
- ARC Centre of Excellence for Mathematical and Statistical Frontiers, Queensland University of Technology, Brisbane, QLD 4001, Australia
- School of Mathematical Sciences, Queensland University of Technology, Brisbane, QLD 4001, Australia
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11
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Boelts J, Lueckmann JM, Gao R, Macke JH. Flexible and efficient simulation-based inference for models of decision-making. eLife 2022; 11:77220. [PMID: 35894305 PMCID: PMC9374439 DOI: 10.7554/elife.77220] [Citation(s) in RCA: 7] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/25/2022] [Accepted: 07/26/2022] [Indexed: 11/22/2022] Open
Abstract
Inferring parameters of computational models that capture experimental data is a central task in cognitive neuroscience. Bayesian statistical inference methods usually require the ability to evaluate the likelihood of the model—however, for many models of interest in cognitive neuroscience, the associated likelihoods cannot be computed efficiently. Simulation-based inference (SBI) offers a solution to this problem by only requiring access to simulations produced by the model. Previously, Fengler et al. introduced likelihood approximation networks (LANs, Fengler et al., 2021) which make it possible to apply SBI to models of decision-making but require billions of simulations for training. Here, we provide a new SBI method that is substantially more simulation efficient. Our approach, mixed neural likelihood estimation (MNLE), trains neural density estimators on model simulations to emulate the simulator and is designed to capture both the continuous (e.g., reaction times) and discrete (choices) data of decision-making models. The likelihoods of the emulator can then be used to perform Bayesian parameter inference on experimental data using standard approximate inference methods like Markov Chain Monte Carlo sampling. We demonstrate MNLE on two variants of the drift-diffusion model and show that it is substantially more efficient than LANs: MNLE achieves similar likelihood accuracy with six orders of magnitude fewer training simulations and is significantly more accurate than LANs when both are trained with the same budget. Our approach enables researchers to perform SBI on custom-tailored models of decision-making, leading to fast iteration of model design for scientific discovery.
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Affiliation(s)
- Jan Boelts
- University of Tübingen, Tübingen, Germany
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12
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Biswas S, Chen Z, Karslake JD, Farhat A, Ames A, Raiymbek G, Freddolino PL, Biteen JS, Ragunathan K. HP1 oligomerization compensates for low-affinity H3K9me recognition and provides a tunable mechanism for heterochromatin-specific localization. SCIENCE ADVANCES 2022; 8:eabk0793. [PMID: 35857444 PMCID: PMC9269880 DOI: 10.1126/sciadv.abk0793] [Citation(s) in RCA: 6] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/21/2021] [Accepted: 05/24/2022] [Indexed: 05/31/2023]
Abstract
HP1 proteins traverse a complex and crowded chromatin landscape to bind with low affinity but high specificity to histone H3K9 methylation (H3K9me) and form transcriptionally inactive genomic compartments called heterochromatin. Here, we visualize single-molecule dynamics of an HP1 homolog, the fission yeast Swi6, in its native chromatin environment. By tracking single Swi6 molecules, we identify mobility states that map to discrete biochemical intermediates. Using Swi6 mutants that perturb H3K9me recognition, oligomerization, or nucleic acid binding, we determine how each biochemical property affects protein dynamics. We estimate that Swi6 recognizes H3K9me3 with ~94-fold specificity relative to unmodified nucleosomes in living cells. While nucleic acid binding competes with Swi6 oligomerization, as few as four tandem chromodomains can overcome these inhibitory effects to facilitate Swi6 localization at heterochromatin formation sites. Our studies indicate that HP1 oligomerization is essential to form dynamic, higher-order complexes that outcompete nucleic acid binding to enable specific H3K9me recognition.
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Affiliation(s)
- Saikat Biswas
- Department of Biological Chemistry, University of Michigan, Ann Arbor, MI 48109, USA
| | - Ziyuan Chen
- Department of Biophysics, University of Michigan, Ann Arbor, MI 48104, USA
| | - Joshua D. Karslake
- Department of Biophysics, University of Michigan, Ann Arbor, MI 48104, USA
| | - Ali Farhat
- Department of Computational Medicine and Bioinformatics, University of Michigan, Ann Arbor, MI 48109, USA
| | - Amanda Ames
- Department of Biological Chemistry, University of Michigan, Ann Arbor, MI 48109, USA
| | - Gulzhan Raiymbek
- Department of Biological Chemistry, University of Michigan, Ann Arbor, MI 48109, USA
| | - Peter L. Freddolino
- Department of Biological Chemistry, University of Michigan, Ann Arbor, MI 48109, USA
- Department of Computational Medicine and Bioinformatics, University of Michigan, Ann Arbor, MI 48109, USA
| | - Julie S. Biteen
- Department of Biophysics, University of Michigan, Ann Arbor, MI 48104, USA
- Department of Chemistry, University of Michigan, Ann Arbor, MI 48104, USA
| | - Kaushik Ragunathan
- Department of Biological Chemistry, University of Michigan, Ann Arbor, MI 48109, USA
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13
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Craiu RV, Gustafson P, Rosenthal JS. Reflections on Bayesian inference and Markov chain Monte Carlo. CAN J STAT 2022. [DOI: 10.1002/cjs.11707] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/09/2022]
Affiliation(s)
- Radu V. Craiu
- Department of Statistical Sciences University of Toronto Toronto Ontario Canada
| | - Paul Gustafson
- Department of Statistics University of British Columbia Vancouver British Columbia Canada
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14
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Frazier DT, Nott DJ, Drovandi C, Kohn R. Bayesian inference using synthetic likelihood: asymptotics and adjustments. J Am Stat Assoc 2022. [DOI: 10.1080/01621459.2022.2086132] [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)
- David T. Frazier
- Department of Econometrics and Business Statistics, Monash University, Clayton VIC 3800, Australia
- Australian Centre of Excellence for Mathematical and Statistical Frontiers (ACEMS)
| | - David J. Nott
- Department of Statistics and Applied Probability, National University of Singapore, Singapore 117546
- Operations Research and Analytics Cluster, National University of Singapore, Singapore 119077
| | - Christopher Drovandi
- School of Mathematical Sciences, Queensland University of Technology, Brisbane 4000 Australia
- Australian Centre of Excellence for Mathematical and Statistical Frontiers (ACEMS)
| | - Robert Kohn
- Australian School of Business, School of Economics, University of New South Wales, Sydney NSW 2052, Australia
- Australian Centre of Excellence for Mathematical and Statistical Frontiers (ACEMS)
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15
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Approximate Bayesian computation using asymptotically normal point estimates. Comput Stat 2022. [DOI: 10.1007/s00180-022-01226-3] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/03/2022]
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16
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Kaji T, Ročková V. Metropolis-Hastings via Classification. J Am Stat Assoc 2022. [DOI: 10.1080/01621459.2022.2060836] [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]
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17
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Matsubara T, Knoblauch J, Briol F, Oates CJ. Robust generalised Bayesian inference for intractable likelihoods. J R Stat Soc Series B Stat Methodol 2022. [DOI: 10.1111/rssb.12500] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/27/2022]
Affiliation(s)
- Takuo Matsubara
- Newcastle University Newcastle upon TyneUK
- The Alan Turing Institute LondonUK
| | | | | | - Chris J. Oates
- Newcastle University Newcastle upon TyneUK
- The Alan Turing Institute LondonUK
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19
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Priddle JW, Sisson SA, Frazier DT, Turner I, Drovandi C. Efficient Bayesian Synthetic Likelihood With Whitening Transformations. J Comput Graph Stat 2021. [DOI: 10.1080/10618600.2021.1979012] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/24/2022]
Affiliation(s)
- Jacob W. Priddle
- School of Mathematical Sciences, Queensland University of Technology, Brisbane, Australia
| | | | - David T. Frazier
- Department of Econometrics and Business Statistics, Monash University, Clayton, Australia
| | - Ian Turner
- School of Mathematical Sciences, Queensland University of Technology, Brisbane, Australia
| | - Christopher Drovandi
- School of Mathematical Sciences, Queensland University of Technology, Brisbane, Australia
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20
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Quantifying the impact of electric fields on single-cell motility. Biophys J 2021; 120:3363-3373. [PMID: 34242588 DOI: 10.1016/j.bpj.2021.06.034] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/22/2021] [Revised: 05/17/2021] [Accepted: 06/28/2021] [Indexed: 11/20/2022] Open
Abstract
Cell motility in response to environmental cues forms the basis of many developmental processes in multicellular organisms. One such environmental cue is an electric field (EF), which induces a form of motility known as electrotaxis. Electrotaxis has evolved in a number of cell types to guide wound healing and has been associated with different cellular processes, suggesting that observed electrotactic behavior is likely a combination of multiple distinct effects arising from the presence of an EF. To determine the different mechanisms by which observed electrotactic behavior emerges, and thus to design EFs that can be applied to direct and control electrotaxis, researchers require accurate quantitative predictions of cellular responses to externally applied fields. Here, we use mathematical modeling to formulate and parameterize a variety of hypothetical descriptions of how cell motility may change in response to an EF. We calibrate our model to observed data using synthetic likelihoods and Bayesian sequential learning techniques and demonstrate that EFs bias cellular motility through only one of a selection of hypothetical mechanisms. We also demonstrate how the model allows us to make predictions about cellular motility under different EFs. The resulting model and calibration methodology will thus form the basis for future data-driven and model-based feedback control strategies based on electric actuation.
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21
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Efficient inference for stochastic differential equation mixed-effects models using correlated particle pseudo-marginal algorithms. Comput Stat Data Anal 2021. [DOI: 10.1016/j.csda.2020.107151] [Citation(s) in RCA: 7] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/23/2022]
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22
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Frazier DT, Drovandi C. Robust Approximate Bayesian Inference With Synthetic Likelihood. J Comput Graph Stat 2021. [DOI: 10.1080/10618600.2021.1875839] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/22/2022]
Affiliation(s)
- David T. Frazier
- Department of Econometrics and Business Statistics, Monash University, Melbourne, Australia
- Australian Centre of Excellence for Mathematical and Statistical Frontiers (ACEMS)
| | - Christopher Drovandi
- Australian Centre of Excellence for Mathematical and Statistical Frontiers (ACEMS)
- School of Mathematical Sciences, Queensland University of Technology, Brisbane, Australia
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23
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Affiliation(s)
- Nadja Klein
- Statistics, School of Business and Economics, Humboldt-Universität zu Berlin
,
Berlin
,
Germany
| | - David J. Nott
- Department of Statistics and Applied Probability and Institute of Operations Research and Analytics, National University of Singapore
,
Singapore
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24
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Schälte Y, Hasenauer J. Efficient exact inference for dynamical systems with noisy measurements using sequential approximate Bayesian computation. Bioinformatics 2020; 36:i551-i559. [PMID: 32657404 PMCID: PMC7355286 DOI: 10.1093/bioinformatics/btaa397] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/06/2023] Open
Abstract
MOTIVATION Approximate Bayesian computation (ABC) is an increasingly popular method for likelihood-free parameter inference in systems biology and other fields of research, as it allows analyzing complex stochastic models. However, the introduced approximation error is often not clear. It has been shown that ABC actually gives exact inference under the implicit assumption of a measurement noise model. Noise being common in biological systems, it is intriguing to exploit this insight. But this is difficult in practice, as ABC is in general highly computationally demanding. Thus, the question we want to answer here is how to efficiently account for measurement noise in ABC. RESULTS We illustrate exemplarily how ABC yields erroneous parameter estimates when neglecting measurement noise. Then, we discuss practical ways of correctly including the measurement noise in the analysis. We present an efficient adaptive sequential importance sampling-based algorithm applicable to various model types and noise models. We test and compare it on several models, including ordinary and stochastic differential equations, Markov jump processes and stochastically interacting agents, and noise models including normal, Laplace and Poisson noise. We conclude that the proposed algorithm could improve the accuracy of parameter estimates for a broad spectrum of applications. AVAILABILITY AND IMPLEMENTATION The developed algorithms are made publicly available as part of the open-source python toolbox pyABC (https://github.com/icb-dcm/pyabc). SUPPLEMENTARY INFORMATION Supplementary data are available at Bioinformatics online.
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Affiliation(s)
- Yannik Schälte
- Helmholtz Zentrum München, Institute of Computational Biology, Neuherberg 85764, Germany
- Department of Mathematics, Chair of Mathematical Modeling of Biological Systems, Technical University Munich, Garching 85748, Germany
| | - Jan Hasenauer
- Helmholtz Zentrum München, Institute of Computational Biology, Neuherberg 85764, Germany
- Department of Mathematics, Chair of Mathematical Modeling of Biological Systems, Technical University Munich, Garching 85748, Germany
- Research Unit Biomathematics, University of Bonn, Bonn 53113, Germany
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25
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Kazarnikov A, Haario H. Statistical approach for parameter identification by Turing patterns. J Theor Biol 2020; 501:110319. [PMID: 32416093 DOI: 10.1016/j.jtbi.2020.110319] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/29/2020] [Revised: 04/16/2020] [Accepted: 05/04/2020] [Indexed: 01/09/2023]
Abstract
Prevailing theories in biological pattern formation, such as in morphogenesis or multicellular structures development, have been based on purely chemical processes, with the Turing models as the prime example. Recent studies have challenged the approach, by underlining the role of mechanical forces. A quantitative discrimination of competing theories is difficult, however, due to the elusive character of the processes: different mechanisms may result in similar patterns, while patterns obtained with a fixed model and fixed parameter values, but with small random perturbations of initial values, will significantly differ in shape, while being of the "same" type. In this sense each model parameter value corresponds to a family of patterns, rather than a fixed solution. For this situation we create a likelihood that allows a statistically sound way to distinguish the model parameters that correspond to given patterns. The method allows us to identify model parameters of reaction-diffusion systems by using Turing patterns only, i.e., the steady-state solutions of the respective equations without the use of transient data or initial values. The method is tested with three classical models of pattern formation: the FitzHugh-Nagumo model, Gierer-Meinhardt system and Brusselator reaction-diffusion system. We quantify the accuracy achieved by different amounts of training data by Bayesian sampling methods. We demonstrate how a large enough ensemble of patterns leads to detection of very small but systematic structural changes, practically impossible to distinguish with the naked eye.
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Affiliation(s)
- Alexey Kazarnikov
- Department of Mathematics and Physics, LUT University, Yliopistonkatu 34, 53850 Lappeenranta, Finland; Southern Mathematical Institute of the Vladikavkaz Scientific Centre of the Russian Academy of Sciences, 362027 Vladikavkaz, Russia.
| | - Heikki Haario
- Department of Mathematics and Physics, LUT University, Yliopistonkatu 34, 53850 Lappeenranta, Finland; Finnish Meteorological Institute, FI-00101, P.O. Box 503, Helsinki, Finland
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26
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Kokko J, Remes U, Thomas O, Pesonen H, Corander J. PYLFIRE: Python implementation of likelihood-free inference by ratio estimation. Wellcome Open Res 2019; 4:197. [PMID: 32133422 PMCID: PMC7041362 DOI: 10.12688/wellcomeopenres.15583.1] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Accepted: 11/13/2019] [Indexed: 11/21/2022] Open
Abstract
Likelihood-free inference for simulator-based models is an emerging methodological branch of statistics which has attracted considerable attention in applications across diverse fields such as population genetics, astronomy and economics. Recently, the power of statistical classifiers has been harnessed in likelihood-free inference to obtain either point estimates or even posterior distributions of model parameters. Here we introduce PYLFIRE, an open-source Python implementation of the inference method LFIRE (likelihood-free inference by ratio estimation) that uses penalised logistic regression. PYLFIRE is made available as part of the general ELFI inference software http://elfi.ai to benefit both the user and developer communities for likelihood-free inference.
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Affiliation(s)
- Jan Kokko
- Department of Mathematics and Statistics, University of Helsinki, Helsinki, Finland
| | - Ulpu Remes
- Department of Mathematics and Statistics, University of Helsinki, Helsinki, Finland
| | - Owen Thomas
- Department of Biostatistics, University of Oslo, Oslo, Norway
| | - Henri Pesonen
- Department of Biostatistics, University of Oslo, Oslo, Norway
| | - Jukka Corander
- Department of Mathematics and Statistics, University of Helsinki, Helsinki, Finland
- Department of Biostatistics, University of Oslo, Oslo, Norway
- Parasites and Microbes, Wellcome Trust Sanger Institute, Hinxton, UK
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27
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Picchini U, Forman JL. Bayesian inference for stochastic differential equation mixed effects models of a tumour xenography study. J R Stat Soc Ser C Appl Stat 2019. [DOI: 10.1111/rssc.12347] [Citation(s) in RCA: 10] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Affiliation(s)
- Umberto Picchini
- Chalmers University of Technology and University of Gothenburg and Lund University Sweden
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28
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Picchini U. Likelihood-free stochastic approximation EM for inference in complex models. COMMUN STAT-SIMUL C 2019. [DOI: 10.1080/03610918.2017.1401082] [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)
- Umberto Picchini
- Centre for Mathematical Sciences, Lund University, Sölvegatan 18, Lund, Sweden
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29
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An Z, South LF, Nott DJ, Drovandi CC. Accelerating Bayesian Synthetic Likelihood With the Graphical Lasso. J Comput Graph Stat 2019. [DOI: 10.1080/10618600.2018.1537928] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/27/2022]
Affiliation(s)
- Ziwen An
- School of Mathematical Sciences, Queensland University of Technology, Brisbane, Australia
- Australian Research Council Centre of Excellence for Mathematical and Statistics Frontiers (ACEMS), Australia
| | - Leah F. South
- School of Mathematical Sciences, Queensland University of Technology, Brisbane, Australia
- Australian Research Council Centre of Excellence for Mathematical and Statistics Frontiers (ACEMS), Australia
| | - David J. Nott
- Department of Statistics and Applied Probability, National University of Singapore, Singapore
| | - Christopher C. Drovandi
- School of Mathematical Sciences, Queensland University of Technology, Brisbane, Australia
- Australian Research Council Centre of Excellence for Mathematical and Statistics Frontiers (ACEMS), Australia
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30
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Järvenpää M, Gutmann MU, Vehtari A, Marttinen P. Gaussian process modelling in approximate Bayesian computation to estimate horizontal gene transfer in bacteria. Ann Appl Stat 2018. [DOI: 10.1214/18-aoas1150] [Citation(s) in RCA: 18] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
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31
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32
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Karabatsos G. On Bayesian Testing of Additive Conjoint Measurement Axioms Using Synthetic Likelihood. PSYCHOMETRIKA 2018; 83:321-332. [PMID: 28842870 DOI: 10.1007/s11336-017-9581-x] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/20/2016] [Revised: 06/14/2017] [Indexed: 06/07/2023]
Abstract
This article introduces a Bayesian method for testing the axioms of additive conjoint measurement. The method is based on an importance sampling algorithm that performs likelihood-free, approximate Bayesian inference using a synthetic likelihood to overcome the analytical intractability of this testing problem. This new method improves upon previous methods because it provides an omnibus test of the entire hierarchy of cancellation axioms, beyond double cancellation. It does so while accounting for the posterior uncertainty that is inherent in the empirical orderings that are implied by these axioms, together. The new method is illustrated through a test of the cancellation axioms on a classic survey data set, and through the analysis of simulated data.
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33
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Karabatsos G, Leisen F. An approximate likelihood perspective on ABC methods. STATISTICS SURVEYS 2018. [DOI: 10.1214/18-ss120] [Citation(s) in RCA: 15] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
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34
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Fasiolo M, Wood SN, Hartig F, Bravington MV. An extended empirical saddlepoint approximation for intractable likelihoods. Electron J Stat 2018. [DOI: 10.1214/18-ejs1433] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
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