Giovanni Brigati, Gabriel Stoltz, Andi Q. Wang, Lihan Wang
We study the long-time convergence behavior of underdamped Langevin dynamics, when the spatial equilibrium satisfies a weighted Poincar'e inequality, with a general velocity distribution, which allows for fat-tail or subexponential potential energies, and provide constructive and fully explicit estimates in $mathrm{L}^2$-norm with $mathrm{L}^infty$ initial conditions. A key ingredient is a space-time weighted Poincar'e--Lions inequality, which in turn implies a weak Poincar'e--Lions inequality.
{"title":"Explicit convergence rates of underdamped Langevin dynamics under weighted and weak Poincaré--Lions inequalities","authors":"Giovanni Brigati, Gabriel Stoltz, Andi Q. Wang, Lihan Wang","doi":"arxiv-2407.16033","DOIUrl":"https://doi.org/arxiv-2407.16033","url":null,"abstract":"We study the long-time convergence behavior of underdamped Langevin dynamics,\u0000when the spatial equilibrium satisfies a weighted Poincar'e inequality, with a\u0000general velocity distribution, which allows for fat-tail or subexponential\u0000potential energies, and provide constructive and fully explicit estimates in\u0000$mathrm{L}^2$-norm with $mathrm{L}^infty$ initial conditions. A key\u0000ingredient is a space-time weighted Poincar'e--Lions inequality, which in turn\u0000implies a weak Poincar'e--Lions inequality.","PeriodicalId":501215,"journal":{"name":"arXiv - STAT - Computation","volume":"15 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141775383","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
H. Sherry Zhang, Dianne Cook, Nicolas Langrené, Jessica Wai Yin Leung
The projection pursuit (PP) guided tour interactively optimises a criteria function known as the PP index, to explore high-dimensional data by revealing interesting projections. The optimisation in PP can be non-trivial, involving non-smooth functions and optima with a small squint angle, detectable only from close proximity. To address these challenges, this study investigates the performance of a recently introduced swarm-based algorithm, Jellyfish Search Optimiser (JSO), for optimising PP indexes. The performance of JSO for visualising data is evaluated across various hyper-parameter settings and compared with existing optimisers. Additionally, this work proposes novel methods to quantify two properties of the PP index, smoothness and squintability that capture the complexities inherent in PP optimisation problems. These two metrics are evaluated along with JSO hyper-parameters to determine their effects on JSO success rate. Our numerical results confirm the positive impact of these metrics on the JSO success rate, with squintability being the most significant. The JSO algorithm has been implemented in the tourr package and functions to calculate smoothness and squintability are available in the ferrn package.
{"title":"Studying the Performance of the Jellyfish Search Optimiser for the Application of Projection Pursuit","authors":"H. Sherry Zhang, Dianne Cook, Nicolas Langrené, Jessica Wai Yin Leung","doi":"arxiv-2407.13663","DOIUrl":"https://doi.org/arxiv-2407.13663","url":null,"abstract":"The projection pursuit (PP) guided tour interactively optimises a criteria\u0000function known as the PP index, to explore high-dimensional data by revealing\u0000interesting projections. The optimisation in PP can be non-trivial, involving\u0000non-smooth functions and optima with a small squint angle, detectable only from\u0000close proximity. To address these challenges, this study investigates the\u0000performance of a recently introduced swarm-based algorithm, Jellyfish Search\u0000Optimiser (JSO), for optimising PP indexes. The performance of JSO for\u0000visualising data is evaluated across various hyper-parameter settings and\u0000compared with existing optimisers. Additionally, this work proposes novel\u0000methods to quantify two properties of the PP index, smoothness and\u0000squintability that capture the complexities inherent in PP optimisation\u0000problems. These two metrics are evaluated along with JSO hyper-parameters to\u0000determine their effects on JSO success rate. Our numerical results confirm the\u0000positive impact of these metrics on the JSO success rate, with squintability\u0000being the most significant. The JSO algorithm has been implemented in the tourr\u0000package and functions to calculate smoothness and squintability are available\u0000in the ferrn package.","PeriodicalId":501215,"journal":{"name":"arXiv - STAT - Computation","volume":"63 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141743467","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Lingbin Bian, Nizhuan Wang, Yuanning Li, Adeel Razi, Qian Wang, Han Zhang, Dinggang Shen, the UNC/UMN Baby Connectome Project Consortium
The segregation and integration of infant brain networks undergo tremendous changes due to the rapid development of brain function and organization. Traditional methods for estimating brain modularity usually rely on group-averaged functional connectivity (FC), often overlooking individual variability. To address this, we introduce a novel approach utilizing Bayesian modeling to analyze the dynamic development of functional modules in infants over time. This method retains inter-individual variability and, in comparison to conventional group averaging techniques, more effectively detects modules, taking into account the stationarity of module evolution. Furthermore, we explore gender differences in module development under awake and sleep conditions by assessing modular similarities. Our results show that female infants demonstrate more distinct modular structures between these two conditions, possibly implying relative quiet and restful sleep compared with male infants.
{"title":"Evaluating the evolution and inter-individual variability of infant functional module development from 0 to 5 years old","authors":"Lingbin Bian, Nizhuan Wang, Yuanning Li, Adeel Razi, Qian Wang, Han Zhang, Dinggang Shen, the UNC/UMN Baby Connectome Project Consortium","doi":"arxiv-2407.13118","DOIUrl":"https://doi.org/arxiv-2407.13118","url":null,"abstract":"The segregation and integration of infant brain networks undergo tremendous\u0000changes due to the rapid development of brain function and organization.\u0000Traditional methods for estimating brain modularity usually rely on\u0000group-averaged functional connectivity (FC), often overlooking individual\u0000variability. To address this, we introduce a novel approach utilizing Bayesian\u0000modeling to analyze the dynamic development of functional modules in infants\u0000over time. This method retains inter-individual variability and, in comparison\u0000to conventional group averaging techniques, more effectively detects modules,\u0000taking into account the stationarity of module evolution. Furthermore, we\u0000explore gender differences in module development under awake and sleep\u0000conditions by assessing modular similarities. Our results show that female\u0000infants demonstrate more distinct modular structures between these two\u0000conditions, possibly implying relative quiet and restful sleep compared with\u0000male infants.","PeriodicalId":501215,"journal":{"name":"arXiv - STAT - Computation","volume":"25 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141743684","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We assess an emerging simulation research method -- Inverse Generative Social Science (IGSS) citep{Epstein23a} -- that harnesses the power of evolution by natural selection to model and explain complex targets. Drawing on a review of recent papers that use IGSS, and by applying it in two different studies of conflict, we here assess its potential both as a modelling approach and as formal theory. We find that IGSS has potential for research in studies of organistions. IGSS offers two huge advantages over most other approaches to modelling. 1) IGSS has the potential to fit complex non-linear models to a target and 2) the models have the potential to be interpreted as social theory. The paper presents IGSS to a new audience, illustrates how it can contribute, and provides software that can be used as a basis of an IGSS study.
{"title":"Examining inverse generative social science to study targets of interest","authors":"Thomas Chesney, Asif Jaffer, Robert Pasley","doi":"arxiv-2407.13474","DOIUrl":"https://doi.org/arxiv-2407.13474","url":null,"abstract":"We assess an emerging simulation research method -- Inverse Generative Social\u0000Science (IGSS) citep{Epstein23a} -- that harnesses the power of evolution by\u0000natural selection to model and explain complex targets. Drawing on a review of recent papers that use IGSS, and by applying it in two\u0000different studies of conflict, we here assess its potential both as a modelling\u0000approach and as formal theory. We find that IGSS has potential for research in studies of organistions. IGSS\u0000offers two huge advantages over most other approaches to modelling. 1) IGSS has\u0000the potential to fit complex non-linear models to a target and 2) the models\u0000have the potential to be interpreted as social theory. The paper presents IGSS to a new audience, illustrates how it can contribute,\u0000and provides software that can be used as a basis of an IGSS study.","PeriodicalId":501215,"journal":{"name":"arXiv - STAT - Computation","volume":"44 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141743468","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Vincent Guigues, Anton J. Kleywegt, Giovanni Amorim, Andre Krauss, Victor Hugo Nascimento
This is the User Manual of LASPATED library. This library is available on GitHub (at https://github.com/vguigues/LASPATED)) and provides a set of tools to analyze spatiotemporal data. A video tutorial for this library is available on Youtube. It is made of a Python package for time and space discretizations and of two packages (one in Matlab and one in C++) implementing the calibration of the probabilistic models for stochastic spatio-temporal data proposed in the companion paper arXiv:2203.16371v2.
{"title":"LASPATED: A Library for the Analysis of Spatio-Temporal Discrete Data (User Manual)","authors":"Vincent Guigues, Anton J. Kleywegt, Giovanni Amorim, Andre Krauss, Victor Hugo Nascimento","doi":"arxiv-2407.13889","DOIUrl":"https://doi.org/arxiv-2407.13889","url":null,"abstract":"This is the User Manual of LASPATED library. This library is available on\u0000GitHub (at https://github.com/vguigues/LASPATED)) and provides a set of tools\u0000to analyze spatiotemporal data. A video tutorial for this library is available\u0000on Youtube. It is made of a Python package for time and space discretizations\u0000and of two packages (one in Matlab and one in C++) implementing the calibration\u0000of the probabilistic models for stochastic spatio-temporal data proposed in the\u0000companion paper arXiv:2203.16371v2.","PeriodicalId":501215,"journal":{"name":"arXiv - STAT - Computation","volume":"20 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141743466","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Background: Statisticians evaluating the impact of policy interventions such as screening or vaccination will need to make use of mathematical and computational models of disease progression and spread. Calibration is the process of identifying the parameters of these models, with a Bayesian framework providing a natural way in which to do this in a probabilistic fashion. Markov Chain Monte Carlo (MCMC) is one of a number of computational tools that is useful in carrying out this calibration. Objective: In the context of complex models in particular, a key problem that arises is one of non-identifiability. In this setting, one approach which can be used is to consider and ensure that appropriately informative priors are specified on the joint parameter space. We give examples of how this arises and may be addressed in practice. Methods: Using a basic SIS model the calibration process and the associated challenge of non-identifiability is discussed. How this problem arises in the context of a larger model for HPV and cervical cancer is also illustrated. Results: The conditions which allow the problem of non-identifiability to be resolved are demonstrated for the SIS model. For the larger HPV model, how this impacts on the calibration process is also discussed.
{"title":"Incorporating additional evidence as prior information to resolve non-identifiability in Bayesian disease model calibration","authors":"Daria Semochkina, Cathal Walsh","doi":"arxiv-2407.13451","DOIUrl":"https://doi.org/arxiv-2407.13451","url":null,"abstract":"Background: Statisticians evaluating the impact of policy interventions such\u0000as screening or vaccination will need to make use of mathematical and\u0000computational models of disease progression and spread. Calibration is the\u0000process of identifying the parameters of these models, with a Bayesian\u0000framework providing a natural way in which to do this in a probabilistic\u0000fashion. Markov Chain Monte Carlo (MCMC) is one of a number of computational\u0000tools that is useful in carrying out this calibration. Objective: In the\u0000context of complex models in particular, a key problem that arises is one of\u0000non-identifiability. In this setting, one approach which can be used is to\u0000consider and ensure that appropriately informative priors are specified on the\u0000joint parameter space. We give examples of how this arises and may be addressed\u0000in practice. Methods: Using a basic SIS model the calibration process and the\u0000associated challenge of non-identifiability is discussed. How this problem\u0000arises in the context of a larger model for HPV and cervical cancer is also\u0000illustrated. Results: The conditions which allow the problem of\u0000non-identifiability to be resolved are demonstrated for the SIS model. For the\u0000larger HPV model, how this impacts on the calibration process is also\u0000discussed.","PeriodicalId":501215,"journal":{"name":"arXiv - STAT - Computation","volume":"9 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141743469","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
To study convergence of SMACOF we introduce a modification mSMACOF that rotates the configurations from each of the SMACOF iterations to principal components. This modification, called mSMACOF, has the same stress values as SMACOF in each iteration, but unlike SMACOF it produces a sequence of configurations that properly converges to a solution. We show that the modified algorithm can be implemented by iterating ordinary SMACOF to convergence, and then rotating the SMACOF solution to principal components. The speed of linear convergence of SMACOF and mSMACOF is the same, and is equal to the largest eigenvalue of the derivative of the Guttman transform, ignoring the trivial unit eigenvalues that result from rotational indeterminacy.
{"title":"Convergence of SMACOF","authors":"Jan De Leeuw","doi":"arxiv-2407.12945","DOIUrl":"https://doi.org/arxiv-2407.12945","url":null,"abstract":"To study convergence of SMACOF we introduce a modification mSMACOF that\u0000rotates the configurations from each of the SMACOF iterations to principal\u0000components. This modification, called mSMACOF, has the same stress values as\u0000SMACOF in each iteration, but unlike SMACOF it produces a sequence of\u0000configurations that properly converges to a solution. We show that the modified\u0000algorithm can be implemented by iterating ordinary SMACOF to convergence, and\u0000then rotating the SMACOF solution to principal components. The speed of linear\u0000convergence of SMACOF and mSMACOF is the same, and is equal to the largest\u0000eigenvalue of the derivative of the Guttman transform, ignoring the trivial\u0000unit eigenvalues that result from rotational indeterminacy.","PeriodicalId":501215,"journal":{"name":"arXiv - STAT - Computation","volume":"40 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141743470","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Matthew J. Heiner, Samuel B. Johnson, Joshua R. Christensen, David B. Dahl
We propose and demonstrate an alternate, effective approach to simple slice sampling. Using the probability integral transform, we first generalize Neal's shrinkage algorithm, standardizing the procedure to an automatic and universal starting point: the unit interval. This enables the introduction of approximate (pseudo-) targets through importance reweighting, a technique that has popularized elliptical slice sampling. Reasonably accurate pseudo-targets can boost sampler efficiency by requiring fewer rejections and by reducing target skewness. This strategy is effective when a natural, possibly crude, approximation to the target exists. Alternatively, obtaining a marginal pseudo-target from initial samples provides an intuitive and automatic tuning procedure. We consider two metrics for evaluating the quality of approximation; each can be used as a criterion to find an optimal pseudo-target or as an interpretable diagnostic. We examine performance of the proposed sampler relative to other popular, easily implemented MCMC samplers on standard targets in isolation, and as steps within a Gibbs sampler in a Bayesian modeling context. We extend the transformation method to multivariate slice samplers and demonstrate with a constrained state-space model for which a readily available forward-backward algorithm provides the target approximation.
{"title":"Quantile Slice Sampling","authors":"Matthew J. Heiner, Samuel B. Johnson, Joshua R. Christensen, David B. Dahl","doi":"arxiv-2407.12608","DOIUrl":"https://doi.org/arxiv-2407.12608","url":null,"abstract":"We propose and demonstrate an alternate, effective approach to simple slice\u0000sampling. Using the probability integral transform, we first generalize Neal's\u0000shrinkage algorithm, standardizing the procedure to an automatic and universal\u0000starting point: the unit interval. This enables the introduction of approximate\u0000(pseudo-) targets through importance reweighting, a technique that has\u0000popularized elliptical slice sampling. Reasonably accurate pseudo-targets can\u0000boost sampler efficiency by requiring fewer rejections and by reducing target\u0000skewness. This strategy is effective when a natural, possibly crude,\u0000approximation to the target exists. Alternatively, obtaining a marginal\u0000pseudo-target from initial samples provides an intuitive and automatic tuning\u0000procedure. We consider two metrics for evaluating the quality of approximation;\u0000each can be used as a criterion to find an optimal pseudo-target or as an\u0000interpretable diagnostic. We examine performance of the proposed sampler\u0000relative to other popular, easily implemented MCMC samplers on standard targets\u0000in isolation, and as steps within a Gibbs sampler in a Bayesian modeling\u0000context. We extend the transformation method to multivariate slice samplers and\u0000demonstrate with a constrained state-space model for which a readily available\u0000forward-backward algorithm provides the target approximation.","PeriodicalId":501215,"journal":{"name":"arXiv - STAT - Computation","volume":"49 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141743685","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Hawkes stochastic point process models have emerged as valuable statistical tools for analyzing viral contagion. The spatiotemporal Hawkes process characterizes the speeds at which viruses spread within human populations. Unfortunately, likelihood-based inference using these models requires $O(N^2)$ floating-point operations, for $N$ the number of observed cases. Recent work responds to the Hawkes likelihood's computational burden by developing efficient graphics processing unit (GPU)-based routines that enable Bayesian analysis of tens-of-thousands of observations. We build on this work and develop a high-performance computing (HPC) strategy that divides 30 Markov chains between 4 GPU nodes, each of which uses multiple GPUs to accelerate its chain's likelihood computations. We use this framework to apply two spatiotemporal Hawkes models to the analysis of one million COVID-19 cases in the United States between March 2020 and June 2023. In addition to brute-force HPC, we advocate for two simple strategies as scalable alternatives to successful approaches proposed for small data settings. First, we use known county-specific population densities to build a spatially varying triggering kernel in a manner that avoids computationally costly nearest neighbors search. Second, we use a cut-posterior inference routine that accounts for infections' spatial location uncertainty by iteratively sampling latent locations uniformly within their respective counties of occurrence, thereby avoiding full-blown latent variable inference for 1,000,000 infection locations.
{"title":"Scaling Hawkes processes to one million COVID-19 cases","authors":"Seyoon Ko, Marc A. Suchard, Andrew J. Holbrook","doi":"arxiv-2407.11349","DOIUrl":"https://doi.org/arxiv-2407.11349","url":null,"abstract":"Hawkes stochastic point process models have emerged as valuable statistical\u0000tools for analyzing viral contagion. The spatiotemporal Hawkes process\u0000characterizes the speeds at which viruses spread within human populations.\u0000Unfortunately, likelihood-based inference using these models requires $O(N^2)$\u0000floating-point operations, for $N$ the number of observed cases. Recent work\u0000responds to the Hawkes likelihood's computational burden by developing\u0000efficient graphics processing unit (GPU)-based routines that enable Bayesian\u0000analysis of tens-of-thousands of observations. We build on this work and\u0000develop a high-performance computing (HPC) strategy that divides 30 Markov\u0000chains between 4 GPU nodes, each of which uses multiple GPUs to accelerate its\u0000chain's likelihood computations. We use this framework to apply two\u0000spatiotemporal Hawkes models to the analysis of one million COVID-19 cases in\u0000the United States between March 2020 and June 2023. In addition to brute-force\u0000HPC, we advocate for two simple strategies as scalable alternatives to\u0000successful approaches proposed for small data settings. First, we use known\u0000county-specific population densities to build a spatially varying triggering\u0000kernel in a manner that avoids computationally costly nearest neighbors search.\u0000Second, we use a cut-posterior inference routine that accounts for infections'\u0000spatial location uncertainty by iteratively sampling latent locations uniformly\u0000within their respective counties of occurrence, thereby avoiding full-blown\u0000latent variable inference for 1,000,000 infection locations.","PeriodicalId":501215,"journal":{"name":"arXiv - STAT - Computation","volume":"23 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141720745","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Due to the high dimensionality or multimodality that is common in modern astronomy, sampling Bayesian posteriors can be challenging. Several publicly available codes based on different sampling algorithms can solve these complex models, but the execution of the code is not always efficient or fast enough. The article introduces a C language general-purpose code, Nii-C (https://github.com/shengjin/nii-c.git), that implements a framework of Automatic Parallel Tempering Markov Chain Monte Carlo. Automatic in this context means that the parameters that ensure an efficient parallel tempering process can be set by a control system during the initial stages of a sampling process. The auto-tuned parameters consist of two parts, the temperature ladders of all parallel tempering Markov chains and the proposal distributions for all model parameters across all parallel tempering chains. In order to reduce dependencies in the compilation process and increase the code's execution speed, Nii-C code is constructed entirely in the C language and parallelised using the Message-Passing Interface protocol to optimise the efficiency of parallel sampling. These implementations facilitate rapid convergence in the sampling of high-dimensional and multi-modal distributions, as well as expeditious code execution time. The Nii-C code can be used in various research areas to trace complex distributions due to its high sampling efficiency and quick execution speed. This article presents a few applications of the Nii-C code.
由于现代天文学中常见的高维度或多模态性，贝叶斯后验的采样可能具有挑战性。一些基于不同采样算法的公开代码可以求解这些复杂模型，但代码执行的效率和速度并不总是足够快。本文介绍了一种 C 语言通用代码 Nii-C(https://github.com/shengjin/nii-c.git)，它实现了一种自动并行调节马尔可夫链蒙特卡罗框架。这里所说的自动是指在采样过程的初始阶段，可以通过控制系统设置确保高效并行回火过程的参数。自动调整参数由两部分组成，即所有平行回火马尔可夫链的温度梯度和所有平行回火链上所有模型参数的建议分布。为了减少编译过程中的依赖性并提高代码执行速度，Nii-C 代码完全用 C 语言编写，并使用消息传递接口协议进行并行化，以优化并行采样的效率。这些实现有助于在高维和多模态分布采样时快速收敛，并加快代码执行时间。Nii-C 代码的采样效率高、执行速度快，因此可用于多个研究领域，对复杂分布进行追踪。本文将介绍 Nii-C 代码的一些应用。
{"title":"Automatic Parallel Tempering Markov Chain Monte Carlo with Nii-C","authors":"Sheng Jin, Wenxin Jiang, Dong-Hong Wu","doi":"arxiv-2407.09915","DOIUrl":"https://doi.org/arxiv-2407.09915","url":null,"abstract":"Due to the high dimensionality or multimodality that is common in modern\u0000astronomy, sampling Bayesian posteriors can be challenging. Several publicly\u0000available codes based on different sampling algorithms can solve these complex\u0000models, but the execution of the code is not always efficient or fast enough.\u0000The article introduces a C language general-purpose code, Nii-C\u0000(https://github.com/shengjin/nii-c.git), that implements a framework of\u0000Automatic Parallel Tempering Markov Chain Monte Carlo. Automatic in this\u0000context means that the parameters that ensure an efficient parallel tempering\u0000process can be set by a control system during the initial stages of a sampling\u0000process. The auto-tuned parameters consist of two parts, the temperature\u0000ladders of all parallel tempering Markov chains and the proposal distributions\u0000for all model parameters across all parallel tempering chains. In order to\u0000reduce dependencies in the compilation process and increase the code's\u0000execution speed, Nii-C code is constructed entirely in the C language and\u0000parallelised using the Message-Passing Interface protocol to optimise the\u0000efficiency of parallel sampling. These implementations facilitate rapid\u0000convergence in the sampling of high-dimensional and multi-modal distributions,\u0000as well as expeditious code execution time. The Nii-C code can be used in\u0000various research areas to trace complex distributions due to its high sampling\u0000efficiency and quick execution speed. This article presents a few applications\u0000of the Nii-C code.","PeriodicalId":501215,"journal":{"name":"arXiv - STAT - Computation","volume":"74 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141720751","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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