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":null,"pages":null},"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":null,"pages":null},"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":null,"pages":null},"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":null,"pages":null},"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":null,"pages":null},"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}
Gauss proposed the problem of how to enumerate the number of solutions for placing $N$ queens on an $Ntimes N$ chess board, so no two queens attack each other. The N-queen problem is a classic problem in combinatorics. We describe a variety of Monte Carlo (MC) methods for counting the number of solutions. In particular, we propose a quantile re-ordering based on the Lorenz curve of a sum that is related to counting the number of solutions. We show his approach leads to an efficient polynomial-time solution. Other MC methods include vertical likelihood Monte Carlo, importance sampling, slice sampling, simulated annealing, energy-level sampling, and nested-sampling. Sampling binary matrices that identify the locations of the queens on the board can be done with a Swendsen-Wang style algorithm. Our Monte Carlo approach counts the number of solutions in polynomial time.
高斯提出了这样一个问题：如何枚举出在一个 N 次 N 元的棋盘上摆放 N 个皇后的解的个数，从而避免两个皇后互相攻击。N 皇后问题是组合数学中的一个经典问题。我们介绍了各种计算解数的蒙特卡罗（MC）方法。特别是，我们提出了一种基于洛伦兹曲线的量子重排序方法，它与计算解的数量有关。我们证明了他的方法能带来高效的多项式时间解决方案。其他 MC 方法包括理论似然蒙特卡罗、重要性采样、切片采样、模拟嵌套、能量级采样和嵌套采样。对确定棋盘上皇后位置的二进制矩阵进行采样，可采用斯文森-旺（Swendsen-Wang）式算法。我们的蒙特卡罗方法可以在多项式时间内计算出解决方案的数量。
{"title":"Counting $N$ Queens","authors":"Nick Polson, Vadim Sokolov","doi":"arxiv-2407.08830","DOIUrl":"https://doi.org/arxiv-2407.08830","url":null,"abstract":"Gauss proposed the problem of how to enumerate the number of solutions for\u0000placing $N$ queens on an $Ntimes N$ chess board, so no two queens attack each\u0000other. The N-queen problem is a classic problem in combinatorics. We describe a\u0000variety of Monte Carlo (MC) methods for counting the number of solutions. In\u0000particular, we propose a quantile re-ordering based on the Lorenz curve of a\u0000sum that is related to counting the number of solutions. We show his approach\u0000leads to an efficient polynomial-time solution. Other MC methods include\u0000vertical likelihood Monte Carlo, importance sampling, slice sampling, simulated\u0000annealing, energy-level sampling, and nested-sampling. Sampling binary matrices\u0000that identify the locations of the queens on the board can be done with a\u0000Swendsen-Wang style algorithm. Our Monte Carlo approach counts the number of\u0000solutions in polynomial time.","PeriodicalId":501215,"journal":{"name":"arXiv - STAT - Computation","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-07-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141720746","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}
Håvard HegrePeace Research Institute OsloDepartment of Peace and Conflict Research, Uppsala University, Paola VescoPeace Research Institute OsloDepartment of Peace and Conflict Research, Uppsala University, Michael ColaresiDepartment of Peace and Conflict Research, Uppsala UniversityUniversity of Pittsburgh, Jonas VestbyPeace Research Institute Oslo, Alexa TimlickPeace Research Institute Oslo, Noorain Syed KazmiPeace Research Institute Oslo, Friederike BeckerInstitute of Statistics, Marco BinettiCenter for Crisis Early Warning, University of the Bundeswehr Munich, Tobias BodentienInstitute of Statistics, Tobias BohneCenter for Crisis Early Warning, University of the Bundeswehr Munich, Patrick T. BrandtSchool of Economic, Political, and Policy Sciences, University of Texas, Dallas, Thomas ChadefauxTrinity College Dublin, Simon DrauzInstitute of Statistics, Christoph DworschakUniversity of York, Vito D'OrazioWest Virginia University, Cornelius FritzPennsylvania State University, Hannah FrankTrinity College Dublin, Kristian Skrede GleditschUniversity of EssexPeace Research Institute Oslo, Sonja HäffnerCenter for Crisis Early Warning, University of the Bundeswehr Munich, Martin HoferUniversity College London, Finn L. KlebeUniversity College London, Luca MacisDepartment of Economics and Statistics Cognetti de Martiis, University of Turin, Alexandra MalagaInstitute for Economic Analysis, Barcelona, Marius MehrlUniversity of Leeds, Nils W. MetternichUniversity College London, Daniel MittermaierCenter for Crisis Early Warning, University of the Bundeswehr Munich, David MuchlinskiGeorgia Tech, Hannes MuellerInstitute for Economic Analysis, BarcelonaBarcelona School of Economics, Christian OswaldCenter for Crisis Early Warning, University of the Bundeswehr Munich, Paola PisanoDepartment of Economics and Statistics Cognetti de Martiis, University of Turin, David RandahlDepartment of Peace and Conflict Research, Uppsala University, Christopher RauhUniversity of Cambridge, Lotta RüterInstitute of Statistics, Thomas SchincariolTrinity College Dublin, Benjamin SeimonFundació Economia Analitica, Elena SilettiDepartment of Economics and Statistics Cognetti de Martiis, University of Turin, Marco TagliapietraDepartment of Economics and Statistics Cognetti de Martiis, University of Turin, Chandler ThornhillGeorgia Tech, Johan VegeliusDepartment of Medical Sciences, Uppsala University, Julian WalterskirchenCenter for Crisis Early Warning, University of the Bundeswehr Munich
This draft article outlines a prediction challenge where the target is to forecast the number of fatalities in armed conflicts, in the form of the UCDP `best' estimates, aggregated to the VIEWS units of analysis. It presents the format of the contributions, the evaluation metric, and the procedures, and a brief summary of the contributions. The article serves a function analogous to a pre-analysis plan: a statement of the forecasting models made publicly available before the true future prediction window commences. More information on the challenge, and all data referred to in this document, can be found at https://viewsforecasting.org/research/prediction-challenge-2023.
{"title":"The 2023/24 VIEWS Prediction Challenge: Predicting the Number of Fatalities in Armed Conflict, with Uncertainty","authors":"Håvard HegrePeace Research Institute OsloDepartment of Peace and Conflict Research, Uppsala University, Paola VescoPeace Research Institute OsloDepartment of Peace and Conflict Research, Uppsala University, Michael ColaresiDepartment of Peace and Conflict Research, Uppsala UniversityUniversity of Pittsburgh, Jonas VestbyPeace Research Institute Oslo, Alexa TimlickPeace Research Institute Oslo, Noorain Syed KazmiPeace Research Institute Oslo, Friederike BeckerInstitute of Statistics, Marco BinettiCenter for Crisis Early Warning, University of the Bundeswehr Munich, Tobias BodentienInstitute of Statistics, Tobias BohneCenter for Crisis Early Warning, University of the Bundeswehr Munich, Patrick T. BrandtSchool of Economic, Political, and Policy Sciences, University of Texas, Dallas, Thomas ChadefauxTrinity College Dublin, Simon DrauzInstitute of Statistics, Christoph DworschakUniversity of York, Vito D'OrazioWest Virginia University, Cornelius FritzPennsylvania State University, Hannah FrankTrinity College Dublin, Kristian Skrede GleditschUniversity of EssexPeace Research Institute Oslo, Sonja HäffnerCenter for Crisis Early Warning, University of the Bundeswehr Munich, Martin HoferUniversity College London, Finn L. KlebeUniversity College London, Luca MacisDepartment of Economics and Statistics Cognetti de Martiis, University of Turin, Alexandra MalagaInstitute for Economic Analysis, Barcelona, Marius MehrlUniversity of Leeds, Nils W. MetternichUniversity College London, Daniel MittermaierCenter for Crisis Early Warning, University of the Bundeswehr Munich, David MuchlinskiGeorgia Tech, Hannes MuellerInstitute for Economic Analysis, BarcelonaBarcelona School of Economics, Christian OswaldCenter for Crisis Early Warning, University of the Bundeswehr Munich, Paola PisanoDepartment of Economics and Statistics Cognetti de Martiis, University of Turin, David RandahlDepartment of Peace and Conflict Research, Uppsala University, Christopher RauhUniversity of Cambridge, Lotta RüterInstitute of Statistics, Thomas SchincariolTrinity College Dublin, Benjamin SeimonFundació Economia Analitica, Elena SilettiDepartment of Economics and Statistics Cognetti de Martiis, University of Turin, Marco TagliapietraDepartment of Economics and Statistics Cognetti de Martiis, University of Turin, Chandler ThornhillGeorgia Tech, Johan VegeliusDepartment of Medical Sciences, Uppsala University, Julian WalterskirchenCenter for Crisis Early Warning, University of the Bundeswehr Munich","doi":"arxiv-2407.11045","DOIUrl":"https://doi.org/arxiv-2407.11045","url":null,"abstract":"This draft article outlines a prediction challenge where the target is to\u0000forecast the number of fatalities in armed conflicts, in the form of the UCDP\u0000`best' estimates, aggregated to the VIEWS units of analysis. It presents the\u0000format of the contributions, the evaluation metric, and the procedures, and a\u0000brief summary of the contributions. The article serves a function analogous to\u0000a pre-analysis plan: a statement of the forecasting models made publicly\u0000available before the true future prediction window commences. More information\u0000on the challenge, and all data referred to in this document, can be found at\u0000https://viewsforecasting.org/research/prediction-challenge-2023.","PeriodicalId":501215,"journal":{"name":"arXiv - STAT - Computation","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-07-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141720747","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}
Måns Magnusson, Jakob Torgander, Paul-Christian Bürkner, Lu Zhang, Bob Carpenter, Aki Vehtari
The generality and robustness of inference algorithms is critical to the success of widely used probabilistic programming languages such as Stan, PyMC, Pyro, and Turing.jl. When designing a new general-purpose inference algorithm, whether it involves Monte Carlo sampling or variational approximation, the fundamental problem arises in evaluating its accuracy and efficiency across a range of representative target models. To solve this problem, we propose posteriordb, a database of models and data sets defining target densities along with reference Monte Carlo draws. We further provide a guide to the best practices in using posteriordb for model evaluation and comparison. To provide a wide range of realistic target densities, posteriordb currently comprises 120 representative models and has been instrumental in developing several general inference algorithms.
{"title":"posteriordb: Testing, Benchmarking and Developing Bayesian Inference Algorithms","authors":"Måns Magnusson, Jakob Torgander, Paul-Christian Bürkner, Lu Zhang, Bob Carpenter, Aki Vehtari","doi":"arxiv-2407.04967","DOIUrl":"https://doi.org/arxiv-2407.04967","url":null,"abstract":"The generality and robustness of inference algorithms is critical to the\u0000success of widely used probabilistic programming languages such as Stan, PyMC,\u0000Pyro, and Turing.jl. When designing a new general-purpose inference algorithm,\u0000whether it involves Monte Carlo sampling or variational approximation, the\u0000fundamental problem arises in evaluating its accuracy and efficiency across a\u0000range of representative target models. To solve this problem, we propose\u0000posteriordb, a database of models and data sets defining target densities along\u0000with reference Monte Carlo draws. We further provide a guide to the best\u0000practices in using posteriordb for model evaluation and comparison. To provide\u0000a wide range of realistic target densities, posteriordb currently comprises 120\u0000representative models and has been instrumental in developing several general\u0000inference algorithms.","PeriodicalId":501215,"journal":{"name":"arXiv - STAT - Computation","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-07-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141574477","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 introduce a fast algorithm for Gaussian process regression in low dimensions, applicable to a widely-used family of non-stationary kernels. The non-stationarity of these kernels is induced by arbitrary spatially-varying vertical and horizontal scales. In particular, any stationary kernel can be accommodated as a special case, and we focus especially on the generalization of the standard Mat'ern kernel. Our subroutine for kernel matrix-vector multiplications scales almost optimally as $O(Nlog N)$, where $N$ is the number of regression points. Like the recently developed equispaced Fourier Gaussian process (EFGP) methodology, which is applicable only to stationary kernels, our approach exploits non-uniform fast Fourier transforms (NUFFTs). We offer a complete analysis controlling the approximation error of our method, and we validate the method's practical performance with numerical experiments. In particular we demonstrate improved scalability compared to to state-of-the-art rank-structured approaches in spatial dimension $d>1$.
{"title":"Gaussian process regression with log-linear scaling for common non-stationary kernels","authors":"P. Michael Kielstra, Michael Lindsey","doi":"arxiv-2407.03608","DOIUrl":"https://doi.org/arxiv-2407.03608","url":null,"abstract":"We introduce a fast algorithm for Gaussian process regression in low\u0000dimensions, applicable to a widely-used family of non-stationary kernels. The\u0000non-stationarity of these kernels is induced by arbitrary spatially-varying\u0000vertical and horizontal scales. In particular, any stationary kernel can be\u0000accommodated as a special case, and we focus especially on the generalization\u0000of the standard Mat'ern kernel. Our subroutine for kernel matrix-vector\u0000multiplications scales almost optimally as $O(Nlog N)$, where $N$ is the\u0000number of regression points. Like the recently developed equispaced Fourier\u0000Gaussian process (EFGP) methodology, which is applicable only to stationary\u0000kernels, our approach exploits non-uniform fast Fourier transforms (NUFFTs). We\u0000offer a complete analysis controlling the approximation error of our method,\u0000and we validate the method's practical performance with numerical experiments.\u0000In particular we demonstrate improved scalability compared to to\u0000state-of-the-art rank-structured approaches in spatial dimension $d>1$.","PeriodicalId":501215,"journal":{"name":"arXiv - STAT - Computation","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-07-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141574479","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}
Cyrus Mostajeran, Nathaël Da Costa, Graham Van Goffrier, Rodolphe Sepulchre
We present a geometric framework for the processing of SPD-valued data that preserves subspace structures and is based on the efficient computation of extreme generalized eigenvalues. This is achieved through the use of the Thompson geometry of the semidefinite cone. We explore a particular geodesic space structure in detail and establish several properties associated with it. Finally, we review a novel inductive mean of SPD matrices based on this geometry.
我们提出了一个处理 SPD 值数据的几何框架，该框架保留了子空间结构，并以高效计算极端广义特征值为基础。这是通过使用半定锥的汤普森几何来实现的。我们详细探讨了一种特殊的大地空间结构，并建立了与之相关的几个属性。最后，我们回顾了基于这种几何的 SPD 矩阵的一种新颖的归纳平均值。
{"title":"Geometric statistics with subspace structure preservation for SPD matrices","authors":"Cyrus Mostajeran, Nathaël Da Costa, Graham Van Goffrier, Rodolphe Sepulchre","doi":"arxiv-2407.03382","DOIUrl":"https://doi.org/arxiv-2407.03382","url":null,"abstract":"We present a geometric framework for the processing of SPD-valued data that\u0000preserves subspace structures and is based on the efficient computation of\u0000extreme generalized eigenvalues. This is achieved through the use of the\u0000Thompson geometry of the semidefinite cone. We explore a particular geodesic\u0000space structure in detail and establish several properties associated with it.\u0000Finally, we review a novel inductive mean of SPD matrices based on this\u0000geometry.","PeriodicalId":501215,"journal":{"name":"arXiv - STAT - Computation","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-07-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141574481","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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