Projections of future climate change rely heavily on climate models, and combining climate models through a multi-model ensemble is both more accurate than a single climate model and valuable for uncertainty quantification. However, Bayesian approaches to multi-model ensembles have been criticized for making oversimplified assumptions about bias and variability, as well as treating different models as statistically independent. This paper extends the Bayesian hierarchical approach of Sansom et al. (2017) by explicitly accounting for spatial variability and inter-model dependence. We propose a Bayesian hierarchical model that accounts for bias between climate models and observations, spatial and inter-model dependence, the emergent relationship between historical and future periods, and natural variability. Extensive simulations show that our model provides better estimates and uncertainty quantification than the commonly used simple model mean. These results are illustrated using data from the CMIP5 model archive. As examples, for Central North America our projected mean temperature for 2070--2100 is about 0.8 K lower than the simple model mean, while for East Asia it is about 0.5 K higher; however, in both cases, the widths of the 90% credible intervals are of the order 3--6 K, so the uncertainties overwhelm the relatively small differences in projected mean temperatures.
Holocene (the last 12,000 years) temperature variation, including the transition out of the last Ice Age to a warmer climate, is reconstructed at multiple locations in southern Finland, Sweden and Estonia based on pollen fossil data from lake sediment cores. A novel Bayesian statistical approach is proposed that allows the reconstructed temperature histories to interact through shared environmental response parameters and spatial dependence. The prior distribution for past temperatures is partially based on numerical climate simulation. The features in the reconstructions are consistent with t…
In climate change study, the infrared spectral signatures of climate change have recently been conceptually adopted, and widely applied to identifying and attributing atmospheric composition change. We propose a Bayesian hierarchical model for spatial clustering of the high-dimensional functional data based on the effects of functional covariates and local features. We couple the functional mixed-effects model with a generalized spatial partitioning method for: (1) producing spatially contiguous clusters for the high-dimensional spatio-functional data; (2) improving the computational efficienc…
Mixed modeling of extreme values and random effects is relatively unexplored topic. Computational difficulties in using the maximum likelihood method for mixed models and the fact that maximum likelihood method uses available data and does not use the prior information motivate us to use Bayesian method. Our simulation studies indicate that random effects modeling produces more reliable estimates when heterogeneity is present. The application of the proposed model to the climate data and return values of some economic indexes reveals the same pattern as the simulation results and confirms the …
We outline a model and algorithm to perform inference on the palaeoclimate and palaeoclimate volatility from pollen proxy data. We use a novel multivariate non-linear non-Gaussian state space model consisting of an observation equation linking climate to proxy data and an evolution equation driving climate change over time. The link from climate to proxy data is defined by a pre-calibrated forward model, as developed in Salter-Townshend and Haslett (2012) and Sweeney (2012). Climatic change is represented by a temporally-uncertain Normal-Inverse Gaussian Levy process, being able to capture lar…
Earth System Models (ESMs) are the state of the art for projecting the effects of climate change. However, longstanding uncertainties in their ability to simulate regional and local precipitation extremes and related processes inhibit decision making. Stakeholders would be best supported by probabilistic projections of changes in extreme precipitation at relevant space-time scales. Here we propose an empirical Bayesian model that extends an existing skill and consensus based weighting framework and test the hypothesis that nontrivial, physics-guided measures of ESM skill can help produce relia…
Roy and Bhattacharya (2020) provided Bayesian characterization of infinite series, and their most important application, namely, to the Dirichlet series characterizing the (in)famous Riemann Hypothesis, revealed insights that are not in support of the most celebrated conjecture for over 150 years. In contrast with deterministic series considered by Roy and Bhattacharya (2020), in this article we take up random infinite series for our investigation. Remarkably, our method does not require any simplifying assumption. Albeit the Bayesian characterization theory for random series is no different f…
Bayesian palaeoclimate reconstruction from zero-inflated count-compositional pollen data: A case study of Lago Grande di Monticchio in southern Italy
Hamilton Institute and Department of Mathematics and Statistics, Maynooth University（梅努斯大学汉密尔顿研究所与数学统计系）；School of Mathematics and Statistics, University College Dublin（都柏林大学学院数学统计学院）；Department of Biosciences, Durham University（杜伦大学生物科学系）
Heat waves resulting from prolonged extreme temperatures pose a significant risk to human health globally. Given the limitations of observations of extreme temperature, climate models are often used to characterize extreme temperature globally, from which one can derive quantities like return values to summarize the magnitude of a low probability event for an arbitrary geographic location. However, while these derived quantities are useful on their own, it is also often important to apply a spatial statistical model to such data in order to, e.g., understand how the spatial dependence properti…
A prevailing viewpoint in palaeoclimate science is that a single palaeoclimate record contains insufficient information to discriminate between most competing explanatory models. Results we present here suggest the contrary. Using SMC^2 combined with novel Brownian bridge type proposals for the state trajectories, we show that even with relatively short time series it is possible to estimate Bayes factors to sufficient accuracy to be able to select between competing models. The results show that Monte Carlo methodology and computer power have now advanced to the point where a full Bayesian ana…
Quantifying long-term historical climate is fundamental to understanding recent climate change. Most instrumentally recorded climate data are only available for the past 200 years, so proxy observations from natural archives are often considered. We describe a model-based approach to reconstructing climate defined in terms of raw tree-ring measurement data that simultaneously accounts for non-climatic and climatic variability. In this approach we specify a joint model for the tree-ring data and climate variable that we fit using Bayesian inference. We consider a range of prior densities and co…
Laboratory of Information and Decision Systems, Massachusetts Institute of Technology（麻省理工学院信息与决策系统实验室）
This paper presents a novel decentralized high-dimensional Bayesian optimization (DEC-HBO) algorithm that, in contrast to existing HBO algorithms, can exploit the interdependent effects of various input components on the output of the unknown objective function f for boosting the BO performance and still preserve scalability in the number of input dimensions without requiring prior knowledge or the existence of a low (effective) dimension of the input space. To realize this, we propose a sparse yet rich factor graph representation of f to be exploited for designing an acquisition function that…
A large fraction of papers in the climate literature includes erroneous uses of significance tests. A Bayesian analysis is presented to highlight the meaning of significance tests and why typical misuse occurs. It is concluded that a significance test very rarely provides useful quantitative information. The significance statistic is not a quantitative measure of how confident we can be of the 'reality' of a given result.
This paper investigates the cross-correlations across multiple climate model errors. We build a Bayesian hierarchical model that accounts for the spatial dependence of individual models as well as cross-covariances across different climate models. Our method allows for a nonseparable and nonstationary cross-covariance structure. We also present a covariance approximation approach to facilitate the computation in the modeling and analysis of very large multivariate spatial data sets. The covariance approximation consists of two parts: a reduced-rank part to capture the large-scale spatial depen…
Numerical climate models are used to project future climate change due to both anthropogenic and natural causes. Differences between projections from different climate models are a major source of uncertainty about future climate. Emergent relationships shared by multiple climate models have the potential to constrain our uncertainty when combined with historical observations. We combine projections from 13 climate models with observational data to quantify the impact of emergent relationships on projections of future warming in the Arctic at the end of the 21st century. We propose a hierarchi…
Multiple studies have suggested the spread of COVID-19 is affected by factors such as climate, BCG vaccinations, pollution and blood type. We perform a joint study of these factors using the death growth rates of 40 regions worldwide with both machine learning and Bayesian methods. We find weak, non-significant (< 3$σ$) evidence for temperature and relative humidity as factors in the spread of COVID-19 but little or no evidence for BCG vaccination prevalence or $\text{PM}_{2.5}$ pollution. The only variable detected at a statistically significant level (>3$σ$) is the rate of positive COVID-19 …
Realistic depictions of past land cover are needed to investigate prehistoric environmental changes, effects of anthropogenic deforestation, and long term land cover-climate feedbacks. Observation based reconstructions of past land cover are rare and commonly used model based reconstructions exhibit considerable differences. Recently \citet[Spatial Statistics, 24:14--31,][]{PirzaLPG2018_24} developed a statistical interpolation method that produces spatially complete reconstructions of past land cover from pollen assemblage. These reconstructions incorporate a number of auxiliary datasets rais…
Fossil-based palaeoclimate reconstruction is an important area of ecological science that has gained momentum in the backdrop of the global climate change debate. The hierarchical Bayesian paradigm provides an interesting platform for studying such important scientific issue. However, our cross-validation based assessment of the existing Bayesian hierarchical models with respect to two modern proxy data sets based on chironomid and pollen, respectively, revealed that the models are inadequate for the data sets. In this paper, we model the species assemblages (compositional data) by the zero-in…
The global phenomenon of forest degradation is a pressing issue with severe implications for climate stability and biodiversity protection. In this work we generate Bayesian updating deforestation detection (BUDD) algorithms by incorporating Sentinel-1 backscatter and interferometric coherence with Sentinel-2 normalized vegetation index data. We show that the algorithm provides good performance in validation AOIs. We compare the effectiveness of different combinations of the three data modalities as inputs into the BUDD algorithm and compare against existing benchmarks based on optical imagery…
Fluvial floods drive severe risk to riverine communities. There is a strong evidence of increasing flood hazards in many regions around the world. The choice of methods and assumptions used in flood hazard estimates can impact the design of risk management strategies. In this study, we characterize the expected flood hazards conditioned on the uncertain model structures, model parameters and prior distributions of the parameters. We construct a Bayesian framework for river stage return level estimation using a nonstationary statistical model that relies exclusively on Indian Ocean Dipole Index…
Changes in the frequency, duration, and severity of climate extremes are forecast to occur under global climate change. The impacts of climate extremes on forest productivity and health are complicated by potential interactions with disturbance events and stand dynamics. The effects of stand dynamics on forest responses to climate and disturbance are particularly important given forest characteristics driven by stand dynamics can be modified through forest management with the goal of increasing forest resistance and resilience to climate change. We develop a hierarchical Bayesian state-space m…
Regression-based optimal fingerprinting techniques for climate change detection and attribution require the estimation of the forced signal as well as the internal variability covariance matrix in order to distinguish between their influences in the observational record. While previously developed approaches have taken into account the uncertainty linked to the estimation of the forced signal, there has been less focus on uncertainty in the covariance matrix describing natural variability, despite the fact that the specification of this covariance matrix is known to meaningfully impact the res…
Projections of storm surge return levels are a basic requirement for effective management of coastal risks. A common approach to estimate hazards posed by extreme sea levels is to use a statistical model, which may use a time series of a climate variable as a covariate to modulate the statistical model and account for potentially nonstationary storm surge behavior. Previous work using nonstationary statistical approaches, however, has demonstrated the importance of accounting for the many inherent modeling uncertainties. Additionally, previous assessments of coastal flood hazard using statisti…
Parameters in climate models are usually calibrated manually, exploiting only small subsets of the available data. This precludes both optimal calibration and quantification of uncertainties. Traditional Bayesian calibration methods that allow uncertainty quantification are too expensive for climate models; they are also not robust in the presence of internal climate variability. For example, Markov chain Monte Carlo (MCMC) methods typically require $O(10^5)$ model runs and are sensitive to internal variability noise, rendering them infeasible for climate models. Here we demonstrate an approac…
Correlation Networks (CNs) inherently suffer from redundant information in their network topology. Bayesian Networks (BNs), on the other hand, include only non-redundant information (from a probabilistic perspective) resulting in a sparse topology from which generalizable physical features can be extracted. We advocate the use of BNs to construct data-driven complex networks as they can be regarded as the probabilistic backbone of the underlying complex system. Results are illustrated at the hand of a global climate dataset.
How will the climate system respond to anthropogenic forcings? One approach to this question relies on climate model projections. Current climate projections are considerably uncertain. Characterizing and, if possible, reducing this uncertainty is an area of ongoing research. We consider the problem of making projections of the North Atlantic meridional overturning circulation (AMOC). Uncertainties about climate model parameters play a key role in uncertainties in AMOC projections. When the observational data and the climate model output are high-dimensional spatial data sets, the data are typ…
We develop a new efficient methodology for Bayesian global sensitivity analysis for large-scale multivariate data. The focus is on computationally demanding models with correlated variables. A multivariate Gaussian process is used as a surrogate model to replace the expensive computer model. To improve the computational efficiency and performance of the model, compactly supported correlation functions are used. The goal is to generate sparse matrices, which give crucial advantages when dealing with large datasets, where we use cross-validation to determine the optimal degree of sparsity. This …
The interdependence between nodes in graphs is key to improve class predictions on nodes and utilized in approaches like Label Propagation (LP) or in Graph Neural Networks (GNN). Nonetheless, uncertainty estimation for non-independent node-level predictions is under-explored. In this work, we explore uncertainty quantification for node classification in three ways: (1) We derive three axioms explicitly characterizing the expected predictive uncertainty behavior in homophilic attributed graphs. (2) We propose a new model Graph Posterior Network (GPN) which explicitly performs Bayesian posterior…
Structural equation models comprise a large class of popular statistical models, including factor analysis models, certain mixed models, and extensions thereof. Model estimation is complicated by the fact that we typically have multiple interdependent response variables and multiple latent variables (which may also be called random effects or hidden variables), often leading to slow and inefficient MCMC samples. In this paper, we describe and illustrate a general, efficient approach to Bayesian SEM estimation in Stan, contrasting it with previous implementations in R package blavaan (Merkle & …
Max Planck Institute for Intelligent Systems（马克斯·普朗克智能系统研究所）；University College London（伦敦大学学院）；Université Laval（拉瓦尔大学）；Università degli Studi di Milano（米兰大学）；Montanuniversität Leoben（莱奥本矿业大学）
We present a set of high-probability inequalities that control the concentration of weighted averages of multiple (possibly uncountably many) simultaneously evolving and interdependent martingales. Our results extend the PAC-Bayesian analysis in learning theory from the i.i.d. setting to martingales opening the way for its application to importance weighted sampling, reinforcement learning, and other interactive learning domains, as well as many other domains in probability theory and statistics, where martingales are encountered. We also present a comparison inequality that bounds the expecta…
Estimating climate effects on future ocean storm severity is plagued by large uncertainties, yet for safe design and operation of offshore structures, best possible estimates of climate effects are required given available data. We explore the variability in estimates of 100-year return value of significant wave height (Hs) over time, for output of WAVEWATCHIII models from 7 representative CMIP5 GCMs, and the FIO-ESM v2.0 CMIP6 GCM, for neighbourhoods of locations east of Madagascar and south of Australia. Non-stationary extreme value analysis of peaks-over-threshold and block maxima using Bay…
Bayesian calibration of computer models tunes unknown input parameters by comparing outputs with observations. For model outputs that are distributed over space, this becomes computationally expensive because of the output size. To overcome this challenge, we employ a basis representation of the model outputs and observations: we match these decompositions to carry out the calibration efficiently. In the second step, we incorporate the non-stationary behaviour, in terms of spatial variations of both variance and correlations, in the calibration. We insert two integrated nested Laplace approxim…
Model selection in extreme value regression for estimation of changes in return values over time applied to extreme annual regional CMIP6 desert temperatures
Lancaster University（兰卡斯特大学）；MetOcean Research Ltd（MetOcean研究有限公司）
The accurate prediction of precipitation is important to allow for reliable warnings of flood or drought risk in a changing climate. However, to make trust-worthy predictions of precipitation, at a local scale, is one of the most difficult challenges for today's weather and climate models. This is because important features, such as individual clouds and high-resolution topography, cannot be resolved explicitly within simulations due to the significant computational cost of high-resolution simulations. Climate models are typically run at $\sim$50-100 km resolution which is insufficient to repr…
This paper is due to appear as a chapter of the forthcoming Handbook of Approximate Bayesian Computation (ABC) by S. Sisson, L. Fan, and M. Beaumont. We describe the challenge of calibrating climate simulators, and discuss the differences in emphasis in climate science compared to many of the more traditional ABC application areas. The primary difficulty is how to do inference with a computationally expensive simulator which we can only afford to run a small number of times, and we describe how Gaussian process emulators are used as surrogate models in this case. We introduce the idea of histo…
Towards a Technology-Driven Adaptive Decision Support System for Integrated Pavement and Maintenance strategies (TDADSS-IPM): focus on risk assessment framework for climate change adaptation
Technical University of Denmark（丹麦技术大学）；Volunteer researcher and hydraulic engineering expert（志愿研究员与水利工程专家）；The Danish Road Directorate（丹麦道路管理局）
A systematic Bayesian framework is developed for physics constrained parameter inference ofstochastic differential equations (SDE) from partial observations. The physical constraints arederived for stochastic climate models but are applicable for many fluid systems. A condition isderived for global stability of stochastic climate models based on energy conservation. Stochasticclimate models are globally stable when a quadratic form, which is related to the cubic nonlinearoperator, is negative definite. A new algorithm for the efficient sampling of such negative definite matrices is developed a…
Building on recent research for prediction of hurricane trajectories using recurrent neural networks (RNNs), we have developed improved methods and generalized the approach to predict Bayesian intervals in addition to simple point estimates. Tropical storms are capable of causing severe damage, so accurately predicting their trajectories can bring significant benefits to cities and lives, especially as they grow more intense due to climate change effects. By implementing the Bayesian interval using dropout in an RNN, we improve the actionability of the predictions, for example by estimating th…
