Bayesian inference for palaeoclimate with time uncertainty and stochastic volatility

type="main" xml:id="rssc12065-abs-0001"> We propose and fit a Bayesian model to infer palaeoclimate over several thousand years. The data that we use arise as ancient pollen counts taken from sediment cores together with radiocarbon dates which provide (uncertain) ages. When combined with a modern pollen–climate data set, we can calibrate ancient pollen into ancient climate. We use a normal–inverse Gaussian process prior to model the stochastic volatility of palaeoclimate over time, and we present a novel modularized Markov chain Monte Chain algorithm to enable fast computation. We illustrate our approach with a case-study from Sluggan Moss, Northern Ireland, and provide an R package, Bclim , for use at other sites.

[1]  J. Christen,et al.  A New Robust Statistical Model for Radiocarbon Data , 2009 .

[2]  Brian Huntley,et al.  Reconstructing palaeoclimates from biological proxies: Some often overlooked sources of uncertainty , 2012 .

[3]  Michael Salter-Townshend,et al.  Fast approximate inverse Bayesian inference in non-parametric multivariate regression with application to palaeoclimate reconstruction , 2009 .

[4]  H. Rue,et al.  Approximate Bayesian inference for latent Gaussian models by using integrated nested Laplace approximations , 2009 .

[5]  Philip Naysmith,et al.  A Report on Phase 2 of the Fifth International Radiocarbon Intercomparison (VIRI) , 2010, Radiocarbon.

[6]  Christian Ohlwein,et al.  Review of probabilistic pollen-climate transfer methods , 2012 .

[7]  Simon Brewer,et al.  A method for climate and vegetation reconstruction through the inversion of a dynamic vegetation model , 2010 .

[8]  F. Ieva,et al.  A new robust statistical model for interpretation of differences in serial test results from an individual , 2015, Clinical chemistry and laboratory medicine.

[9]  J. Christen,et al.  Flexible paleoclimate age-depth models using an autoregressive gamma process , 2011 .

[10]  D. Nychka,et al.  The Value of Multiproxy Reconstruction of Past Climate , 2010 .

[11]  H. Rue,et al.  An explicit link between Gaussian fields and Gaussian Markov random fields: the stochastic partial differential equation approach , 2011 .

[12]  J. Haslett,et al.  A simple monotone process with application to radiocarbon‐dated depth chronologies , 2008 .

[13]  Nick Webber,et al.  A Monte Carlo Method for the Normal Inverse Gaussian Option Valuation Model using an Inverse Gaussian Bridge , 2003 .

[14]  A. Smith,et al.  A 12 500 year record of vegetational history at Sluggan Bog, Co. Antrim, N. Ireland (incorporating a pollen zone scheme for the non‐specialist) , 1991 .

[15]  R. Rotondi,et al.  On Bayesian inference for the Inverse Gaussian distribution , 1991 .

[16]  Karin Ackermann,et al.  Bayesian Forecasting And Dynamic Models Springer Series In Statistics , 2016 .

[17]  James O. Berger,et al.  Modularization in Bayesian analysis, with emphasis on analysis of computer models , 2009 .

[18]  Peter John Huybers,et al.  A Bayesian Algorithm for Reconstructing Climate Anomalies in Space and Time. Part I: Development and Applications to Paleoclimate Reconstruction Problems , 2010 .

[19]  B. McShane,et al.  A statistical analysis of multiple temperature proxies: Are reconstructions of surface temperatures over the last 1000 years reliable? , 2011, 1104.4002.

[20]  C. Buck,et al.  IntCal13 and Marine13 Radiocarbon Age Calibration Curves 0–50,000 Years cal BP , 2013, Radiocarbon.

[21]  M. West,et al.  Bayesian forecasting and dynamic models , 1989 .

[22]  G. Hull.  Immigrant Entrepreneurs: The Face of the New Nashville , 2010 .

[23]  Michael Salter-Townshend,et al.  Fast inversion of a flexible regression model for multivariate pollen counts data , 2012 .

[24]  Dimitris Karlis,et al.  Bayesian estimation of NIG models via Markov chain Monte Carlo methods , 2004 .

[25]  C. Buck,et al.  IntCal13 and Marine13 Radiocarbon Age Calibration Curves 0–50,000 Years cal BP , 2013, Radiocarbon.

[26]  Stephen J. Brooks,et al.  Chironomid-inferred air temperatures from Lateglacial and Holocene sites in north-west Europe: progress and problems , 2001 .

[27]  Brian Huntley,et al.  The use of climate response surfaces to reconstruct palaeoclimate from Quaternary pollen and plant macrofossil data , 1993 .

[28]  Caitlin E. Buck,et al.  A review of statistical chronology models for high-resolution, proxy-based Holocene palaeoenvironmental reconstruction , 2011 .

[29]  James Sweeney,et al.  Advances in Bayesian model development and inversion in multivariate inverse inference problems : with application to palaeoclimate reconstruction , 2012 .

[30]  M. Hughes,et al.  An efficient forward model of the climate controls on interannual variation in tree-ring width , 2011 .

[31]  Nicholas G. Polson,et al.  Particle Learning and Smoothing , 2010, 1011.1098.

[32]  C. Ramsey.  Deposition models for chronological records , 2008 .

[33]  M. Hughes,et al.  Northern hemisphere temperatures during the past millennium: Inferences, uncertainties, and limitations , 1999 .

[34]  Noel A Cressie,et al.  Statistics for Spatio-Temporal Data , 2011 .

[35]  Simon P. Wilson,et al.  Bayesian palaeoclimate reconstruction , 2006 .

[36]  Murali Haran,et al.  Piecing together the past: statistical insights into paleoclimatic reconstructions , 2010 .

[37]  Wolfgang Cramer,et al.  A simulation model for the transient effects of climate change on forest landscapes , 1993 .

[38]  Michael Frankfurter,et al.  Numerical Recipes In C The Art Of Scientific Computing , 2016 .

[39]  Lasse Holmström,et al.  Discussion of: A statistical analysis of multiple temperature proxies: Are reconstructions of surface temperatures over the last 1000 years reliable? , 2011 .

[40]  O. Barndorff-Nielsen.  Normal Inverse Gaussian Distributions and , 1997 .

[41]  O. Barndorff-Nielsen.  Normal Inverse Gaussian Distributions and Stochastic Volatility Modelling , 1997 .

[42]  Brian Huntley,et al.  Late Devensian and Holocene palaeoecology and palaeoenvironments of the Morrone Birkwoods, Aberdeenshire, Scotland , 1994 .

[43]  L. Mark Berliner,et al.  Hierarchical Bayesian Time Series Models , 1996 .

[44]  Adrian E. Raftery,et al.  Model-Based Clustering, Discriminant Analysis, and Density Estimation , 2002 .

[45]  Pieter M. Grootes,et al.  GISP2 Oxygen Isotope Ratios , 2000, Quaternary Research.

[46]  Steve Juggins,et al.  Quantitative reconstructions in palaeolimnology: new paradigm or sick science? , 2013 .

[47]  M. Hughes,et al.  Global-scale temperature patterns and climate forcing over the past six centuries , 1998 .