Cross‐validation based assessment of a new Bayesian palaeoclimate model

Abstract

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-inflated multinomial distribution while modelling the species response functions using Dirichlet process-based Gaussian mixtures. This modelling strategy yielded significantly improved performances, and a formal Bayesian test of model adequacy, developed recently, showed that our new model is adequate for both the modern data sets. Furthermore, combining together the zero-inflated assumption, Importance Resampling Markov Chain Monte Carlo (IRMCMC) and the recently developed Transformationbased Markov Chain Monte Carlo (TMCMC), we develop a powerful and efficient computational methodology. Copyright

Margin based ontology sparse vector learning algorithm and applied in biology science

“…An estimate of the sparse vector is obtained from the general regression obtains after solving the optimization problem below:trueminβ∈Rplfalse(bold-italicβfalse)+λfalse‖bold-italicβfalse‖1,where l(β)=12‖y-Vβ‖22 is the loss term, ‖β‖1=∑i=1p|βi| is the l1-norm balance term that measures the sparseness of vector β, and λ>0 is the balance parameter which controls the sparsity level. On the selection of the balance parameter λ, readers can refer to Mancinelli et al, 2013, Mukhopadhyay and Bhattacharya, 2013, Ishibuchi and Nojima, 2013, and Varmuza et al (2014) for more details about the method of cross-validation.…”

Posterior Consistency of Bayesian Inverse Regression and Inverse Reference Distributions

“…Bhattacharya (2013) provide a Bayesian decision theoretic justification of the key idea and show that the relevant IRD based posterior probability analogue of the aforementioned P -values have the uniform distribution on [0, 1]. Furthermore, ample simulation studies and successful applications to several real, palaeoclimate models and data sets reported in Bhattacharya (2013), Bhattacharya (2006) and Mukhopadhyay and Bhattacharya (2013), vindicate the practicality and usefulness of the IRD approach.…”

“…In a nutshell, if T (X n ) falls within the desired 100(1−α)% (0 < α < 1) of the IRD, then the model is said to fit the data; otherwise, the model does not fit the data. Typical examples of T (X n ), which turned out to be useful in the palaeoclimate modeling context are (see Mukhopadhyay and Bhattacharya (2013)) are:…”

Transdimensional transformation based Markov chain Monte Carlo

“…We then calculated the acceptance probability of this proposal in the usual TMCMC set-up to either accept the new proposal (t) + ar (t) or to remain at (t) . Such a strategy has also been employed by Mukhopadhyay and Bhattacharya (2013) to improve mixing in the con- text of palaeoclimate modeling. The strategy is akin to the so-called generalized Gibbs/MH methods in fixed-dimensional set-ups have the potential of improving mixing (see, for example, Liu, Liang and Wong (2000), Liu (2001); see also Liu and Yu (1999)).…”