Block-Wise Pseudo-Marginal Metropolis-Hastings

The pseudo-marginal Metropolis-Hastings approach is increasingly used for Bayesian inference in statistical models where the likelihood is analytically intractable but can be estimated unbiasedly, such as random effects models and state-space models, or for data subsampling in big data settings. In a seminal paper, Deligiannidis et al. (2015) show how the pseudo-marginal Metropolis-Hastings (PMMH) approach can be made much more e cient by correlating the underlying random numbers used to form the estimate of the likelihood at the current and proposed values of the unknown parameters. Their proposed approach greatly speeds up the standard PMMH algorithm, as it requires a much smaller number of particles to form the optimal likelihood estimate. We present a closely related alternative PMMH approach that divides the underlying random numbers mentioned above into blocks so that the likelihood estimates for the proposed and current values of the likelihood only di er by the random numbers in one block. Our approach is less general than that of Deligiannidis et al. (2015), but has the following advantages. First, it provides a more direct way to control the correlation between the logarithms of the estimates of the likelihood at the current and proposed values of the parameters. Second, the mathematical properties of the method are simplified and made more transparent compared to the treatment in Deligiannidis et al. (2015). Third, blocking is shown to be a natural way to carry out PMMH in, for example, panel data models and subsampling problems. We obtain theory and guidelines for selecting the optimal number of particles, and document large speed-ups in a panel data example and a subsampling problem

On the order of BEC transition in weakly interacting gases predicted by mean-field theory

Predictions from Hartree-Fock (HF), Popov (P), Yukalov-Yukalova (YY) and $t$-matrix approximations regarding the thermodynamics from the normal to the BEC phase in weakly interacting Bose gases are considered. By analyzing the dependence of the chemical potential $\mu$ on temperature $T$ and particle density $\rho$ we show that none of them predicts a second-order phase transition as required by symmetry-breaking general considerations. In this work we find that the isothermal compressibility $\kappa_{T}$ predicted by these theories does not diverge at criticality as expected in a true second-order phase transition. Moreover the isotherms $\mu=\mu(\rho,T)$ typically exhibit a non-singled valued behavior in the vicinity of the BEC transition, a feature forbidden by general thermodynamic principles. This behavior can be avoided if a first order phase transition is appealed. The facts described above show that although these mean field approximations give correct results near zero temperature they are endowed with thermodynamic anomalies in the vicinity of the BEC transition. We address the implications of these results in the interpretation of current experiments with ultracold trapped alkali gases.Comment: 16 pages, 5 figure

Characterizing and modeling preferential flow using magnetic resonance imaging and multifractal theory.

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Alternative Splicing Variation: Accessing and Exploiting in Crop Improvement Programs

Alternative splicing (AS) is a gene regulatory mechanism modulating gene expression in multiple ways. AS is prevalent in all eukaryotes including plants. AS generates two or more mRNAs from the precursor mRNA (pre-mRNA) to regulate transcriptome complexity and proteome diversity. Advances in next-generation sequencing, omics technology, bioinformatics tools, and computational methods provide new opportunities to quantify and visualize AS-based quantitative trait variation associated with plant growth, development, reproduction, and stress tolerance. Domestication, polyploidization, and environmental perturbation may evolve novel splicing variants associated with agronomically beneficial traits. To date, pre-mRNAs from many genes are spliced into multiple transcripts that cause phenotypic variation for complex traits, both in model plant Arabidopsis and field crops. Cataloguing and exploiting such variation may provide new paths to enhance climate resilience, resource-use efficiency, productivity, and nutritional quality of staple food crops. This review provides insights into AS variation alongside a gene expression analysis to select for novel phenotypic diversity for use in breeding programs. AS contributes to heterosis, enhances plant symbiosis (mycorrhiza and rhizobium), and provides a mechanistic link between the core clock genes and diverse environmental clues