On the Precise Laplace Approximation for Large Deviations of Markov Chain The Nondegenerate Case

Abstract. Let Ln be the empirical measure of a uniformly er-godic nonreversible Markov chain on a compact metric space and Φ be a smooth functional. This paper gives a precise asymptotic evalua-tion of the form E(exp(nΦ(Ln))) up to order 1 + o(1), in the case the Hessian of J −Φ is nondegenerate, where J is the rate function of the large deviations of empirical measure

Asymptotic expansions for the Laplace approximations of sums of Banach space-valued random variables

Let X_i, i\in N, be i.i.d. B-valued random variables, where B is a real separable Banach space. Let \Phi be a smooth enough mapping from B into R. An asymptotic evaluation of Z_n=E(\exp (n\Phi (\sum_{i=1}^nX_i/n))), up to a factor (1+o(1)), has been gotten in Bolthausen [Probab. Theory Related Fields 72 (1986) 305-318] and Kusuoka and Liang [Probab. Theory Related Fields 116 (2000) 221-238]. In this paper, a detailed asymptotic expansion of Z_n as n\to \infty is given, valid to all orders, and with control on remainders. The results are new even in finite dimensions.Comment: Published at http://dx.doi.org/10.1214/009117904000001017 in the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org

Nearly optimal Bayesian Shrinkage for High Dimensional Regression

During the past decade, shrinkage priors have received much attention in Bayesian analysis of high-dimensional data. In this paper, we study the problem for high-dimensional linear regression models. We show that if the shrinkage prior has a heavy and flat tail, and allocates a sufficiently large probability mass in a very small neighborhood of zero, then its posterior properties are as good as those of the spike-and-slab prior. While enjoying its efficiency in Bayesian computation, the shrinkage prior can lead to a nearly optimal contraction rate and selection consistency as the spike-and-slab prior. Our numerical results show that under posterior consistency, Bayesian methods can yield much better results in variable selection than the regularization methods, such as Lasso and SCAD. We also establish a Bernstein von-Mises type results comparable to Castillo et al (2015), this result leads to a convenient way to quantify uncertainties of the regression coefficient estimates, which has been beyond the ability of regularization methods

Dual roles of spent mushroom substrate on soil improvement and enhanced drought tolerance of wheat Triticum aestivum

This study examines the effects of the spent substrate of oyster mushroom (SMS) for growing wheat at different drought conditions. The SMS not only served as the sole fertilizer to produce normal growth and grain yield of wheat but also improved the soil quality after harvest to raise the soil organic matter, maintain the soil alkalinity and increase field capacity unlike the synthetic fertilizer amendment. Simultaneously, SMS treatment enhanced drought tolerance of wheat by enabling germination at 8.5% soil water content and completing sexual reproduction to grain production even at 6.3% soil water content

Two-orbital Systems with Crystal Field Splitting and Interorbital Hopping

The nondegenerate two-orbital Hubbard model is studied within the dynamic mean-field theory to reveal the influence of two important factors, i.e. crystal field splitting and interorbital hopping, on orbital selective Mott transition (OSMT) and realistic compound Ca$_{2-x}$Sr$_{x}$RuO$_{4}$. A distinctive feature of the optical conductivity of the two nondegenerate bands is found in OSMT phase, where the metallic character of the wide band is indicated by a nonzero Drude peak, while the insulating narrow band has its Drude peak drop to zero in the mean time. We also find that the OSMT regime expands profoundly with the increase of interorbital hopping integrals. On the contrary, it is shown that large and negative level splitting of the two orbitals diminishes the OSMT regime completely. Applying the present findings to compound Ca$_{2-x}$Sr$_{x}$RuO$_{4}$, we demonstrate that in the doping region from $x=0.2$ to 2.0, the negative level splitting is unfavorable to the OSMT phase.Comment: 7 pages with 5 figure