Monte Carlo Methods in Bayesian Inference: Theory, Methods and Applications

Monte Carlo methods are becoming more and more popular in statistics due to the fast development of efficient computing technologies. One of the major beneficiaries of this advent is the field of Bayesian inference. The aim of this thesis is two-fold: (i) to explain the theory justifying the validity of the simulation-based schemes in a Bayesian setting (why they should work) and (ii) to apply them in several different types of data analysis that a statistician has to routinely encounter. In Chapter 1, I introduce key concepts in Bayesian statistics. Then we discuss Monte Carlo Simulation methods in detail. Our particular focus in on, Markov Chain Monte Carlo, one of the most important tools in Bayesian inference. We discussed three different variants of this including Metropolis-Hastings Algorithm, Gibbs Sampling and slice sampler. Each of these techniques is theoretically justified and I also discussed the potential questions one needs too resolve to implement them in real-world settings. In Chapter 2, we present Monte Carlo techniques for the commonly used Gaussian models including univariate, multivariate and mixture models. In Chapter 3, I focused on several variants of regression including linear and generalized linear models involving continuous, categorical and count responses. For all these cases, the required posterior distributions are rigorously derived. I complement the methodological description with analysis of multiple real datasets and provide tables and diagrams to summarize the inference. In the last Chapter, a few additional key aspects of Bayesian modeling are mentioned. In conclusion, this thesis emphasizes on the Monte Carlo Simulation application in Bayesian Statistics. It also shows that the Bayesian Statistics, which treats all unknown parameters as random variables with their distributions, becomes efficient, useful and easy to implement through Monte Carlo simulations in lieu of the difficult numerical/theoretical calculations

Characterization of microstructure and oxidation resistance of Y and Ge modified silicide coating on Nb-Si based alloy

Y and Ge modified silicide coating was prepared on the Nb-Si based alloy by Si–Ge–Y co-deposition at 1300°C for 10h. The coating consists of an outer layer and a transitional layer(Fig.1a). The outer layer is consist of( Nb , X )(Si, Ge)2(X represents Ti, Cr, Ge and Hf elements) and the transitional layer is composed of ( Nb , X )5(Si, Ge)3. The mass gain of the coated specimen is 2.78 mg cm−2 after oxidation at 1250 °C for 100 h(Fig.1b), which reveals that Ge and Y modified silicide coating exhibits better oxidation resistance than Ge-modified silicide coating and Y element is significantly beneficial for the oxidation resistance. The results indicate that Y refines grain size due to the formation of Y3Al5O12 particles at grain boundaries, which could promote the rapid formation of protective SiO2 and GeO2 scale, and then oxygen diffusion could be decreased. Therefore, the oxidation resistance of the coating is improved. Please click Additional Files below to see the full abstract

The Accurate Location Estimation of Sensor Node Using Received Signal Strength Measurements in Large-Scale Farmland

The range measurement is the premise for location, and the precise range measurement is the assurance of accurate location. Hence, it is essential to know the accurate internode distance. It is noted that the path loss model plays an important role in improving the quality and reliability of ranging accuracy. Therefore, it is necessary to investigate the path loss model in actual propagation environment. Through the analysis of experiments performed at the wheat field, we find that the best fitted parametric exponential decay model (OFPEDM) can achieve a higher distance estimation accuracy and adaptability to environment variations in comparison to the traditional path loss models. Based on the proposed OFPEDM, we perform the RSSI-based location experiments in wheat field. Through simulating the location characteristics in MATLAB, we find that for all the unknown nodes, the location errors range from 0.0004 m to 5.1739 m. The location error in this RSSI-based location algorithm is acceptable in the wide areas such as wheat field. The findings in this research may provide reference for location estimation in large-scale farmland

Dissimilar thermal transport properties in κ\kappa-Ga2_2O3_3 and β\beta-Ga2_2O3_3 revealed by machine-learning homogeneous nonequilibrium molecular dynamics simulations

The lattice thermal conductivity (LTC) of Ga$_2$O$_3$ is an important property due to the challenge in the thermal management of high-power devices. We develop machine-learned neuroevolution potentials for single-crystalline $\beta$-Ga$_2$O$_3$ and $\kappa$-Ga$_2$O$_3$, and apply them to perform homogeneous nonequilibrium molecular dynamics simulations to predict their LTCs. The LTC of $\beta$-Ga$_2$O$_3$ was determined to be 10.3 $\pm$ 0.2 W/(m K), 19.9 $\pm$ 0.2 W/(m K), and 12.6 $\pm$ 0.2 W/(m K) along [100], [010], and [001], respectively, aligning with previous experimental measurements. For the first time, we predict the LTC of $\kappa$-Ga$_2$O$_3$ along [100], [010], and [001] to be 4.5 $\pm$ 0.0 W/(m K), 3.9 $\pm$ 0.0 W/(m K), and 4.0 $\pm$ 0.1 W/(m K), respectively, showing a nearly isotropic thermal transport property. The reduced LTC of $\kappa$-Ga$_2$O$_3$ versus $\beta$-Ga$_2$O$_3$ stems from its restricted low-frequency phonons up to 5 THz. Furthermore, we find that the $\beta$ phase exhibits a typical temperature dependence slightly stronger than $\sim T^{-1}$, whereas the $\kappa$ phase shows a weaker temperature dependence, ranging from $\sim T^{-0.5}$ to $\sim T^{-0.7}$.Comment: 8 pages, 7 figure

The genome evolution and domestication of tropical fruit mango

Background: Mango is one of the world’s most important tropical fruits. It belongs to the family Anacardiaceae, which includes several other economically important species, notably cashew, sumac and pistachio from other genera. Many species in this family produce family-specific urushiols and related phenols, which can induce contact dermatitis. Results: We generate a chromosome-scale genome assembly of mango, providing a reference genome for the Anacardiaceae family. Our results indicate the occurrence of a recent whole-genome duplication (WGD) event in mango. Duplicated genes preferentially retained include photosynthetic, photorespiration, and lipid metabolic genes that may have provided adaptive advantages to sharp historical decreases in atmospheric carbon dioxide and global temperatures. A notable example of an extended gene family is the chalcone synthase (CHS) family of genes, and particular genes in this family show universally higher expression in peels than in flesh, likely for the biosynthesis of urushiols and related phenols. Genome resequencing reveals two distinct groups of mango varieties, with commercial varieties clustered with India germplasms and demonstrating allelic admixture, and indigenous varieties from Southeast Asia in the second group. Landraces indigenous in China formed distinct clades, and some showed admixture in genomes. Conclusions: Analysis of chromosome-scale mango genome sequences reveals photosynthesis and lipid metabolism are preferentially retained after a recent WGD event, and expansion of CHS genes is likely associated with urushiol biosynthesis in mango. Genome resequencing clarifies two groups of mango varieties, discovers allelic admixture in commercial varieties, and shows distinct genetic background of landraces

Efficient Commitment to Functional CD34+ Progenitor Cells from Human Bone Marrow Mesenchymal Stem-Cell-Derived Induced Pluripotent Stem Cells

The efficient commitment of a specialized cell type from induced pluripotent stem cells (iPSCs) without contamination from unknown substances is crucial to their use in clinical applications. Here, we propose that CD34+ progenitor cells, which retain hematopoietic and endothelial cell potential, could be efficiently obtained from iPSCs derived from human bone marrow mesenchymal stem cells (hBMMSC-iPSCs) with defined factors. By treatment with a cocktail containing mesodermal, hematopoietic, and endothelial inducers (BMP4, SCF, and VEGF, respectively) for 5 days, hBMMSC-iPSCs expressed the mesodermal transcription factors Brachyury and GATA-2 at higher levels than untreated groups (P<0.05). After culturing with another hematopoietic and endothelial inducer cocktail, including SCF, Flt3L, VEGF and IL-3, for an additional 7–9 days, CD34+ progenitor cells, which were undetectable in the initial iPSC cultures, reached nearly 20% of the total culture. This was greater than the relative number of progenitor cells produced from human-skin-fibroblast-derived iPSCs (hFib-iPSCs) or from the spontaneous differentiation groups (P<0.05), as assessed by flow cytometry analysis. These induced cells expressed hematopoietic transcription factors TAL-1 and SCL. They developed into various hematopoietic colonies when exposed to semisolid media with hematopoietic cytokines such as EPO and G-CSF. Hematopoietic cell lineages were identified by phenotype analysis with Wright-Giemsa staining. The endothelial potential of the cells was also verified by the confirmation of the formation of vascular tube-like structures and the expression of endothelial-specific markers CD31 and VE-CADHERIN. Efficient induction of CD34+ progenitor cells, which retain hematopoietic and endothelial cell potential with defined factors, provides an opportunity to obtain patient-specific cells for iPSC therapy and a useful model for the study of the mechanisms of hematopoiesis and drug screening