Power-expected-posterior prior Bayes factor consistency for nested linear models with increasing dimensions

The power-expected-posterior prior is used in this paper for comparing nested linear models.The asymptotic behaviour of the method is investigated for different values of the power parameter of the prior.Focus is given on the consistency of the Bayes factor of comparing the full model M_(p) versus a generic submodel M_(l).In each case,we allow the true generating model to be either M_(p) or M_(l) and we keep the dimension of M_(l) fixed,while the dimension of M_(p) can be either fixed or(grow as)O(n),with n denoting the sample size.

Distribution of chlorophyll a and some ecological factors in the Daya Bay

The marine environment, productivity and potential biotic resources in the waters of the Daya Bay were investigated by South China Sea Institute of Oceanology, Academia Sinica from 1984 to 1986. The present paper deals mainly with the annual variation and distribution characteristics in chlorophyll a and with some of the ecological factors involved in chlorophyll distribution within the bay. Correlation models are established and discussed. The results could be helpful for further probing into ecosystem and for the exploitation-utilization of aquatic resources in this region.

Major and trace element geochemistry of the mid-Bay of Bengal surface sediments: implications for provenance

The major and trace elements in 110 surface sediment samples collected from the middle of the Bay of Bengal（mid-Bay of Bengal） are analyzed to investigate provenance. Si levels are highest, followed by Al, and the distributions of these two elements are identical. The average CIA＊（chemical index of alteration） value is 72.07,indicating that the degree of weathering of the sediments in the study area is intermediate between those of sediments of the Himalayan and Indian rivers. Factor analyses and discrimination function analyses imply that the two main provenances are the Himalayan and the Indian continent. The inverse model calculation of the Tinormalized element ratios of the Bay of Bengal sediments indicate an estimated average contribution of 83.5%and 16.5% from the Himalayan and peninsular Indian rivers to the study area, respectively. The Himalayan source contributes more sediment to the eastern part of the study area, whereas the western part receives more sediment from the Indian Peninsula than did the eastern part. The primary mechanisms for deposition of sediments in the study area are the transport of Himalayan matter by turbidity currents and river-diluted water and the transport of Indian matter to the study area by a surface circulation in the Bay of Bengal, particularly the East India Coastal Current.

Prior-based Bayesian information criterion

We present a new approach to model selection and Bayes factor determination,based on Laplaceexpansions(as in BIC),which we call Prior-based Bayes Information Criterion(PBIC).In thisapproach,the Laplace expansion is only done with the likelihood function,and then a suitableprior distribution is chosen to allow exact computation of the(approximate)marginal likelihoodarising from the Laplace approximation and the prior.The result is a closed-form expression similar to BIC,but now involves a term arising from the prior distribution(which BIC ignores)andalso incorporates the idea that different parameters can have different effective sample sizes(whereas BIC only allows one overall sample size n).We also consider a modification of PBIC whichis more favourable to complex models.

Hypothesis testing of Poisson rates in COVID-19 offspring distributions

In the present study,we undertake the task of hypothesis testing in the context of Poissondistributed data.The primary objective of our investigation is to ascertain whether two distinct sets of discrete data share the same Poisson rate.We delve into a comprehensive review and comparative analysis of various frequentist and Bayesian methodologies specifically designed to address this problem.Among these are the conditional test,the likelihood ratio test,and the Bayes factor.Additionally,we employ the posterior predictive p-value in our analysis,coupled with its corresponding calibration procedures.As the culmination of our investigation,we apply these diverse methodologies to test both simulated datasets and real-world data.The latter consists of the offspring distributions linked to COVID-19 cases in two disparate geographies-Hong Kong and Rwanda.This allows us to provide a practical demonstration of the methodologies’applications and their potential implications in the field of epidemiology.

SAMPLE-SIZE DETERMINATION FOR TWO INDEPENDENT BINOMIAL EXPERIMENTS

Sample size determination is commonly encountered in modern medical studies for two inde- pendent binomial experiments. A new approach for calculating sample size is developed by combining Bayesian and frequentist idea when a hypothesis test between two binomial proportions is conducted. Sample size is calculated according to Bayesian posterior decision function and power of the most powerful test under 0-1 loss function. Sample sizes are investigated for two cases that two proportions are equal to some fixed value or a random value. A simulation study and a real example are used to illustrate the proposed methodologies.

Lack of evolutionary changes identified in SARS-CoV-2 for the re-emerging outbreak of COVID-19 in Beijing,China

Although significant achievements have shown that the coronavirus disease 2019(COVID‐19)resurgence in Beijing,China,was initiated by contaminated frozen products and transported via cold chain transportation,international travelers with asymptomatic symptoms or false‐negative nucleic acid may have another possible transmission mode that spread the virus to Beijing.One of the key differences between these two assumptions was whether the virus actively replicated since,so far,no reports showed viruses could stop evolution in alive hosts.We studied severe acute respiratory syndrome coronavirus 2(SARS‐CoV‐2)sequences in this outbreak by a modified leaf‐dating method with the Bayes factor.The numbers of single nucleotide variants(SNVs)found in SARS‐CoV‐2 sequences were significantly lower than those called from B.1.1 records collected at the matching time worldwide(P=0.047).In addition,results of the leaf‐dating method showed ages of viruses sampled from this outbreak were earlier than their recorded dates of collection(Bayes factors>10),while control sequences(selected randomly with ten replicates)showed no differences in their collection dates(Bayes factors<10).Our results which indicated that the re‐emergence of SARS‐CoV‐2 in Beijing in June 2020 was caused by a virus that exhibited a lack of evolutionary changes compared to viruses collected at the corresponding time,provided evolutionary evidence to the contaminated imported frozen food should be responsible for the reappearance of COVID‐19 cases in Beijing.The method developed here might also be helpful to provide the very first clues for potential sources of COVID‐19 cases in the future.