Chang Xuan Mao
The number of species can be estimated by sampling individuals from a species assemblage. The problem of estimating generalized species accumulation curve is addressed in a nonparametric Poisson mixture model. A likelihood-based estimator is proposed and illustrated by real examples.
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Bayesian Nonparametric Inference for "Species-sampling" Problems
本文在Pitman-Yor过程先验下综述了物种抽样问题的贝叶斯非参数分析，通过复合二项分布和超几何分布改进后验推断，并揭示了折扣参数可一致估计而尺度参数不可一致估计的性质。
Estimating the Shannon Entropy Using the Pitman--Yor Process
本文提出基于Pitman-Yor过程的熵估计方法，用于解决物种数量未知时的多样性评估问题，通过无限维过程近似提升估计稳定性，并通过实验验证方法有效性。
Global species richness is a key biodiversity metric. Despite recent efforts to estimate global species richness, the resulting estimates have been highly uncertain and often logically inconsistent. Estimates lower down either the taxonomic or geographic hierarchies are often larger than those above. Further, these estimates have been represented in a wide variety of forms, including intervals (a, b), point estimates with no uncertainty, and point estimates with either symmetrical or asymmetrical bounds, making it difficult to combine information across different estimates. Here, we develop a …
Finite Mixtures of Generalized Estimating Equations for Clustering Multivariate Correlated Outcomes
针对多变量相关结局聚类问题，提出MixGEE模型，通过区域特定工作相关结构处理物种间相关性，经模拟验证可靠，应用于凯尔盖朗高原鱼类数据得到三类群落特征。
Investigation of species abundance has become a vital component of many ecological monitoring studies. The primary objective of these studies is to understand how specific species are distributed across the study domain, as well as quantification of the sampling efficiency for detecting these species. To achieve these goals, preselected locations are sampled during scheduled visits, in which the number of species observed at each location is recorded. This results in spatially referenced replicated count data that are often unbalanced in structure and exhibit overdispersion. Motivated by the B…
This paper develops a framework for creating damage accumulation models for engineered wood products by invoking the classical theory of non--dimensionalization. The result is a general class of such models. Both the US and Canadian damage accumulation models are revisited. It is shown how the former may be generalized within that framework while deficiencies are discovered in the latter and overcome. Use of modern Bayesian statistical methods for estimating the parameters in these models is proposed along with an illustrative application of these methods to a ramp load dataset.
We consider the classic problem of estimating T, the total number of species in a population, from repeated counts in a simple random sample. We look first at the Chao-Lee estimator: we initially show that such estimator can be obtained by reconciling two estimators of the unobserved probability, and then develop a sequence of improvements culminating in a Dirichlet prior Bayesian reinterpretation of the estimation problem. By means of this, we obtain simultaneous estimates of T, of the normalized interspecies variance $γ^2$ and of the parameter $λ$ of the prior. Several simulations show that …
Complete computation of turbulent combustion flow involves two separate steps: mapping reaction kinetics to low-dimensional manifolds and looking-up this approximate manifold during CFD run-time to estimate the thermo-chemical state variables. In our previous work, we showed that using a deep architecture to learn the two steps jointly, instead of separately, is 73% more accurate at estimating the source energy, a key state variable, compared to benchmarks and can be integrated within a DNS turbulent combustion framework. In their natural form, such deep architectures do not allow for uncertai…
Consider the random Dirichlet partition of the interval into $n$ fragments with parameter $θ>0$. We recall the unordered Ewens sampling formulae from finite Dirichlet partitions. As this is a key variable for estimation purposes, focus is on the number of distinct visited species in the sampling process. These are illustrated in specific cases. We use these preliminary statistical results on frequencies distribution to address the following sampling problem: what is the estimated number of species when sampling is from Dirichlet populations? The obtained results are in accordance with the ones…
A fundamental question during the outbreak of a novel disease or invasion of an exotic pest is: At what location and date was it first introduced? With this information, future introductions can be anticipated and perhaps avoided. Point process models are commonly used for mapping species distribution and disease occurrence. If the time and location of introductions were known, then point process models could be used to map and understand the factors that influence introductions; however, rarely is the process of introduction directly observed. We propose embedding a point process within hiera…
Bayesian Inference for Evidence Accumulation Models with Regressors
本文提出在分层贝叶斯框架中估计LBA和DDM的新方法，引入个体间相关随机效应及协变量与参数的回归联系，并结合粒子MCMC与变分贝叶斯实现大规模高效推断。
A Bayesian Nonparametric Approach to Species Sampling Problems with Ordering
本文提出一种针对物种标签有序的物种抽样问题的贝叶斯非参数方法，利用有序Pitman-Yor过程先验推导前$r$个有序频率的显式后验分布，并在遗传变异分析中验证其有效性。
Bayesian discovery of species in multiple areas
本文提出一种新的贝叶斯框架，用于处理异质种群中的物种组成和多样性估计，通过分布理论实现样本内分析和样本外预测，扩展了频繁主义估计器的应用范围。
We aim at modelling the appearance of distinct tags in a sequence of labelled objects. Common examples of this type of data include words in a corpus or distinct species in a sample. These sequential discoveries are often summarised via accumulation curves, which count the number of distinct entities observed in an increasingly large set of objects. We propose a novel Bayesian nonparametric method for species sampling modelling by directly specifying the probability of a new discovery, therefore allowing for flexible specifications. The asymptotic behavior and finite sample properties of such …
Estimating the number of unseen species is an important problem in many scientific endeavors. Its most popular formulation, introduced by Fisher, uses $n$ samples to predict the number $U$ of hitherto unseen species that would be observed if $t\cdot n$ new samples were collected. Of considerable interest is the largest ratio $t$ between the number of new and existing samples for which $U$ can be accurately predicted. In seminal works, Good and Toulmin constructed an intriguing estimator that predicts $U$ for all $t\le 1$, thereby showing that the number of species can be estimated for a popula…
Cumulant-based approximation for fast and efficient prediction for species distribution
针对物种分布建模中大数据集计算缓慢的问题，提出基于累积量近似（CBA）的高效模型，结合L1惩罚选择变量，并证明Maxent与Fisher判别分析等价，显著提升计算效率且保持精度。
The Greenland Sea is an important breeding ground for harp and hooded seals. Estimates of the annual seal pup production are critical factors in the abundance estimation needed for management of the species. These estimates are usually based on counts from aerial photographic surveys. However, only a minor part of the whelping region can be photographed, due to its large extent. To estimate the total seal pup production, we propose a Bayesian hierarchical modeling approach motivated by viewing the seal pup appearances as a realization of a log-Gaussian Cox process using covariate information f…
While the analysis of airborne laser scanning (ALS) data often provides reliable estimates for certain forest stand attributes -- such as total volume or basal area -- there is still room for improvement, especially in estimating species-specific attributes. Moreover, while information on the estimate uncertainty would be useful in various economic and environmental analyses on forests, a computationally feasible framework for uncertainty quantifying in ALS is still missing. In this article, the species-specific stand attribute estimation and uncertainty quantification (UQ) is approached using…
SequentialSamplingModels.jl: Simulating and Evaluating Cognitive Models of Response Times in Julia
本文介绍了在Julia中用于模拟和评估反应时间认知模型的顺序采样模型工具SSM.jl，提供了模拟、绘图和贝叶斯推断的功能。
In the context of a species sampling problem we discuss a non-parametric maximum likelihood estimator for the underlying probability mass function. The estimator is known in the computer science literature as the high profile estimator. We prove strong consistency and derive the rates of convergence, for an extended model version of the estimator. We also study a sieved estimator for which similar consistency results are derived. Numerical computation of the sieved estimator is of great interest for practical problems, such as forensic DNA analysis, and we present a computational algorithm bas…
Internet mapping projects generally consist in sampling the network from a limited set of sources by using traceroute probes. This methodology, akin to the merging of spanning trees from the different sources to a set of destinations, leads necessarily to a partial, incomplete map of the Internet. Accordingly, determination of Internet topology characteristics from such sampled maps is in part a problem of statistical inference. Our contribution begins with the observation that the inference of many of the most basic topological quantities -- including network size and degree characteristics -…
We consider the problem of estimating the evolutionary history of a set of species (phylogeny or species tree) from several genes. It is known that the evolutionary history of individual genes (gene trees) might be topologically distinct from each other and from the underlying species tree, possibly confounding phylogenetic analysis. A further complication in practice is that one has to estimate gene trees from molecular sequences of finite length. We provide the first full data-requirement analysis of a species tree reconstruction method that takes into account estimation errors at the gene l…
Estimating the size of a set using cascading exclusion
本文提出一种介于生日问题和最大值估计之间的方法，用于估计有限集合的大小，并给出了非渐进行为的理论框架，适用于多种统计问题。
Feature allocation models generalize species sampling models by allowing every observation to belong to more than one species, now called features. Under the popular Bernoulli product model for feature allocation, given $n$ samples, we study the problem of estimating the missing mass $M_{n}$, namely the expected number hitherto unseen features that would be observed if one additional individual was sampled. This is motivated by numerous applied problems where the sampling procedure is expensive, in terms of time and/or financial resources allocated, and further samples can be only motivated by…
Le Cam's method (or the two-point method) is a commonly used tool for obtaining statistical lower bound and especially popular for functional estimation problems. This work aims to explain and give conditions for the tightness of Le Cam's lower bound in functional estimation from the perspective of convex duality. Under a variety of settings it is shown that the maximization problem that searches for the best two-point lower bound, upon dualizing, becomes a minimization problem that optimizes the bias-variance tradeoff among a family of estimators. For estimating linear functionals of a distri…
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