Efficient Markov chain Monte Carlo sampling for hierarchical hidden Markov models

Traditional Markov chain Monte Carlo (MCMC) sampling of hidden Markov models (HMMs) involves latent states underlying an imperfect observation process, and generates posterior samples for top-level parameters concurrently with nuisance latent variables. When potentially many HMMs are embedded within a hierarchical model, this can result in prohibitively long MCMC runtimes. We study combinations of existing methods, which are shown to vastly improve computational efficiency for these hierarchical models while maintaining the modeling flexibility provided by embedded HMMs. The methods include discrete filtering of the HMM likelihood to remove latent states, reduced data representations, and a novel procedure for dynamic block sampling of posterior dimensions. The first two methods have been used in isolation in existing application-specific software, but are not generally available for incorporation in arbitrary model structures. Using the NIMBLE package for R, we develop and test combined computational approaches using three examples from ecological capture–recapture, although our methods are generally applicable to any embedded discrete HMMs. These combinations provide several orders of magnitude improvement in MCMC sampling efficiency, defined as the rate of generating effectively independent posterior samples. In addition to being computationally significant for this class of hierarchical models, this result underscores the potential for vast improvements to MCMC sampling efficiency which can result from combinations of known algorithms.     

Social network analysis and valid Markov chain Monte Carlo tests of null models

Analyses of animal social networks derived from group-based associations often rely on randomisation methods developed in ecology (Manly, Ecology 76:1109–1115, 1995) and made available to the animal behaviour community through implementation of a pair-wise swapping algorithm by Bejder et al. (Anim Behav 56:719–725, 1998). We report a correctable flaw in this method and point the reader to a wider literature on the subject of null models in the ecology literature. We illustrate the importance of correcting the method using a toy network and use it to make a preliminary analysis of a network of associations among eagle rays.

Markov Chain Monte Carlo on optimal adaptive sampling selections

Under a Bayesian population model with a given prior distribution, the optimal sampling strategy with a fixed sample size n is an n-phase adaptive one. That is, the selection of the next sampling units should sequentially depend on the information obtained from the previously selected units, including the observed values of interest. Such an optimal strategy is in general not executable in practice due to its intensive computation. In many survey sampling situations, an important problem is that one would like to select a set of units in addition to a certain number of sampling units which have been observed. If the optimal strategy is an adaptive one, the selection of the additional units should take both the labels and the observed values of the already selected units into account. Hence, a simpler optimal two-phase adaptive sampling strategy under a Bayesian population model is proposed in this article for practical interest. A Markov chain Monte Carlo method is used to approximate the posterior joint distribution of the unobserved population units after the first phase sampling, for the optimal selection of the second phase sample. This approximation method is found to be successful to select the optimal second-phase sample. Finally, this optimal strategy is applied to a set of data from a study of geothermal CO₂ emissions in Yellowstone National Park as a practical illustrative example.     

Ensemble Bayesian model averaging using Markov Chain Monte Carlo sampling

Bayesian model averaging (BMA) has recently been proposed as a statistical method to calibrate forecast ensembles from numerical weather models. Successful implementation of BMA however, requires accurate estimates of the weights and variances of the individual competing models in the ensemble. In their seminal paper (Raftery et al. Mon Weather Rev 133:1155–1174, 2005) has recommended the Expectation–Maximization (EM) algorithm for BMA model training, even though global convergence of this algorithm cannot be guaranteed. In this paper, we compare the performance of the EM algorithm and the recently developed DiffeRential Evolution Adaptive Metropolis (DREAM) Markov Chain Monte Carlo (MCMC) algorithm for estimating the BMA weights and variances. Simulation experiments using 48-hour ensemble data of surface temperature and multi-model streamflow forecasts show that both methods produce similar results, and that their performance is unaffected by the length of the training data set. However, MCMC simulation with DREAM is capable of efficiently handling a wide variety of BMA predictive distributions, and provides useful information about the uncertainty associated with the estimated BMA weights and variances.     

Fitting probability models to population dynamics data

Methods for modeling population dynamics in probability using the generalized point process approach are developed. The life history of these populations is such that seasonal reproduction occurs during a short time. Several models are developed and analyzed. Data about two species: colonial spiders (Stegodyphus dumicola) and a migratory bird (wood thrush, Hylocichla mustelina) are used to estimate model parameters with appropriate log maximum likelihood functions. For the spiders, the model is fitted to provide evolutionary feasible colony size based on maximum likelihood estimates of fecundity and survival data. For the migratory bird species, a maximum likelihood estimates are derived for the fecundity and survival rates of young and adult birds and immigration rate. The presented approach allows computation of quantities of interest such as probability of extinction and average time to extinction.     

Quantifying parameter uncertainty in a coral reef model using Metropolis-Coupled Markov Chain Monte Carlo

Coral reefs are threatened ecosystems, so it is important to have predictive models of their dynamics. Most current models of coral reefs fall into two categories. The first is simple heuristic models which provide an abstract understanding of the possible behaviour of reefs in general, but do not describe real reefs. The second is complex simulations whose parameters are obtained from a range of sources such as literature estimates. We cannot estimate the parameters of these models from a single data set, and we have little idea of the uncertainty in their predictions.We have developed a compromise between these two extremes, which is complex enough to describe real reef data, but simple enough that we can estimate parameters for a specific reef from a time series. In previous work, we fitted this model to a long-term data set from Heron Island, Australia, using maximum likelihood methods. To evaluate predictions from this model, we need estimates of the uncertainty in our parameters. Here, we obtain such estimates using Bayesian Metropolis-Coupled Markov Chain Monte Carlo. We do this for versions of the model in which corals are aggregated into a single state variable (the three-state model), and in which corals are separated into four state variables (the six-state model), in order to determine the appropriate level of aggregation. We also estimate the posterior distribution of predicted trajectories in each case.In both cases, the fitted trajectories were close to the observed data, but we had doubts about the biological plausibility of some parameter estimates. We suggest that informative prior distributions incorporating expert knowledge may resolve this problem. In the six-state model, the posterior distribution of state frequencies after 40 years contained two divergent community types, one dominated by free space and soft corals, and one dominated by acroporid, pocilloporid, and massive corals. The three-state model predicts only a single community type. We conclude that the three-state model hides too much biological heterogeneity, but we need more data if we are to obtain reliable predictions from the six-state model. It is likely that there will be similarly large, but currently unevaluated, uncertainty in the predictions of other coral reef models, many of which are much more complex and harder to fit to real data.     

An Integrated Monte Carlo Methodology for the calibration of water quality models

This paper proposes an Integrated Monte Carlo Methodology (IMCM) to solve the parameter estimation problem in water quality models. The methodology is based on Bayesian approach and Markov Chain Monte Carlo techniques and it operates by means of four modules: Markov Chain Monte Carlo (MCMC), Moving Feasible Ranges (MFR), Statistical Analysis of the Joint Posterior Distribution (SAD) and Uncertainty Propagation Analysis (UPA). The main innovation of the new proposal lies in the combination of MCMC and MFR modules which provides the joint posterior distribution of the calibrated parameters following the classical Bayesian approach. While MCMC module, based on Shuffled Complex Evolution Metropolis (SCEM-UA) algorithm, is specially designed to sample complex joint posterior shapes within certain parameter ranges, the MFR readjusts these ranges until the coverage of the feasible parameter space is guaranteed. Once the joint posterior distribution is properly defined, the SAD provides the parameter statistics and the UPA performs an analysis of the uncertainty propagation through the model. The possibilities of the new proposal have been tested on the basis of a simple model featuring different activated sludge batch experiments. IMCM has been implemented in Matlab and it is prepared to be easily connected to any software package.     

The use of Monte Carlo simulation techniques to predict population blood lead levels

Effective management of the risks posed by lead depends on an understanding of the relationship between exposure (the presence and accessibility of lead in the environment) and dose (blood lead levels). Our paper begins by outlining the type of information most valuable to a decision maker addressing the lead problem. A useful exposure-dose characterisation must address multiple contamination sources simultaneously, provide estimates of the number of people with blood lead levels exceeding critical thresholds, and assess the influence of modifying factors (e.g. the soil and dust ingestion rate) on population blood lead variability. We describe a pilot effort to develop an urban setting lead exposure-dose model, and use this model to compare three approaches for generating model input quantities: (1) worst-case estimates, (2) central estimates and (3) Monte Carlo simulation. Using the criteria outlined above, we find that the Monte Carlo technique provides the most useful model output. We describe the population blood lead level distribution generated by the model, as well as the relative influence of environmental and behavioural factors on the variability of the population distribution. Finally, we assess the impact of parameter uncertainty on the model output, and contend this type of information can help identify areas in which further empirical study would be most valuable.     

基于QSAR模型的蒙特卡洛方法分析有机化学物质对大型蚤(Daphnia magna)的毒性

本文建立一系列758种有机化合物对大型蚤(Daphnia magna)毒性的定量结构-活性关系(QSARs)。用简化的分子线性输入系统(SMILES)代表分子结构。用CORAL(关联和逻辑)软件作为工具来开发QSAR模型。这些模型使用蒙特卡罗方法建立,依据的原理是QSAR是一个“随机事件”,假设检验一组随机数据分布在可见的训练集和不可见的验证集。检验了三组分布于可见的训练、校准、测试集中的数据以及不可见的验证集。最佳模型的预测潜能,也就是其不可见的验证集的统计特征如下:n = 87,r² = 0.8377,RMSE = 0.564。建议和讨论了所构建模型的机械解释和适用领域。
精选自Alla P. Toropova, Andrey A. Toropov, Aleksandar M. Veselinovi?, Jovana B. Veselinovi?, Danuta Leszczynska, Jerzy Leszczynski. Monte Carlo based QSAR models for toxicity of organic chemicals to Daphnia magna. Environmental Toxicology and Chemistry: Volume 35, Issue 11, pages 2691–2697, November 2016. DOI: 10.1002/etc.3466
详情请见http://onlinelibrary.wiley.com/doi/10.1002/etc.3466/full
     

Fitting animal survival models with temporal random effects

Estimating temporal variance in animal demographic parameters is of particular importance in population biology. We implement the Schall’s algorithm for incorporating temporal random effects in survival models using recovery data. Our frequentist approach is based on a formulation of band-recovery models with random effects as generalized linear mixed models and a linearization of the link function conditional on the random effects. A simulation study shows that our procedure provides unbiased and precise estimates. The method is then implemented on two case studies using recovery data on fish and birds.     

Identification of pollution sources in rivers using a hydrodynamic diffusion wave model and improved Bayesian-Markov chain Monte Carlo algorithm

● A hydrodynamic-Bayesian inference model was developed for water pollution tracking. ● Model is not stuck in local optimal solutions for high-dimensional problem. ● Model can estimate source parameters accurately with known river water levels. ● Both sudden spill incident and normal sewage inputs into the river can be tracked. ● Model is superior to the traditional approaches based on the test cases. Water quality restoration in rivers requires identification of the locations and discharges of pollution sources, and a reliable mathematical model to accomplish this identification is essential. In this paper, an innovative framework is presented to inversely estimate pollution sources for both accident preparedness and normal management of the allowable pollutant discharge. The proposed model integrates the concepts of the hydrodynamic diffusion wave equation and an improved Bayesian-Markov chain Monte Carlo method (MCMC). The methodological framework is tested using a designed case of a sudden wastewater spill incident (i.e., source location, flow rate, and starting and ending times of the discharge) and a real case of multiple sewage inputs into a river (i.e., locations and daily flows of sewage sources). The proposed modeling based on the improved Bayesian-MCMC method can effectively solve high-dimensional search and optimization problems according to known river water levels at pre-set monitoring sites. It can adequately provide accurate source estimation parameters using only one simulation through exploration of the full parameter space. In comparison, the inverse models based on the popular random walk Metropolis (RWM) algorithm and microbial genetic algorithm (MGA) do not produce reliable estimates for the two scenarios even after multiple simulation runs, and they fall into locally optimal solutions. Since much more water level data are available than water quality data, the proposed approach also provides a cost-effective solution for identifying pollution sources in rivers with the support of high-frequency water level data, especially for rivers receiving significant sewage discharges.     

Designs with a priori information for nonmarket valuation with choice experiments: A Monte Carlo study

Good practice in experimental design is essential for choice experiments used in nonmarket valuation. We review the practice of experimental design for choice experiments in environmental economics and we compare it with advances in experimental design. We then evaluate the statistical efficiency of four different designs by means of Monte Carlo experiments. Correct and incorrect specifications are investigated with gradually more precise information on the true parameter values. The data generating process (DGP) is based on estimates from data of a real study. Results indicate that D-efficient designs are promising, especially when based on Bayesian algorithms with informative prior. However, if good quality a priori information is lacking, and if there is strong uncertainty about the real DGP—conditions which are quite common in environmental valuation—then practitioners might be better off with shifted designs built from conventional fractional factorial designs for linear models.     

Stability and exploitation in two-species discrete time population models with delay

A two species model is developed which incorporates interactions at both the adult stage and the juvenile stage, as well as delays between birth and sexual maturity.The local stability of the model is examined. In particular, four necessary conditions are given and a simple sufficiency condition derived, which may avoid the need to calculate eigenvalues.The optimal steady state escapement levels are then derived under the assumption that neither species is completely removed. The optimal levels are those which maximize the discounted present value of the net economic yield.Finally, the results are applied to two models; one a familiar interspecific competition model and the other a two sex whaling model proposed by the author.     

Assessing the effects of disease and bleaching on Florida Keys corals by fitting population models to data

Coral diseases have increased in frequency over the past few decades and have important influences on the structure and composition of coral reef communities. However, there is limited information on the etiologies of many coral diseases, and pathways through which coral diseases are acquired and transmitted are still in question. Furthermore, it is difficult to assess the impacts of disease on coral populations because outbreaks often co-occur with temperature-induced bleaching and anthropogenic stressors. We developed spatially explicit population models of coral disease and bleaching dynamics to quantify the impact of six common diseases on Florida Keys corals, including aspergillosis, dark spots, white band, white plague, white patch, and Caribbean yellow band. Models were fit to an 8-year data set of coral abundance, disease prevalence, and bleaching prevalence. Model selection was used to assess alternative pathways for disease transmission, and the influence of environmental stressors, including sea temperature and human population density, on disease prevalence and coral mortality. Classic disease transmission from contagious to susceptible colonies provided the best-fit model only for aspergillosis. For other diseases, external disease forcing, such as through a vector or directly from pathogens in the environment, provided the best fit to observed data. Estimates of disease reproductive ratio values (R₀) were less than one for each disease, indicating coral colonies were below densities required for diseases to become established through contagious spread alone. Incidences of white band and white patch disease were associated with greater susceptibility or slower recovery of bleached colonies, and no disease outbreaks were associated with periods of elevated sea temperatures alone. Projections of best-fit models indicated that, atleast during the period of this study, disease and bleaching did not have substantial impacts on populations and impaired rates of population growth appeared to be attributable to other stressors. By applying epidemiological models to field data, our study gives qualitative insights into the dynamics of coral diseases, relative stressor impacts, and directions for future research.     

Mapping species distributions in one dimension by non-homogeneous hidden Markov models: the case of freshwater pearl mussels in the River Dee

The investigation of species distributions in rivers involves data which are inherently sequential and unlikely to be fully independent. To take these characteristics into account, we develop a Bayesian hierarchical model for mapping the distribution of freshwater pearl mussels in the River Dee (Scotland). At the top of the hierarchy the likelihood is used to describe the sequence of sites in which mussels were observed or not. Given that false observations can occur, and that “not observed” means both that the species was not present and that it was not observed, a Markov prior is introduced at the second level of the hierarchy to represent the sequence of sites in which mussels are estimated to occur. The Markov prior allows modelling the spatial dependency between neighbouring sites. A third level in the hierarchy is given by the representation of the transition probabilities of the Markov chain in terms of site-specific explanatory variables, through a logistic regression. The selection of the explanatory variables which influence the Markov process is performed by means of a simulation-based procedure, in the complex case of association between covariates. Four features were found to be associated with reduced chance of finding a local mussel population: tributaries, bridges, dredging, and waste water treatment works. These results complement the results of a previous study, providing new evidence for the causes of the deterioration of a highly threatened species.     

Modeling oil dispersion under breaking waves. Part II: Coupling Lagrangian particle tracking with population balance model

Environmental Fluid Mechanics - Oil dispersion under a deep-water plunging breaker of height 0.15 m was studied by coupling the Lagrangian particle tracking code (NEMO3D) with the...     

Local population dynamics of an invasive tree species with a complex life-history cycle: A stochastic matrix model

Biological invasions are widely accepted as having a major impact on ecosystem functioning worldwide, giving urgency to a better understanding of the factors that control their spread. Modelling tools have been developed for this purpose but are often discrete-space, discrete-time spatial-mechanistic models that adopt a computer simulation approach and resist mathematical analysis. We constructed a simple demographic matrix model to explore the local population dynamics of an invasive species with a complex life history and whose invasive success depends on resource availability, which occurs stochastically. As a case study we focused on the American black cherry (Prunus serotina Ehrh.), a gap-dependent tree able both to constitute a long-living seedling bank under unfavourable light conditions and to resprout vigorously once cut-down, which is invading European temperate forests. The model used was a stage-classified matrix population model (i.e., Lefkovitch matrix), integrating environmental stochasticity. Stochastic matrix projection analysis was combined with elasticity analysis and stochastic simulations to search for the species’ ‘Achille heel’. As expected, the population growth rate (i.e., Lyapunov exponent), which measures the risk of P. serotina invasion at the stand scale, increased with light frequency. There was a critical value above which the population of P. serotina explodes and below which it locally goes extinct. The resprouting capacity usually speed up the invasion but appeared to play a minor role. The mean duration of stand invasion was measured and important life stage transitions that mostly contribute to the local stochastic growth rate were identified. Some relevant management implications are discussed and the interest of such models for the understanding of demographic characteristics of invasive species is stressed.     

Revealing life‐history traits by contrasting genetic estimations with predictions of effective population size

Effective population size, a central concept in conservation biology, is now routinely estimated from genetic surveys and can also be theoretically predicted from demographic, life‐history, and mating‐system data. By evaluating the consistency of theoretical predictions with empirically estimated effective size, insights can be gained regarding life‐history characteristics and the relative impact of different life‐history traits on genetic drift. These insights can be used to design and inform management strategies aimed at increasing effective population size. We demonstrated this approach by addressing the conservation of a reintroduced population of Asiatic wild ass (Equus hemionus). We estimated the variance effective size (N_ev) from genetic data () and formulated predictions for the impacts on N_ev of demography, polygyny, female variance in lifetime reproductive success (RS), and heritability of female RS. By contrasting the genetic estimation with theoretical predictions, we found that polygyny was the strongest factor affecting genetic drift because only when accounting for polygyny were predictions consistent with the genetically measured N_ev. The comparison of effective‐size estimation and predictions indicated that 10.6% of the males mated per generation when heritability of female RS was unaccounted for (polygyny responsible for 81% decrease in N_ev) and 19.5% mated when female RS was accounted for (polygyny responsible for 67% decrease in N_ev). Heritability of female RS also affected N_ev; (heritability responsible for 41% decrease in N_ev). The low effective size is of concern, and we suggest that management actions focus on factors identified as strongly affecting , namely, increasing the availability of artificial water sources to increase number of dominant males contributing to the gene pool. This approach, evaluating life‐history hypotheses in light of their impact on effective population size, and contrasting predictions with genetic measurements, is a general, applicable strategy that can be used to inform conservation practice.