Hamiltonian Markov Chain Research Articles

Impact of APOE ε4 and ε2 on plasma neurofilament light chain and cognition in autosomal dominant Alzheimer’s disease

BackgroundApolipoprotein E (APOE) genotypes have been suggested to influence cognitive impairment and clinical onset in presenilin-1 (PSEN1) E280A carriers for autosomal dominant Alzheimer’s disease (ADAD). Less is known about their impact on the trajectory of biomarker changes. Neurofilament light chain (NfL), a marker of neurodegeneration, begins to accumulate in plasma about 20 years prior to the clinical onset of ADAD. In this study we investigated the impact of APOE ε4 and ε2 variants on age-related plasma NfL increases and cognition in PSEN1 E280A mutation carriers.MethodsWe analyzed cross-sectional data from PSEN1 E280A mutation carriers and non-carriers recruited from the Alzheimer’s Prevention Initiative Registry of ADAD. All participants over 18 years with available APOE genotype, plasma NfL, and neuropsychological evaluation were included in this study. APOE genotypes and plasma NfL concentrations were characterized for each participant. Cubic spline models using a Hamiltonian Markov chain Monte Carlo method were used to characterize the respective impact of at least one APOE ε4 or ε2 allele on age-related log-transformed plasma NfL increases. Linear regression models were estimated to explore the impact of APOE ε4 and ε2 variants and plasma NfL on a composite cognitive test score in the ADAD mutation carrier and non-carrier groups.ResultsAnalyses included 788 PSEN1 E280A mutation carriers (169 APOE ε4 + , 114 ε2 +) and 650 mutation non-carriers (165 APOE ε4 + , 80 ε2 +), aged 18–75 years. APOE ε4 allele carriers were distinguished from ε4 non-carriers by greater age-related NfL elevations in the ADAD mutation carrier group, beginning about three years after the mutation carriers’ estimated median age at mild cognitive impairment onset. APOE ε2 allele carriers had lower plasma NfL concentrations than ε2 non-carriers in both the ADAD mutation carrier and non-carrier groups, unrelated to age, and an attenuated relationship between higher NfL levels on cognitive decline in the ADAD mutation carrier group.ConclusionsAPOE ε4 accelerates age-related plasma NfL increases and APOE ε2 attenuates the relationship between higher plasma NfL levels and cognitive decline in ADAD. NfL may be a useful biomarker to assess clinical efficacy of APOE-modifying drugs with the potential to help in the treatment and prevention of ADAD.

Bayesian inference of the spatial distribution of steel corrosion in reinforced concrete structures using corrosion-induced crack width

Observations of corrosion-induced crack widths offer crucial information about the corrosion states of steel reinforcements in reinforced concrete (RC) structures, enabling a cost-effective method for inferring corrosion states through inverse analysis. However, the uncertainty associated with the relationship between corrosion-induced cracking and steel weight loss necessitates a probabilistic inference method, especially when considering the spatial distributions of steel weight loss, which provides important information to estimate the load-bearing capacity loss of corroded RC structures. This paper proposes a Bayesian framework to infer the steel weight loss distribution in RC structures based on the observed corrosion-induced crack width. To reduce the dimensions of the Bayesian inference, a Karhunen-Loève transform is applied to extract the principal distribution features of the steel weight loss. The forward model of the Bayesian inference adopts a data-driven sequence-to-sequence transduction approach to predict corrosion-induced crack width from steel weight loss. This model incorporates a novel nonlinear convolution kernel for input encoding and a sparse polynomial chaos expansion for decoding, which proves more accurate and efficient than finite element simulations. The Hamiltonian Markov chain Monte Carlo (HMCMC) sampler is used to efficiently sample from the posterior distribution of the Bayesian inference. The case study of the proposed method demonstrated that Bayesian inference provides robust range estimation for the steel weight loss distribution, with its 95% confidence interval encompassing most observations. Additionally, the method efficiently inferred high-dimensional steel weight loss sequences up to 61 dimensions, taking advantage of the dimension reduction technique and the gradient-informed HMCMC sampler.

Hamiltonian MCMC methods for estimating rare events probabilities in high-dimensional problems

Accurate and efficient estimation of rare events probabilities is of significant importance, since often the occurrences of such events have widespread impacts. The focus in this work is on precisely quantifying these probabilities, often encountered in reliability analysis of complex engineering systems, based on an introduced framework termed Approximate Sampling Target with Post-processing Adjustment (ASTPA), which herein is integrated with and supported by gradient-based Hamiltonian Markov Chain Monte Carlo (HMCMC) methods. The developed techniques in this paper are applicable from low- to high-dimensional stochastic spaces, and the basic idea is to construct a relevant target distribution by weighting the original random variable space through a one-dimensional output likelihood model, using the limit-state function. To sample from this target distribution, we exploit HMCMC algorithms, a family of MCMC methods that adopts physical system dynamics, rather than solely using a proposal probability distribution, to generate distant sequential samples, and we develop a new Quasi-Newton mass preconditioned HMCMC scheme (QNp-HMCMC), which is particularly efficient and suitable for high-dimensional spaces. To eventually compute the rare event probability, an original post-sampling step is devised using an inverse importance sampling procedure based on the already obtained samples. The statistical properties of the estimator are analyzed as well, and the performance of the proposed methodology is examined in detail and compared against Subset Simulation in a series of challenging low- and high-dimensional problems.

Effects of APOE4 and education on the clinical onset of autosomal dominant Alzheimer’s disease due to the PSEN1 E280A mutation (S39.004)

<h3>Objective:</h3> Determine the impact of APOE4 genotype and education on the clinical onset of autosomal dominant Alzheimer’s disease. <h3>Background:</h3> Autosomal dominant Alzheimer’s disease (ADAD) is genetically determined, but variability in age of symptom onset suggests it may be influenced by additional genetic and environmental risk factors. Although the e4 allele of the apolipoprotein E (APOE4) gene and education level both influence clinical onset of dementia in sporadic Alzheimer’s disease (AD), it is unclear whether APOE4 affects onset of ADAD. Here, we investigated the effects of APOE4 and education on the clinical onset of ADAD. <h3>Design/Methods:</h3> We analyzed retrospective data from 675 presenilin-1 (<i>PSEN1</i>) E280A mutation carriers (141 APOE4 carriers, 534 APOE4 non-carriers) and 594 <i>PSEN1</i> non-carriers (148 APOE4 carriers, 446 APOE4 non-carriers) from a Colombian kindred with ADAD. We used the Mini-Mental State Examination (MMSE) as a proxy for clinical impairment. Model parameters in both <i>PSEN1</i> carriers and non-carriers were estimated using a Hamiltonian Markov chain Monte Carlo method. The age-related trajectories of APOE4 carriers versus non-carriers were compared in both <i>PSEN1</i> carriers and non-carriers. <h3>Results:</h3> In <i>PSEN1</i> carriers, lower MMSE scores began to significantly differentiate APOE4 carriers from non-carriers at age 45, the average age of mild cognitive impairment onset in this kindred. Years of education moderated the effect of APOE such that APOE4 carriers with lower educational levels had lower average MMSE scores in comparison to APOE4 non-carriers. <h3>Conclusions:</h3> Our findings suggest 1) age-related changes in global cognitive function may be accelerated in ADAD mutation carriers who are APOE4 carriers, compared to APOE4 non-carriers; and 2) higher educational levels may have a protective effect against cognitive impairment, even in the presence of genetic risk factors. Further longitudinal studies are necessary to clarify the impact of both education and APOE4 genotype on ADAD clinical progression. <b>Disclosure:</b> Mr. Barksdale has nothing to disclose. The institution of Dr. Langella has received research support from Alzheimer’s Association. Dr. Vasquez has nothing to disclose. David Fernando Aguillon, Sr. has nothing to disclose. Yinghua Chen has nothing to disclose. Dr. Su has nothing to disclose. Dr. ACOSTA-BAENA has nothing to disclose. Juliana Acosta Uribe has nothing to disclose. Ana Baena has nothing to disclose. Gloria Garcia-Ospina has nothing to disclose. Margarita Giraldo-Chica has nothing to disclose. Victoria Tirado has nothing to disclose. Mrs. Munoz has nothing to disclose. Miss Guzman Martinez has nothing to disclose. Dr. Rios Romenets has nothing to disclose. Mr. Oliveira has nothing to disclose. Dr. Yang has received personal compensation in the range of $500-$4,999 for serving as a invited speaker with Genentech, Inc.. The institution of Clara Vila-Castelar has received research support from Alzheimer’s Association. The institution of Clara Vila-Castelar has received research support from NIA . The institution of Dr. Pruzin has received research support from Alzheimer’s Association. Dr. Ghisays has received personal compensation for serving as an employee of Banner Alzheimer’s Institute. Joseph Arboleda-Velasquez has nothing to disclose. Dr. Kosik has received personal compensation in the range of $50,000-$99,999 for serving as an officer or member of the Board of Directors for Rainwater Foundation. The institution of Dr. Kosik has received research support from National Institute of Health. The institution of Dr. Kosik has received research support from Hillblom Foundation. The institution of Dr. Kosik has received research support from Adelson Medical Foundation. The institution of Dr. Kosik has received research support from Alzheimer Association/Rainwater Foundation. The institution of Dr. Kosik has received research support from Thome Memorial FOundation. Dr. Reiman has received personal compensation in the range of $50,000-$99,999 for serving on a Scientific Advisory or Data Safety Monitoring board for Denali, Green Valley, Zinfandel, and Takeda. Dr. Reiman has received stock or an ownership interest from Alkahest, Alzheon, Aural Analytics, Denali, and United Neuroscience.. Dr. Reiman has received intellectual property interests from a discovery or technology relating to health care. Dr. Reiman has received personal compensation in the range of $500-$4,999 for serving as a Member, National Advisory Council on Aging (NACA) with NIA. Francisco Lopera has nothing to disclose. Dr. Quiroz has received personal compensation in the range of $500-$4,999 for serving as a Consultant for Biogen. Dr. Quiroz has received intellectual property interests from a discovery or technology relating to health care.

Probabilistic structural identification and condition assessment of prestressed concrete bridges based on Bayesian inference using deflection measurements

This paper presents a model-based probabilistic structural identification that uses the deflection of prestressed concrete bridges (PSCBs) as observational information to perform Bayesian inference on the state variables associated with creep, structural rigidity, dead loads, shrinkage and prestress. The creep development is modeled as a stochastic process, and the structural rigidity is modeled as a stochastic field using the Karhunen–Loève transform. By incorporating the stochastic process/field into the inference frame, detailed information on structural states can be extracted. Considering the high dimension of the state variables, their posterior distributions are derived by the Hamiltonian Markov chain Monte Carlo (HMCMC) algorithm. As an illustrative example, two sets of deflection measurement of a case bridge are used to update the state variables in a sequential manner. Bayesian inference can calibrate the state variables, while the uncertainties associated with the state variables can be reduced. A K-means analysis can reveal the typical modes in the joint posterior distribution of the state variables, corresponding to the typical failure modes in the attributive analysis of the excessive deflection. The updated state variables are used in the probabilistic condition assessment associated with the deflection evolution.

A Gender Study of Food Stress and Implications for International Students Acculturation

Acculturative stress can be a big problem for international students. Among the adaptation difficulties they may face, adjusting to new foods in a new environment is crucial to their well-being. Existing studies related to dietary acculturation point to gender differences, mostly on objective health impacts. Using the information processing approach, this study aims to examine the subjective perception of dietary acculturation difficulties, with a focus on the influence of social connectedness. Using the Bayesian inference approach with the Hamiltonian Markov Chain Monte Carlo (MCMC) technique on a sample of 268 students from a Japanese international university, we found that female students are more likely to have perceived difficulties in the process of adjusting to new foods, but social connectedness lessens this effect. We also found no significant differences between domestic and international students regarding perceived difficulties of food adjustment in this study site, likely due to its highly multicultural environment. We suggest international universities provide better information about the food situations on campuses, especially for female students, and organize more cultural exchange events and food-related social activities to help students overcome barriers of food stress.

Effect of APOE4 on Plasma Phospho‐tau 217 and Neurofilament Light in the PSEN1 E280A Autosomal Dominant Alzheimer’s Disease Colombian Kindred

AbstractBackgroundThe Colombian kindred affected by the autosomal dominant AD causative mutation PSEN1 E280A are an invaluable population in determining the utility of blood biomarkers (BB) and how additional risk factors may affect BB years to decades prior to symptom onset. Neurofilament light (NfL) (Quiroz et al., 2020) and phospho‐tau 217 (p‐tau217) (Palmqvist et al., 2020) diverge about 20 years prior to onset of clinical symptoms in carriers compared to non‐carriers. How APOE4 carriage may influence NfL and p‐tau217 in the kindred is unknown. We assessed cross‐sectional effects of APOE4 carriage on plasma NfL and p‐tau217 in the PSEN1 E280A kindred.MethodWe used a single molecule array immunoassay to quantify plasma NfL and a Meso Scale Discovery based plasma immunoassay to quantify p‐tau217. 1428 persons (age 18 to 75, mean 35.8, 23% APOE4 carriers, 54% PSEN1 E280A carriers) had available data for NfL analyses. A total of 612 persons (age 18 to 60, mean 35.9, 25% APOE4 carriers, 62% PSEN1 E280A carriers) had available data for p‐tau217 analyses. Age related trajectories were derived from cross‐sectional log‐transformed p‐tau217 and NfL concentrations modelled using a restricted cubic spline model. Model parameters were estimated using a Hamiltonian Markov chain Monte Carlo method in E280A mutation and APOE4 carriage defined groups. The primary comparison was made between APOE4 carrier and noncarriers within E280A carriers and noncarriers separately.ResultIn PSEN1 E280A mutation carriers, plasma NfL concentrations begin to differentiate those who were APOE4 carriers from non‐carriers at age 47.4 (figure 1). Plasma NfL concentrations did not differentiate APOE4 carriers versus non‐carriers in those without the PSEN1 E280A mutation though concentration of NfL trended higher in APOE4 carriers in the higher age range of the sample. Plasma p‐tau217 concentrations did not differentiate APOE4 carriers from non‐carriers in PSEN1 E280A mutation carriers or non‐carriers.ConclusionAPOE4 carriage results in accelerated NfL plasma increases in PSEN1 E280A mutation carriers starting at about the age of symptom onset. The inability to detect APOE4‐related ptau217 and NfL differences in the other groups may be related to the younger age of participants and limitations in statistical power.

APOE ε4 and global cognitive functioning in individuals with autosomal dominant Alzheimer’s disease due to the PSEN1 E280A variant

AbstractBackgroundAPOE‐ε4 allele (APOE4) increases the risk for sporadic Alzheimer’s disease (AD) and is associated with an earlier onset of AD dementia. However, previous studies have shown conflicting results on the association of APOE4 with the age of dementia onset in individuals with autosomal dominant AD (ADAD). Here, we examined the impact of APOE4 genotype on the age‐related trajectory of global cognitive function in mutation carriers and non‐carriers from the Colombian ADAD kindred.MethodData were obtained from a retrospective cohort of individuals from the largest known early‐onset ADAD kindred, residing in Antioquia, Colombia. Analyses included 675 PSEN1 E280A carriers (ages 18 to 75; 141 with an APOE4 allele: APOE4+, and 534 without an APOE4 allele: APOE4‐) and 594 non‐carriers. The Mini‐Mental State Examination (MMSE) was used to assess global cognitive functioning. Age‐related trajectories were derived from cross‐sectional log‐transformed MMSE scores modeled using a restricted cubic spline model. Model parameters were estimated using a Hamiltonian Markov chain Monte Carlo method to compare APOE4+ versus APOE4‐ trajectories in the mutation carrier and non‐carrier groups and estimate the age at onset of differences in global cognitive functioning.ResultLower MMSE scores distinguished PSEN1 E280A mutation carriers from non‐carriers at age 31.4, approximately 14 years before the average age of mild cognitive impairment (MCI) onset in this cohort. Among PSEN1 E280A mutation carriers, lower scores in MMSE began to significantly differentiate APOE4+ from APOE4‐ at age 45, the estimated average age of MCI onset in this kindred (figure 1). MMSE scores did not differentiate APOE4+ from APOE4‐ in those without the PSEN1 E280A mutation.ConclusionOur findings suggest that age‐related changes in cognitive function, as measured by the MMSE, are accelerated in ADAD mutation carriers who are APOE4+, compared to those who are APOE4‐. Future longitudinal studies of PSEN1 mutation carriers are needed to further clarify the impact of APOE4 genotype on rates of cognitive decline, heterogeneity of clinical presentation, and clinical progression in the preclinical, MCI, and dementia stages.

Population PBPK modeling using parametric and nonparametric methods of the Simcyp Simulator, and Bayesian samplers

Physiologically‐based pharmacokinetic (PBPK) models usually include a large number of parameters whose values are obtained using in vitro to in vivo extrapolation. However, such extrapolations can be uncertain and may benefit from inclusion of evidence from clinical observations via parametric inference. When clinical interindividual variability is high, or the data sparse, it is essential to use a population pharmacokinetics inferential framework to estimate unknown or uncertain parameters. Several approaches are available for that purpose, but their relative advantages for PBPK modeling are unclear. We compare the results obtained using a minimal PBPK model of a canonical theophylline dataset with quasi‐random parametric expectation maximization (QRPEM), nonparametric adaptive grid estimation (NPAG), Bayesian Metropolis‐Hastings (MH), and Hamiltonian Markov Chain Monte Carlo sampling. QRPEM and NPAG gave consistent population and individual parameter estimates, mostly agreeing with Bayesian estimates. MH simulations ran faster than the others methods, which together had similar performance.

Predicting Verbal Learning and Memory Assessments of Older Adults Using Bayesian Hierarchical Models.

Verbal learning and memory summaries of older adults have usually been used to describe neuropsychiatric complaints. Bayesian hierarchical models are modern and appropriate approaches for predicting repeated measures data where information exchangeability is considered and a violation of the independence assumption in classical statistics. Such models are complex models for clustered data that account for distributions of hyper-parameters for fixed-term parameters in Bayesian computations. Repeated measures are inherently clustered and typically occur in clinical trials, education, cognitive psychology, and treatment follow-up. The Hopkins Verbal Learning Test (HVLT) is a general verbal knowledge and memory assessment administered repeatedly as part of a neurophysiological experiment to examine an individual’s performance outcomes at different time points. Multiple trial-based scores of verbal learning and memory tests were considered as an outcome measurement. In this article, we attempted to evaluate the predicting effect of individual characteristics in considering within and between-group variations by fitting various Bayesian hierarchical models via the hybrid Hamiltonian Monte Carlo (HMC) under the Bayesian Regression Models using ‘Stan’ (BRMS) package of R. Comparisons of the fitted models were done using leave-one-out information criteria (LOO-CV), Widely applicable information criterion (WAIC), and K-fold cross-validation methods. The full hierarchical model with varying intercepts and slopes had the best predictive performance for verbal learning tests [from the Advanced Cognitive Training for Independent and Vital Elderly (ACTIVE) study dataset] using the hybrid Hamiltonian-Markov Chain Monte Carlo approach.

A multidimensional generalized many-facet Rasch model for rubric-based performance assessment

Performance assessment, in which human raters assess examinee performance in a practical task, often involves the use of a scoring rubric consisting of multiple evaluation items to increase the objectivity of evaluation. However, even when using a rubric, assigned scores are known to depend on characteristics of the rubric’s evaluation items and the raters, thus decreasing ability measurement accuracy. To resolve this problem, item response theory (IRT) models that can estimate examinee ability while considering the effects of these characteristics have been proposed. These IRT models assume unidimensionality, meaning that a rubric measures one latent ability. In practice, however, this assumption might not be satisfied because a rubric’s evaluation items are often designed to measure multiple sub-abilities that constitute a targeted ability. To address this issue, this study proposes a multidimensional IRT model for rubric-based performance assessment. Specifically, the proposed model is formulated as a multidimensional extension of a generalized many-facet Rasch model. Moreover, a No-U-Turn variant of the Hamiltonian Markov chain Monte Carlo algorithm is adopted as a parameter estimation method for the proposed model. The proposed model is useful not only for improving the ability measurement accuracy, but also for detailed analysis of rubric quality and rubric construct validity. The study demonstrates the effectiveness of the proposed model through simulation experiments and application to real data.

Alice in Suicideland: Exploring the Suicidal Ideation Mechanism Through Social Connectedness and Help-Seeking Behaviors

On average, one person dies by suicide every 40 s. However, extant studies have largely focused on the risk factors for suicidal behaviors, not so much on the formation of suicidal thoughts. Therefore, we attempt to explain how suicidal thoughts arise and persist inside one’s mind using a multifiltering information mechanism called Mindsponge. Bayesian analysis with Hamiltonian Markov Chain Monte Carlo (MCMC) technique was run on a dataset of multinational students (N = 268) of an international university in Japan. Item 9 in the PHQ-9 was used to survey suicidal ideation. The associations among four main variables, namely, (i) suicidal ideation, (ii) help-seeking willingness (informal and formal sources), (iii) sense of connectedness, and (iv) information inaccessibility (represented by being international students), were tested in four models. Sense of connectedness is negatively associated with suicidal ideation, but its effect becomes less impactful when interacting with international students. The impact of a sense of connectedness on informal help-seeking willingness (toward family members) among international students is also lessened. Informal help-seeking is negatively associated with suicidal ideation, whereas formal help is positive. The findings support our assumption on three fundamental conditions for preventing suicidal thoughts: (i) a high degree of belongingness, (ii) accessibility to help-related information, and (iii) healthy perceived cultural responses towards mental health. Therefore, systematically coordinated programs are necessary to effectively tackle suicidal ideation.

Alice in Suicideland: Exploring the Suicidal Ideation Mechanism through the Sense of Connectedness and Help-Seeking Behaviors.

On average, one person dies by suicide every 40 s. However, extant studies have largely focused on the risk factors for suicidal behaviors, not so much on the formation of suicidal thoughts. Therefore, we attempt to explain how suicidal thoughts arise and persist inside one’s mind using a multifiltering information mechanism called Mindsponge. Bayesian analysis with Hamiltonian Markov Chain Monte Carlo (MCMC) technique was run on a dataset of multinational students (N = 268) of an international university in Japan. Item 9 in the PHQ-9 was used to survey suicidal ideation. The associations among four main variables, namely, (i) suicidal ideation, (ii) help-seeking willingness (informal and formal sources), (iii) sense of connectedness, and (iv) information inaccessibility (represented by being international students), were tested in four models. Sense of connectedness is negatively associated with suicidal ideation, but its effect becomes less impactful when interacting with international students. The impact of a sense of connectedness on informal help-seeking willingness (toward family members) among international students is also lessened. Informal help-seeking is negatively associated with suicidal ideation, whereas formal help is positive. The findings support our assumption on three fundamental conditions for preventing suicidal thoughts: (i) a high degree of belongingness, (ii) accessibility to help-related information, and (iii) healthy perceived cultural responses towards mental health. Therefore, systematically coordinated programs are necessary to effectively tackle suicidal ideation.

Evaluation of the Aichi Biodiversity Targets: the international collaboration trilemma in interdisciplinary research

Context Tourism plays a critical role in biodiversity conservation with at least 12 of the 20 Aichi Biodiversity Targets being directly or indirectly related to tourism. Aims As Target 19 aims to raise the generation, transfer and application of knowledge on biodiversity, the objective of this study is to evaluate the impact of Aichi Biodiversity Targets on the interdisciplinary research output, quality, and collaboration at the national scale regarding biodiversity and tourism. Methods The Hamiltonian Markov Chain Monter Carlo technique, incorporating the bibliometric analysis, was performed on 1176 documents extracted from the Web of Science database. Key results The current investigation revealed two prominent findings. First, the Aichi Biodiversity Targets positively affected scientific productivity, quality and international collaboration at the national level. Still, more than half of the countries on Earth (53.41%) had not acquired any interdisciplinary publication on the topic of biodiversity and tourism. Second, international collaboration was found to be an effective measure to improve scientific quality and quantity in both periods before and after the Aichi Targets. Although the impact of international collaboration on scientific output was similar between the two periods, its impact on scientific quality during 2011–2020 was lower than during 1991–2010. Conclusions Thus, we argue that international cooperation cannot be used as a ‘silver bullet’ strategy for advancing knowledge in the interdisciplinary field between biodiversity and tourism due to the trilemma between quantity, quality and cost. Implications We recommend policymakers, funding evaluators and researchers put culture into perspective to lessen the cost of interdisciplinary research.

BLP estimation using Laplace transformation and overlapping simulation draws

We derive the asymptotic distribution of the parameters of the Berry et al. (1995) (BLP) model in a many markets setting which takes into account simulation noise under the assumption of overlapping simulation draws. We show that as long as the number of simulation draws R and the number of markets T approach infinity, our estimator is m=min(R,T) consistent and asymptotically normal. We do not impose any relationship between the rates at which R and T go to infinity, thus allowing for the case of R≪T. We provide a consistent estimate of the asymptotic variance which can be used to form asymptotically valid confidence intervals. Instead of directly minimizing the BLP GMM objective function, we propose using Hamiltonian Markov Chain Monte Carlo methods to implement a Laplace-type estimator which is asymptotically equivalent to the GMM estimator.

Ranking with hamiltonian dynamics

In data science, a ranking or linear ordering problem is to place items into a linear order based on comparison data. In this article, we consider a Hamiltonian system, in which particles, representing the items to be ordered, exert forces on each other as determined by the comparison data. An ordering of the items can be derived from the relative positions of the particles in any state of the system. The Hamiltonian is designed so that states with low potential energy yield orderings that agree strongly with the comparison data. Although the dynamics are related to the Toda lattice, no usable ranking information seems to be available from that variation of the Hamiltonian. Instead, a Toda-like Hamiltonian plus a confinement potential yields better results. Several algorithms based on Hamiltonian trajectories, minimization of a ranking potential, and a Hamiltonian Markov chain are compared to the widely used RankBoost algorithm. They all perform relatively well on synthetic test data and on problems from a library of test cases, but none is clearly the best in all circumstances. The trajectory-based methods and Markov chain show interesting dynamics. Furthermore, since these methods attach particle positions to the items as well as an ordering, the distances between the particles indicate how rankable the items are.

A Bayesian approach for zero-modified Skellam model with Hamiltonian MCMC

In this paper is presented the zero-modified poisson difference and present possible applications of them in the analysis of paired count data. The estimation and inferences of the model parameters were made considering a Bayesian approach using the algorithm of Hamiltonian Markov chain Monte Carlo methods to simulate samples of the joint posterior distribution of interest. Two applications were made for the analysis of paired count data.

Hamiltonian Markov chain Monte Carlo for partitioned sample spaces with application to Bayesian deep neural nets

Allocating computation over multiple chains to reduce sampling time in MCMC is crucial in making MCMC more applicable in the state of the art models such as deep neural networks. One of the parallelization schemes for MCMC is partitioning the sample space to run different MCMC chains in each component of the partition (VanDerwerken and Schmidler in Parallel Markov chain Monte Carlo. arXiv:1312.7479, 2013; Basse et al. in Artificial intelligence and statistics, pp 1318–1327, 2016). In this work, we take Basse et al. (2016)’s bridge sampling approach and apply constrained Hamiltonian Monte Carlo on partitioned sample spaces. We propose a random dimension partition scheme that combines well with the constrained HMC. We empirically show that this approach can expedite MCMC sampling for any unnormalized target distribution such as Bayesian neural network in a high dimensional setting. Furthermore, in the presence of multi-modality, this algorithm is expected to be more efficient in mixing MCMC chains when proper partition elements are chosen.

BLP Estimation Using Laplace Transformation and Overlapping Simulation Draws

We derive the asymptotic distribution of the parameters of the Berry et al. (1995, BLP) model in a many markets setting which takes into account simulation noise under the assumption of overlapping simulation draws. We show that, as long as the number of simulation draws R and the number of markets T approach infinity, our estimator is √m = √min(R,T) consistent and asymptotically normal. We do not impose any relationship between the rates at which R and T go to infinity, thus allowing for the case of R < < T. We provide a consistent estimate of the asymptotic variance which can be used to form asymptotically valid confidence intervals. Instead of directly minimizing the BLP GMM objective function, we propose using Hamiltonian Markov chain Monte Carlo methods to implement a Laplace-type estimator which is asymptotically equivalent to the GMM estimator.

From individual to joint species distribution models: A comparison of model complexity and predictive performance

AbstractAimSpecies distribution models (SDMs) are widely used to study geographic distributions of taxa in response to natural and anthropogenic environmental conditions. For a community, common approaches include fitting individual SDMs (iSDMs) to all taxa or directly modelling community properties such as richness. However, the parameters of iSDMs are difficult to identify for rare taxa, and community properties do not reveal taxon‐specific responses. Individual models can be combined into a hierarchical multispecies distribution model (mSDM) that constrains taxon‐specific parameters according to overarching community parameters, or a joint model (jSDM) in which interdependencies between taxa are jointly inferred. We compare how individual, hierarchical multispecies and joint SDMs differ in quality of fit, explanatory power and predictive performance, and analyse how these properties depend on the prevalence of taxa.TaxaPresence–absence observations of 245 benthic macroinvertebrate taxa identified at a mixed taxonomic resolution.LocationFour hundred and ninety‐two sites in rivers throughout Switzerland.MethodsIndividual, hierarchical and joint hierarchical generalized linear models (GLM) were developed for all taxa. Parameters were estimated using maximum likelihood estimation or Bayesian inference with Hamiltonian Markov chain Monte Carlo simulations. Predictive performance was assessed with cross‐validation. In addition, the predicted family and species richness of the models was compared with a GLM for richness.ResultsIndividual models show a slightly higher quality of fit largely due to overfitting for rare taxa. The mSDM achieves a similar quality of fit and explanatory power, mitigates overfitting for rare taxa and considerably improves predictive performance over the whole community. The joint models further improve the quality of fit, but decrease predictive performance and increase predictive uncertainty.Main conclusionsWe show that even a relatively simple mSDM combines many of the analytical capabilities of iSDMs and improves predictive performance. Increasingly complex mSDMs and jSDMs provide additional analytical possibilities, but depending on the data and research questions, different levels of complexity may be appropriate.