Hierarchical Probabilistic Model Research Articles

A Bayesian Hierarchical Model for Estimation of Abundance and Spatial Density of Aedes aegypti.

Strategies to minimize dengue transmission commonly rely on vector control, which aims to maintain Ae. aegypti density below a theoretical threshold. Mosquito abundance is traditionally estimated from mark-release-recapture (MRR) experiments, which lack proper analysis regarding accurate vector spatial distribution and population density. Recently proposed strategies to control vector-borne diseases involve replacing the susceptible wild population by genetically modified individuals’ refractory to the infection by the pathogen. Accurate measurements of mosquito abundance in time and space are required to optimize the success of such interventions. In this paper, we present a hierarchical probabilistic model for the estimation of population abundance and spatial distribution from typical mosquito MRR experiments, with direct application to the planning of these new control strategies. We perform a Bayesian analysis using the model and data from two MRR experiments performed in a neighborhood of Rio de Janeiro, Brazil, during both low- and high-dengue transmission seasons. The hierarchical model indicates that mosquito spatial distribution is clustered during the winter (0.99 mosquitoes/premise 95% CI: 0.80–1.23) and more homogeneous during the high abundance period (5.2 mosquitoes/premise 95% CI: 4.3–5.9). The hierarchical model also performed better than the commonly used Fisher-Ford’s method, when using simulated data. The proposed model provides a formal treatment of the sources of uncertainty associated with the estimation of mosquito abundance imposed by the sampling design. Our approach is useful in strategies such as population suppression or the displacement of wild vector populations by refractory Wolbachia-infected mosquitoes, since the invasion dynamics have been shown to follow threshold conditions dictated by mosquito abundance. The presence of spatially distributed abundance hotspots is also formally addressed under this modeling framework and its knowledge deemed crucial to predict the fate of transmission control strategies based on the replacement of vector populations.

Empirical Bayes Approach for Developing Hierarchical Probabilistic Predictive Models and Its Application to the Seismic Reliability Analysis of FRP-Retrofitted RC Bridges

AbstractThis paper proposes a general formulation to develop hierarchical probabilistic predictive models for clustered data. The common clustering factor, shared among the data within a group, causes statistical dependence that needs to be accounted for in the estimation of unknown model parameters. The basic idea of the hierarchical formulation is that the unknown model parameters are endowed with distributions that depend on a set of shared underlying parameters, and this construction is recursive up to the highest level of the hierarchy. The usual improper noninformative prior distributions on variance parameters of hierarchical models can lead to nonexistent posterior distributions that may appear perfectly reasonable in numerical simulations. On the other hand, common proper noninformative prior distributions may also substantially affect posterior statistics. Instead, the empirical Bayes approach is proposed to objectively estimate the variance parameters. The Gibbs sampling algorithm is used to es...

Assessing Approaches for Inferring Species Trees from Multi-Copy Genes

With the availability of genomic sequence data, there is increasing interest in using genes with a possible history of duplication and loss for species tree inference. Here we assess the performance of both nonprobabilistic and probabilistic species tree inference approaches using gene duplication and loss and coalescence simulations. We evaluated the performance of gene tree parsimony (GTP) based on duplication (Only-dup), duplication and loss (Dup-loss), and deep coalescence (Deep-c) costs, the NJst distance method, the MulRF supertree method, and PHYLDOG, which jointly estimates gene trees and species tree using a hierarchical probabilistic model. We examined the effects of gene tree and species sampling, gene tree error, and duplication and loss rates on the accuracy of phylogenetic estimates. In the 10-taxon duplication and loss simulation experiments, MulRF is more accurate than the other methods when the duplication and loss rates are low, and Dup-loss is generally the most accurate when the duplication and loss rates are high. PHYLDOG performs well in 10-taxon duplication and loss simulations, but its run time is prohibitively long on larger data sets. In the larger duplication and loss simulation experiments, MulRF outperforms all other methods in experiments with at most 100 taxa; however, in the larger simulation, Dup-loss generally performs best. In all duplication and loss simulation experiments with more than 10 taxa, all methods perform better with more gene trees and fewer missing sequences, and they are all affected by gene tree error. Our results also highlight high levels of error in estimates of duplications and losses from GTP methods and demonstrate the usefulness of methods based on generic tree distances for large analyses.

THE MASS DISTRIBUTION OF COMPANIONS TO LOW-MASS WHITE DWARFS

Measuring the masses of companions to single-line spectroscopic binary stars is (in general) not possible because of the unknown orbital plane inclination. Even when the mass of the visible star can be measured, only a lower limit can be placed on the mass of the unseen companion. However, since these inclination angles should be isotropically distributed, for a large enough, unbiased sample, the companion mass distribution can be deconvolved from the distribution of observables. In this work, we construct a hierarchical probabilistic model to infer properties of unseen companion stars given observations of the orbital period and projected radial velocity of the primary star. We apply this model to three mock samples of low-mass white dwarfs (LMWDs, $M\lesssim0.45~\Msun$) and a sample of post-common-envelope binaries. We use a mixture of two Gaussians to model the WD and neutron star (NS) companion mass distributions. Our model successfully recovers the initial parameters of these test data sets. We then apply our model to 55 WDs in the extremely low-mass (ELM) WD Survey. Our maximum a posteriori model for the WD companion population has a mean mass $\mu_{\rm WD} = 0.74~\Msun$, with a standard deviation $\sigma_{\rm WD} = 0.24~\Msun$. Our model constrains the NS companion fraction $f_{\rm NS}$ to be $<$16\% at 68\% confidence. We make samples from the posterior distribution publicly available so that future observational efforts may compute the NS probability for newly discovered LMWDs.

Bayesian CP Factorization of Incomplete Tensors with Automatic Rank Determination.

CANDECOMP/PARAFAC (CP) tensor factorization of incomplete data is a powerful technique for tensor completion through explicitly capturing the multilinear latent factors. The existing CP algorithms require the tensor rank to be manually specified, however, the determination of tensor rank remains a challenging problem especially for CP rank . In addition, existing approaches do not take into account uncertainty information of latent factors, as well as missing entries. To address these issues, we formulate CP factorization using a hierarchical probabilistic model and employ a fully Bayesian treatment by incorporating a sparsity-inducing prior over multiple latent factors and the appropriate hyperpriors over all hyperparameters, resulting in automatic rank determination. To learn the model, we develop an efficient deterministic Bayesian inference algorithm, which scales linearly with data size. Our method is characterized as a tuning parameter-free approach, which can effectively infer underlying multilinear factors with a low-rank constraint, while also providing predictive distributions over missing entries. Extensive simulations on synthetic data illustrate the intrinsic capability of our method to recover the ground-truth of CP rank and prevent the overfitting problem, even when a large amount of entries are missing. Moreover, the results from real-world applications, including image inpainting and facial image synthesis, demonstrate that our method outperforms state-of-the-art approaches for both tensor factorization and tensor completion in terms of predictive performance.

A meta-analysis of the magnetic line broadening in the solar atmosphere

A multi-line Bayesian analysis of the Zeeman broadening in the solar atmosphere is presented. A hierarchical probabilistic model, based on the simple but realistic Milne-Eddington approximation to the solution of the radiative transfer equation, is used to explain the data in the optical and near infrared. Our method makes use of the full line profiles of a more than 500 spectral lines from 4000 $\AA$ to 1.8 $\mu$m. Although the problem suffers from a strong degeneracy between the magnetic broadening and any other remaining broadening mechanism, the hierarchical model allows to isolate the magnetic contribution with reliability. We obtain the cumulative distribution function for the field strength and use it to put reliable upper limits to the unresolved magnetic field strength in the solar atmosphere. The field is below 160-180 G with 90% probability.

Decision Making with Second-Order Imprecise Probabilities

In decision analysis, uncertainty is usually described in the framework of probability. However, a large number of experimental and theoretical studies showed that a single nature of probability does not accurately capture human preferences. To avoid this drawback, they use imprecise probabilities. But, as decision maker is usually uncertain about first-order imprecise probabilities, imprecise hierarchical probability models are used. For most of such models, the second levels are precise. There also exist studies on two-level imprecise hierarchical models, which use imprecise probabilities or possibilities at the second level. Most of these works are based on lower prevision theory leading to a large number of optimization problems. In the present paper, we propose an imprecise hierarchical decision-making model where the first and the second level are described by interval probabilities. The method associates with the construction of a nonadditive measure as a lower prevision and uses this capacity in Choquet integral for constructing a utility function.

Multiple Subcategories Parts-Based Representation for One Sample Face Identification

Small sample set, occlusion, and illumination variations are the critical obstacles for a face identification system towards practical application. In this paper, we propose a probabilistic generative model for parts-based data representation to address these difficulties. In our approach, multiple subcategories corresponding to the individual face parts, such as nose, mouth, eye, and so forth, are modeled within a probabilistic graphical model framework to mimic the process of generating a face image. The induced face representation, therefore, encodes rich discriminative information. Model training is totally unsupervised. Once the training is completed, a test sample from the face class can be recognized as a novel combination of learned parts. In summary, the main contributions of this work are threefold: 1) A novel hierarchical probabilistic generative model is proposed, which is capable of achieving an efficient parts-based representation for robust face identification. 2) A constrained variational EM algorithm is developed to learn the model parameters and infer the variables. 3) Two similarity metrics are specially designed for the novel parts-based feature representation, which are effective for matching score guided one sample face identification. The models and similarity metrics are validated on three face databases. Experimental results demonstrate the capabilities of the model to deal with small sample set, occlusions, and illumination variances.

Inverse transport problem of estimating point-like source using a Bayesian parametric method with MCMC

Recovering the origin of an incident after detection of a polluting substance in the environment is crucial to start the remediation procedures. The lack of observations, the measurement errors and the model uncertainties make the problem of source estimation an ill-posed inverse problem that requires regularization to determine a solution. The two most frequent methods of regularization are source parametrization and penalization of undesirable solutions. In this paper, the proposed approach combines both methods in order to obtain a strong regularization that is efficient in case of few and erroneous observations. Point sources with parametric temporal releases and parameter penalizations are incorporated in a Bayesian framework where observations and prior information are combined in a hierarchical probabilistic model and the posterior law is explored with a Markov Chain Monte Carlo sampling algorithm. Estimation of the source parameters is provided by the posterior mean and uncertainties are provided by the posterior variance. To validate the method, several simulated cases with different emission events are considered. Quality of the estimate as well as impact of source model errors are also investigated. Then, a comparison with two existing least squares methods is conducted, in various configurations of sensors and noise level. Finally, the behavior of the method is described on a strongly underdeterminate real case where only one sensor recorded the pollution.

Indoor scene recognition by a mobile robot through adaptive object detection

Mobile robotics has achieved notable progress, however, to increase the complexity of the tasks that mobile robots can perform in natural environments, we need to provide them with a greater semantic understanding of their surrounding. In particular, identifying indoor scenes, such as an Office or a Kitchen, is a highly valuable perceptual ability for an indoor mobile robot, and in this paper we propose a new technique to achieve this goal. As a distinguishing feature, we use common objects, such as Doors or furniture, as a key intermediate representation to recognize indoor scenes. We frame our method as a generative probabilistic hierarchical model, where we use object category classifiers to associate low-level visual features to objects, and contextual relations to associate objects to scenes. The inherent semantic interpretation of common objects allows us to use rich sources of online data to populate the probabilistic terms of our model. In contrast to alternative computer vision based methods, we boost performance by exploiting the embedded and dynamic nature of a mobile robot. In particular, we increase detection accuracy and efficiency by using a 3D range sensor that allows us to implement a focus of attention mechanism based on geometric and structural information. Furthermore, we use concepts from information theory to propose an adaptive scheme that limits computational load by selectively guiding the search for informative objects. The operation of this scheme is facilitated by the dynamic nature of a mobile robot that is constantly changing its field of view. We test our approach using real data captured by a mobile robot navigating in Office and home environments. Our results indicate that the proposed approach outperforms several state-of-the-art techniques for scene recognition.

A high-fidelity cell lineage tracing method for obtaining systematic spatiotemporal gene expression patterns in Caenorhabditis elegans.

Advances in microscopy and fluorescent reporters have allowed us to detect the onset of gene expression on a cell-by-cell basis in a systematic fashion. This information, however, is often encoded in large repositories of images, and developing ways to extract this spatiotemporal expression data is a difficult problem that often uses complex domain-specific methods for each individual data set. We present a more unified approach that incorporates general previous information into a hierarchical probabilistic model to extract spatiotemporal gene expression from 4D confocal microscopy images of developing Caenorhabditis elegans embryos. This approach reduces the overall error rate of our automated lineage tracing pipeline by 3.8-fold, allowing us to routinely follow the C. elegans lineage to later stages of development, where individual neuronal subspecification becomes apparent. Unlike previous methods that often use custom approaches that are organism specific, our method uses generalized linear models and extensions of standard reversible jump Markov chain Monte Carlo methods that can be readily extended to other organisms for a variety of biological inference problems relating to cell fate specification. This modeling approach is flexible and provides tractable avenues for incorporating additional previous information into the model for similar difficult high-fidelity/low error tolerance image analysis problems for systematically applied genomic experiments.

Bayesian inference of T Tauri star properties using multi-wavelength survey photometry

There are many pertinent open issues in the area of star and planet formation. Large statistical samples of young stars across star-forming regions are needed to trigger a breakthrough in our understanding, but most optical studies are based on a wide variety of spectrographs and analysis methods, which introduces large biases. Here we show how graphical Bayesian networks can be employed to construct a hierarchical probabilistic model which allows pre-main sequence ages, masses, accretion rates, and extinctions to be estimated using two widely available photometric survey databases (IPHAS r/i/Halpha and 2MASS J-band magnitudes.) Because our approach does not rely on spectroscopy, it can easily be applied to homogeneously study the large number of clusters for which Gaia will yield membership lists. We explain how the analysis is carried out using the Markov Chain Monte Carlo (MCMC) method and provide Python source code. We then demonstrate its use on 587 known low-mass members of the star-forming region NGC 2264 (Cone Nebula), arriving at a median age of 3.0 Myr, an accretion fraction of 20+/-2% and a median accretion rate of 10^-8.4 Msol/yr. The Bayesian analysis formulated in this work delivers results which are in agreement with spectroscopic studies already in the literature, but achieves this with great efficiency by depending only on photometry. It is a significant step forward from previous photometric studies, because the probabilistic approach ensures that nuisance parameters, such as extinction and distance, are fully included in the analysis with a clear picture on any degeneracies.

Predictive Probability Distributions for Petroleum Unit Resource Projections via Hierarchical Modeling

Combining judgmental assessments using a classical probabilistic hierarchical model helps insure logical coherence of probability assessments by geologists of petroleum volumes in multiple, probabilistically dependent assessment units and allows easy study of how the predictive distribution of total hydrates in all units varies with variation in degrees of between and within unit dependencies.

A Hierarchical Probability Model of Colon Cancer

We consider a model of fixed sizeN= 2lin which there arelgenerations of daughter cells and a stem cell. In each generationithere are 2i−1daughter cells. At each integral time unit the cells split so that the stem cell splits into a stem cell and generation 1 daughter cell and the generationidaughter cells become two cells of generationi+1. The last generation is removed from the population. A stem cell acquires first and second mutations at ratesu1andu2, and a daughter cell acquires first and second mutations at ratesv1andv2. We find the distribution for the time it takes to acquire two mutations asNgoes to ∞ and the mutation rates go to 0. The mutation rates may tend to 0 at different speeds. We also find the distribution for the locations of the mutations. In particular, we determine whether or not the mutations occur on a stem cell and if not, at what generation in the daughter cells they occur. Several outcomes are possible, depending on how fast the rates go to 0. The model considered has been proposed by Komarova (2007) as a model for colon cancer.

A Hierarchical Probability Model of Colon Cancer

We consider a model of fixed sizeN= 2lin which there arelgenerations of daughter cells and a stem cell. In each generationithere are 2i−1daughter cells. At each integral time unit the cells split so that the stem cell splits into a stem cell and generation 1 daughter cell and the generationidaughter cells become two cells of generationi+1. The last generation is removed from the population. A stem cell acquires first and second mutations at ratesu1andu2, and a daughter cell acquires first and second mutations at ratesv1andv2. We find the distribution for the time it takes to acquire two mutations asNgoes to ∞ and the mutation rates go to 0. The mutation rates may tend to 0 at different speeds. We also find the distribution for the locations of the mutations. In particular, we determine whether or not the mutations occur on a stem cell and if not, at what generation in the daughter cells they occur. Several outcomes are possible, depending on how fast the rates go to 0. The model considered has been proposed by Komarova (2007) as a model for colon cancer.

Bayesian Speaker Adaptation Based on a New Hierarchical Probabilistic Model

In this paper, a new hierarchical Bayesian speaker adaptation method called HMAP is proposed that combines the advantages of three conventional algorithms, maximum a posteriori (MAP), maximum-likelihood linear regression (MLLR), and eigenvoice, resulting in excellent performance across a wide range of adaptation conditions. The new method efficiently utilizes intra-speaker and inter-speaker correlation information through modeling phone and speaker subspaces in a consistent hierarchical Bayesian way. The phone variations for a specific speaker are assumed to be located in a low-dimensional subspace. The phone coordinate, which is shared among different speakers, implicitly contains the intra-speaker correlation information. For a specific speaker, the phone variation, represented by speaker-dependent eigenphones, are concatenated into a supervector. The eigenphone supervector space is also a low dimensional speaker subspace, which contains inter-speaker correlation information. Using principal component analysis (PCA), a new hierarchical probabilistic model for the generation of the speech observations is obtained. Speaker adaptation based on the new hierarchical model is derived using the maximum a posteriori criterion in a top-down manner. Both batch adaptation and online adaptation schemes are proposed. With tuned parameters, the new method can handle varying amounts of adaptation data automatically and efficiently. Experimental results on a Mandarin Chinese continuous speech recognition task show good performance under all testing conditions.

Bayesian principal component regression with data-driven component selection

Principal component regression (PCR) has two steps: estimating the principal components and performing the regression using these components. These steps generally are performed sequentially. In PCR, a crucial issue is the selection of the principal components to be included in regression. In this paper, we build a hierarchical probabilistic PCR model with a dynamic component selection procedure. A latent variable is introduced to select promising subsets of components based upon the significance of the relationship between the response variable and principal components in the regression step. We illustrate this model using real and simulated examples. The simulations demonstrate that our approach outperforms some existing methods in terms of root mean squared error of the regression coefficient.

MGMR: leveraging RNA-Seq population data to optimize expression estimation

BackgroundRNA-Seq is a technique that uses Next Generation Sequencing to identify transcripts and estimate transcription levels. When applying this technique for quantification, one must contend with reads that align to multiple positions in the genome (multireads). Previous efforts to resolve multireads have shown that RNA-Seq expression estimation can be improved using probabilistic allocation of reads to genes. These methods use a probabilistic generative model for data generation and resolve ambiguity using likelihood-based approaches. In many instances, RNA-seq experiments are performed in the context of a population. The generative models of current methods do not take into account such population information, and it is an open question whether this information can improve quantification of the individual samplesResultsIn order to explore the contribution of population level information in RNA-seq quantification, we apply a hierarchical probabilistic generative model, which assumes that expression levels of different individuals are sampled from a Dirichlet distribution with parameters specific to the population, and reads are sampled from the distribution of expression levels. We introduce an optimization procedure for the estimation of the model parameters, and use HapMap data and simulated data to demonstrate that the model yields a significant improvement in the accuracy of expression levels of paralogous genes.ConclusionsWe provide a proof of principal of the benefit of drawing on population commonalities to estimate expression. The results of our experiments demonstrate this approach can be beneficial, primarily for estimation at the gene level.

Comparing the reconstruction of regulatory pathways with distinct Bayesian networks inference methods

BackgroundInference of biological networks has become an important tool in Systems Biology. Nowadays it is becoming clearer that the complexity of organisms is more related with the organization of its components in networks rather than with the individual behaviour of the components. Among various approaches for inferring networks, Bayesian Networks are very attractive due to their probabilistic nature and flexibility to incorporate interventions and extra sources of information. Recently various attempts to infer networks with different Bayesian Networks approaches were pursued. The specific interest in this paper is to compare the performance of three different inference approaches: Bayesian Networks without any modification; Bayesian Networks modified to take into account specific interventions produced during data collection; and a probabilistic hierarchical model that allows the inclusion of extra knowledge in the inference of Bayesian Networks. The inference is performed in three different types of data: (i) synthetic data obtained from a Gaussian distribution, (ii) synthetic data simulated with Netbuilder and (iii) Real data obtained in flow cytometry experiments.ResultsBayesian Networks with interventions and Bayesian Networks with inclusion of extra knowledge outperform simple Bayesian Networks in all data sets when considering the reconstruction accuracy and taking the edge directions into account. In the Real data the increase in accuracy is also observed when not taking the edge directions into account.ConclusionsAlthough it comes with a small extra computational cost the use of more refined Bayesian network models is justified. Both the inclusion of extra knowledge and the use of interventions have outperformed the simple Bayesian network model in simulated and Real data sets. Also, if the source of extra knowledge used in the inference is not reliable the inferred network is not deteriorated. If the extra knowledge has a good agreement with the data there is no significant difference in using the Bayesian networks with interventions or Bayesian networks with the extra knowledge.

Each to their own beat: periodicity in temporal inference

Characterizing cortical computation has been a key challenge in neuroscience. It has been suggested that the cerebral cortex is involved in unsupervised learning [1] and the notion that cortical computation is probabilistic is being increasingly accepted [2]. It has also been shown that cortical regions are hierarchically connected [3] and this has important implications on the way information could be represented. Moreover, the classical notion that processing in the cortex is predominantly governed by its feedforward inputs has been largely replaced by the view that feedback signals and other contextual information play a crucial role in the way information is encoded and learnt [2,4,5]. There is increasing emphasis on the influence of ongoing activity [5], ie. the state of the network on the effects of feedforward inputs. The hierarchical temporal memory (HTM) model of cortical computation [6] was used as the starting point for the current work. HTM is a hierarchical probabilistic model that uses spatial and temporal characteristics of its inputs to represent 'invariant causes' in the world. The key assumptions in the model are that learning in the cortex involves learning sequences of coincident patterns in its inputs and that the temporal patterns in inputs are critical for the brain’s ability to learn and infer with ambiguous sensory information. For the current work we are investigating tactile perception and implementing the HTM model using sensory inputs from artificial whiskers. The HTM model emphasizes that temporal patterns in inputs are extremely important features for learning and inference in the brain. This is especially the case with tactile perception since very little information is available at any single instant; how sensory inputs evolve over time conveys indispensable information about stimuli in the world. In modeling unsupervised learning, ‘time’ is commonly treated as indexing sequential inputs [7]. However, we are suggesting that learning, inference and prediction with temporal patterns pose a theoretical need to model some mechanism to encode time not only in terms of a temporal succession of events and causes, but also as a metric of periodicity. This theoretical need is perfectly aligned with well established empirical evidence that the brain engages in a plethora of oscillations at several different scales and frequencies. Our implementation of HTM incorporates a mechanism which attempts to mimic hypothesized effects of local neural oscillations in temporal inference. We are suggesting that cortical networks can dynamically maintain local oscillations to best match the relative frequencies with which inputs tend to occur. Assuming that all inputs to any cortical network are superimposed on its ongoing activity, these local oscillations can discretize the continuous stream of sensory inputs in signaling to subsequent levels in the hierarchy, as well as modulate the signal to suppress or enhance effects of specific components in the inputs based on their timing. We are demonstrating these effects in our implementation of HTM.