Bayesian Allocation Research Articles

Genetic variability and population structure of the Montezuma quail (Cyrtonyx montezumae) in the northern limit of its distribution

Restricted movement among populations decreases genetic variation, which may be the case for the Montezuma quail (Cyrtonyx montezumae), a small game bird that rarely flies long distances. In the northern limit of its distribution, it inhabits oak-juniper-pine savannas of Arizona, New Mexico, and Texas. Understanding genetic structure can provide information about the demographic history of populations that is also important for conservation and management. The objective of this study was to determine patterns of genetic variation in Montezuma quail populations using nine DNA microsatellite loci. We genotyped 119 individuals from four study populations: Arizona, Western New Mexico, Central New Mexico, and West Texas. Compared to other quail, heterozygosity was low (${\bar H_0}$ = 0.22 ± 0.04) and there were fewer alleles per locus (Ā = 2.41 ± 0.27). The global population genetic differentiation index RST = 0.045 suggests little genetic structure, even though a Bayesian allocation analysis suggested three genetic clusters (K = 3). This analysis also suggested admixture between clusters. Nevertheless, an isolation-by-distance analysis indicates a strong correlation (r = 0.937) and moderate evidence (P = 0.032) of non-independence between geographical and genetic distances. Climate change projections indicate an increase in aridity for this region, especially in temperate ecosystems where the species occurs. In this scenario, corridors between the populations may disappear, thus causing their complete isolation.

A Bayesian Allocation Model Based Approach to Mixed Membership Stochastic Blockmodels

ABSTRACT Although detecting communities in networks has attracted considerable recent attention, estimating the number of communities is still an open problem. In this paper, we propose a model, which replicates the generative process of the mixed-membership stochastic block model (MMSB) within the generic allocation framework of Bayesian allocation model (BAM) and BAM-MMSB. In contrast to traditional blockmodels, BAM-MMSB considers the observations as Poisson counts generated by a base Poisson process and marks according to the generative process of MMSB. Moreover, the optimal number of communities for BAM-MMSB is estimated by computing the variational approximations of the marginal likelihood for each model order. Experiments on synthetic and real data sets show that the proposed approach promises a generalized model selection solution that can choose not only the model size but also the most appropriate decomposition.

Variability and Genetic Structure of the Montezuma Quail Cyrtonyx montezumae in the Northern Limit of its Distribution

A species’ geographic distribution of genetic variability is influenced by different factors including size of geographic distribution, dispersal capability, mating system, and migration. For instance, a low migration rate among populations may cause a decrease in genetic variation. Such is the case of the Montezuma quail (Cyrtonyx montezumae), a popular game bird with a limited flight capacity that prevents long-distance dispersal. In the northern limit of the species’ distribution in Arizona, New Mexico, and Texas in the United States, the species inhabits oak forests that are separated from one another by deserts. Consequently, Montezuma quail populations are distributed in patches or islands. Knowledge of the species’ genetic structure is likely to help inform habitat management decisions. The objective of this study was to determine patterns of genetic variation in populations of the Montezuma quail using 9 microsatellite DNA loci. We genotyped 119 individuals harvested from 4 populations: Arizona (AZ), western New Mexico (WNM), eastern New Mexico (ENM), and west Texas (WTX). Montezuma quail populations had low observed heterozygosity (Ho = 0.22 ± 0.04) and a low number of alleles per locus (A = 2.41 ± 0.27) compared to other quail species. A global population genetic differentiation index (RST) of 0.045 suggests a weak genetic structure. Max(RST) occurred among pairwise comparisons AZ-WTX, AZ-ENM, and WNM-WTX. A Bayesian allocation analysis indicates that individuals were separated into 3 groups (K = 3), placing the populations of Arizona and Texas in distinct groups apart from the 2 populations of New Mexico, which are in the same group. Despite this differentiation, the Bayesian allocation analysis suggests admixture among populations, which may be an indicator of migration between them, especially between the populations in New Mexico and Arizona. An isolation-by-distance analysis indicates that there is a strong correlation (R2 = 0.84) and suggestive evidence (P = 0.08) of non-independence between geographical and genetic distances, though Montezuma quail populations in the southwestern United States may not be isolated. Climate change projections indicate an increase in aridity conditions in this region, especially in temperate ecosystems where the species occurs. In this scenario, corridors between the populations may disappear, thus causing their complete isolation.

Bayesian Allocation Model: Marginal Likelihood-Based Model Selection for Count Tensors

In this article, we introduce a dynamic generative model, the Bayesian allocation model (BAM), for modeling count data. BAM covers various probabilistic nonnegative tensor factorization (NTF) and topic models under one general framework. In BAM, allocations are made using a Bayesian network, whose conditional probability tables can be integrated out analytically. We show that, when allocations are viewed as sequential, the resulting marginal process is a special type of Polya urn process, which we name as Polya-Bayes process, an integer valued self-reinforcing process. Exploiting the Polya urn construction, we develop a novel sequential Monte Carlo (SMC) algorithm for marginal likelihood estimation in BAM, leading to a unified scoring method for discrete variable Bayesian networks with hidden nodes, including various NTF and topic models. The SMC estimator for marginal likelihood has the remarkable property of being unbiased in contrast to variational algorithms which are generally biased. We also demonstrate how our novel SMC-based likelihood estimation can be integrated within a Markov chain Monte Carlo algorithm for a principled and correct (in terms of respecting the true posterior distribution) Bayesian model selection and hyperparameter estimation for BAM. We provide several numerical examples, both on artificial and real datasets, that demonstrate the performance of the algorithms for various data regimes.

Bayesian mixture regression analysis for regulation of Pluripotency in ES cells

BackgroundObserved levels of gene expression strongly depend on both activity of DNA binding transcription factors (TFs) and chromatin state through different histone modifications (HMs). In order to recover the functional relationship between local chromatin state, TF binding and observed levels of gene expression, regression methods have proven to be useful tools. They have been successfully applied to predict mRNA levels from genome-wide experimental data and they provide insight into context-dependent gene regulatory mechanisms. However, heterogeneity arising from gene-set specific regulatory interactions is often overlooked.ResultsWe show that regression models that predict gene expression by using experimentally derived ChIP-seq profiles of TFs can be significantly improved by mixture modelling. In order to find biologically relevant gene clusters, we employ a Bayesian allocation procedure which allows us to integrate additional biological information such as three-dimensional nuclear organization of chromosomes and gene function. The data integration procedure involves transforming the additional data into gene similarity values. We propose a generic similarity measure that is especially suitable for situations where the additional data are of both continuous and discrete type, and compare its performance with similar measures in the context of mixture modelling.ConclusionsWe applied the proposed method on a data from mouse embryonic stem cells (ESC). We find that including additional data results in mixture components that exhibit biologically meaningful gene clusters, and provides valuable insight into the heterogeneity of the regulatory interactions.

Designing fecal microbiota transplant trials that account for differences in donor stool efficacy.

Fecal microbiota transplantation is a highly effective intervention for patients suffering from recurrent Clostridium difficile, a common hospital-acquired infection. Fecal microbiota transplantation's success as a therapy for C. difficile has inspired interest in performing clinical trials that experiment with fecal microbiota transplantation as a therapy for other conditions like inflammatory bowel disease, obesity, diabetes, and Parkinson's disease. Results from clinical trials that use fecal microbiota transplantation to treat inflammatory bowel disease suggest that, for at least one condition beyond C. difficile, most fecal microbiota transplantation donors produce stool that is not efficacious. The optimal strategies for identifying and using efficacious donors have not been investigated. We therefore examined the optimal Bayesian response-adaptive strategy for allocating patients to donors and formulated a computationally tractable myopic heuristic. This heuristic computes the probability that a donor is efficacious by updating prior expectations about the efficacy of fecal microbiota transplantation, the placebo rate, and the fraction of donors that produce efficacious stool. In simulations designed to mimic a recent fecal microbiota transplantation clinical trial, for which traditional power calculations predict [Formula: see text] statistical power, we found that accounting for differences in donor stool efficacy reduced the predicted statistical power to [Formula: see text]. For these simulations, using the heuristic Bayesian allocation strategy more than quadrupled the statistical power to [Formula: see text]. We use the results of similar simulations to make recommendations about the number of patients, the number of donors, and the choice of clinical endpoint that clinical trials should use to optimize their ability to detect if fecal microbiota transplantation is effective for treating a condition.

Robust Bayesian allocation

Using the Bayesian posterior distribution of the market parameters we define self-adjusting uncertainty regions for the robust mean-variance problem. Under a normal-inverse-Wishart conjugate assumption for the market, the ensuing robust Bayesian mean-variance optimal portfolios are shrunk by the aversion to estimation risk toward the global minimum variance portfolio. After discussing the theory, we test robust Bayesian allocations in a simulation study and in an application to the management of sectors of the S&P 500. Fully commented code is available for download

Cardinal Bayesian allocation mechanisms without transfers

Abstract In allocating goods with no use of monetary transfers, random allocation mechanisms can be designed in order to elicit information on preference intensities. I study the nontransfer allocation of two ex-ante identical objects under Bayesian incentive compatibility, with symmetric agents and independent private valuations. I find the ex-ante utilitarian-optimal mechanism, in which the probability of receiving a specified object is used as “numeraire” to purchase probability units of the other object. I characterize this mechanism as an appropriate combination of lotteries, auctions and insurance. The latter element ensures that efficient auctions are feasible. If the problem is constrained to guarantee exactly one object per agent, then the optimal mechanism uses no information other than the agentsʼ ordinal preferences.

The Intrinsic Logic of the Augmented Black-Litterman Model

Portfolio management is an art as well as science. We argue that portfolio managers eventually face two fundamental scientific challenges: (a) how to allocate; and (b) how to mimic. These require scientific answers. Other challenges in portfolio management are arts where different tastes, preferences, judgments and beliefs should be allowed. A general portfolio management framework should provide principles for solving the scientific problems, but remain neutral and facilitate interactions with the art part. The Augmented Black-Litterman (ABL) model rightly meets these requirements. This article reveals its intrinsic logic. It features: - An exploration of the motivation and general requirements of portfolio construction; - A dissection of the ABL allocation model; - Three ABL endogenous techniques and their efficiency evidences; - The intrinsic logic of the ABL model; and - Justifications of the model as a unified Bayesian allocation framework. Practitioners can consider this framework a unified allocation theory, which can be used to understand, evaluate and improve existing portfolio construction practices.

Crowded Trades: A Bayesian Remedy for Factor-Based Quants

In quantitative equity fund management, the popular traditional method to gain factor exposures is to perform factor ranking. This method easily leads to some crowded ‘style islands’, where numerous fund managers trade similar portfolios. The Bayesian allocation technique creates more efficient factor-mimicking (FM) portfolios (as evident in Cheung and Mittal, 2009), and these factor style portfolios tend to be more diversified. To further distance ourselves from crowded trades, one may utilise the blending capability of the Bayesian allocation framework to span the space between those islands. More differentiation benefits could also be obtained by customising the factor models. In this article, crowdedness is quantified by the Nomura trade impact cost model, METRIC. Based on this, we show evidence of the potential benefit from applying the new portfolio construction framework. This article features: - Trading cost comparison between factor ranking and Bayesian FM portfolios in simulated crowding events; and - Evidence of cost reduction by switching from the factor-ranking to ABL portfolio construction process.

Transparent Augmented Black-Litterman Allocation: Simple and Unified Framework for Strategy Combination, Factor Mimicking, Hedging, and Stock-Specific Alphas

You have some factor, strategy, and/or stock-specific alpha ideas. Without an optimiser, some straightforward linear algebra gives you the diversified and efficient Bayesian allocation that allows greater performance accountability. All you need is just a factor risk model. How does this sound‘ This paper derives a transparent version of the ABL model (Cheung, 2009B) with an explicit allocation expression, including components for all the needed functionalities. In addition to further insights, it allows more tangible implementation of strategy combination, factor mimicking, hedging, and stock-specific bets in a unified framework. More specifically, it enables the following: -- A unified, open, and optimiser-free allocation framework with parsimonious use of risk model -- Modularised alpha generation: 'portable alphas' with Bayesian assembly -- Implied new efficient techniques respectively for strategy combination, composite factor mimicking, hedging, and stock-specific betting -- Deeper insight into the ultimate Bayesian allocation mechanism -- Complete guidance on Black-Litterman practical issues, making the technique genuinely practical -- An interface between the art and science of portfolio construction.

Robust Bayesian Allocation

Using the Bayesian posterior distribution of the market parameters we define self-adjusting uncertainty regions for the robust mean-variance problem. Under a normal-inverse-Wishart conjugate assumption for the market, the ensuing robust Bayesian mean-variance optimal portfolios are shrunk by the aversion to estimation risk toward the global minimum variance portfolio. After discussing the theory, we test robust Bayesian allocations in a simulation study and in an application to the management of sectors of the S&P 500. Fully commented code is available for download