Bayesian Nonparametric Approach Research Articles

The risk-return relationship and volatility feedback in South Africa: a comparative analysis of the parametric and nonparametric Bayesian approach

<abstract> <p>This study aimed to investigate the risk-return relationship, provided volatility feedback was taken into account, in the South African market. Volatility feedback, a stronger measure of volatility, was treated as an important source of asymmetry in the investigation of the risk-return relationship. This study analyzed the JSE ALSI excess returns and realized variance for the sample period from 15 October 2009 to 15 October 2019. This study modelled the novel and robust Bayesian approach in a parametric and nonparametric framework. A parametric model has modelling assumptions, such as normality, and a finite sample space. A nonparametric approach relaxes modelling assumptions and allows for an infinite sample space; thus, taking into account every possible asymmetric risk-return relationship. Given that South Africa is an emerging market, which is subject to higher levels of volatility, the presence of volatility feedback was expected to be more pronounced. However, contrary to expectations, the test results from both the parametric and nonparametric Bayesian model showed that volatility feedback had an insignificant effect in the South African market. The risk-return relationship was then investigated free from empirical distortions that resulted from volatility feedback. The parametric Bayesian model found a positive risk-return relationship, in line with traditional theoretical expectations. However, the nonparametric Bayesian model found no relationship between risk and return, in line with early South African studies. Since the nonparametric Bayesian approach is more robust than the parametric Bayesian approach, this study concluded that there is no risk-return relationship. Therefore, investors can include South Africa in their investment portfolio with higher risk countries in order to spread their risk and derive diversification benefits. In addition, risk averse investors can find a safe environment within the South African market and earn a return in accordance to their risk tolerance.</p> </abstract>

A solution to the risk-return conundrum: Return exposure and the nonparametric Bayesian approach

The topic of the risk-return relationship is of broad importance in the fields of finance and economics. It has been widely investigated on an international scale, especially by developed markets from as early as the 1950's, with the primary motive being to help market participants optimize their chance to earn higher returns. According to conventional economic theory, the relationship between risk and return is a positive and linear relationship – the higher the risk, the higher the return. However, there are many studies documented in literature which show a positive or negative or no relationship at all. As a result, due to the magnitude of conflicting results over the years, this has caused an ongoing debate to arise regarding the risk-return relationship. International studies have explored a number of theories and models to attempt resolving the inconclusive empirical backing of the risk-return relationship. A valuable contribution of this study is the introduction of the novel concept “returns exposure” which refers to the risk that arises from the asymmetric nature of returns. This measure has a certain level of uncertainty attached to it due to its latent and stochastic nature. As a result, it may be ineffectively accounted for by existing parametric methods such as regression analysis and GARCH type models which are prone to model misspecification. This motivates the use of a more robust method, namely, the nonparametric Bayesian approach. The Bayesian approach has the ability to average out sources of uncertainty and measurement errors and thus effectively account for “return risk” or “returns exposure.” The Bayesian approach can be modelled within a parametric or nonparametric framework. The nonparametric approach is considered more robust as it relaxes modelling assumptions such as normality. Thus, in combination with the nonparametric approach, this provides a more robust estimation of the risk-return relationship.

A bayesian non-parametric approach for estimating COVID-19's vaccine effectiveness in a stochastic epidemic model

ObjectivesThis paper proposes a new stochastic epidemic modeling approach to estimate the effectiveness of COVID-19 vaccinations based on individual vaccination status using only observational data. MethodsTo accomplish this goal, we modified the SEIR model to categorize individuals according to their vaccination status and utilized Bayesian data augmentation techniques to assess vaccine effectiveness with partially observed data. We also implemented a dynamic time warping algorithm to compare transmission probabilities between groups with different vaccination statuses. ResultsOur findings indicated that both the fully vaccinated and boosted groups experienced lowered transmission probabilities, with average reductions of 51% and 49% respectively. Interestingly, we also observed no significant difference between the boosted group and fully vaccinated group regarding re-susceptibility. ConclusionIn conclusion, this proposed stochastic epidemic modeling approach for estimating COVID-19 vaccine effectiveness has significant implications for public health policy and decision-making. It could lead to more precise assessments of vaccine effectiveness and validity tests for clinical trial estimates. Overall, this approach has the potential to be a valuable tool in evaluating vaccine effectiveness and the population impact of the vaccination process.

Nonparametric Bayesian volatility learning under microstructure noise

In this work, we study the problem of learning the volatility under market microstructure noise. Specifically, we consider noisy discrete time observations from a stochastic differential equation and develop a novel computational method to learn the diffusion coefficient of the equation. We take a nonparametric Bayesian approach, where we a priori model the volatility function as piecewise constant. Its prior is specified via the inverse Gamma Markov chain. Sampling from the posterior is accomplished by incorporating the Forward Filtering Backward Simulation algorithm in the Gibbs sampler. Good performance of the method is demonstrated on two representative synthetic data examples. We also apply the method on a EUR/USD exchange rate dataset. Finally we present a limit result on the prior distribution.

Shape modeling with spline partitions

Shape modelling (with methods that output shapes) is a new and important task in Bayesian nonparametrics and bioinformatics. In this work, we focus on Bayesian nonparametric methods for capturing shapes by partitioning a space using curves. In related work, the classical Mondrian process is used to partition spaces recursively with axis-aligned cuts, and is widely lied in multi-dimensional and relational data. The Mondrian process outputs hyper-rectangles. Recently, the random tessellation process was introduced as a generalization of the Mondrian process, partitioning a domain with non-axis aligned cuts in an arbitrary dimensional space, and outputting polytopes. Motivated by these processes, in this work, we propose a novel parallelized Bayesian nonparametric approach to partition a domain with curves, enabling complex data-shapes to be acquired. We apply our method to HIV-1-infected human macrophage image dataset, and also simulated datasets sets to illustrate our approach. We compare to support vector machines, random forests and state-of-the-art computer vision methods such as simple linear iterative clustering super pixel image segmentation. We develop an R package that is available at https://github.com/ShufeiGe/Shape-Modeling-with-Spline-Partitions.

System identification using autoregressive Bayesian neural networks with nonparametric noise models

System identification is of special interest in science and engineering. This article is concerned with a system identification problem arising in stochastic dynamic systems, where the aim is to estimate the parameters of a system along with its unknown noise processes. In particular, we propose a Bayesian nonparametric approach for system identification in discrete time nonlinear random dynamical systems assuming only the order of the Markov process is known. The proposed method replaces the assumption of Gaussian distributed error components with a flexible family of probability density functions based on Bayesian nonparametric priors. Additionally, the functional form of the system is estimated by leveraging Bayesian neural networks, which leads to flexible uncertainty quantification. Hamiltonian Monte Carlo sampler within a Gibbs sampler for posterior inference is proposed and its effectiveness is illustrated in real time series.

Nonparametric Bayesian volatility estimation for gamma-driven stochastic differential equations

We study a nonparametric Bayesian approach to estimation of the volatility function of a stochastic differential equation driven by a gamma process. The volatility function is modelled a priori as piecewise constant, and we specify a gamma prior on its values. This leads to a straightforward procedure for posterior inference via an MCMC procedure. We give theoretical performance guarantees (minimax optimal contraction rates for the posterior) for the Bayesian estimate in terms of the regularity of the unknown volatility function. We illustrate the method on synthetic and real data examples.

Dirichlet Process Mixture of Generalized Inverted Dirichlet Distributions for Positive Vector Data With Extended Variational Inference.

A Bayesian nonparametric approach for estimation of a Dirichlet process (DP) mixture of generalized inverted Dirichlet distributions [i.e., an infinite generalized inverted Dirichlet mixture model (InGIDMM)] has been proposed. The generalized inverted Dirichlet distribution has been proven to be efficient in modeling the vectors that contain only positive elements. Under the classical variational inference (VI) framework, the key challenge in the Bayesian estimation of InGIDMM is that the expectation of the joint distribution of data and variables cannot be explicitly calculated. Therefore, numerical methods are usually applied to simulate the optimal posterior distributions. With the recently proposed extended VI (EVI) framework, we introduce lower bound approximations to the original variational objective function in the VI framework such that an analytically tractable solution can be derived. Hence, the problem in numerical simulation has been overcome. By applying the DP mixture technique, an InGIDMM can automatically determine the number of mixture components from the observed data. Moreover, the DP mixture model with an infinite number of mixture components also avoids the problems of underfitting and overfitting. The performance of the proposed approach is demonstrated with both synthesized data and real-life data applications.

Non-parametric Calibration of Multiple Related Radiocarbon Determinations and their Calendar Age Summarisation

AbstractDue to fluctuations in past radiocarbon (14C) levels, calibration is required to convert 14C determinations Xi into calendar ages θi. In many studies, we wish to calibrate a set of related samples taken from the same site or context, which have calendar ages drawn from the same shared, but unknown, density f(θ). Calibration of X1,…,Xn can be improved significantly by incorporating the knowledge that the samples are related. Furthermore, summary estimates of the underlying shared f(θ) can provide valuable information on changes in population size/activity over time. Most current approaches require a parametric specification for f(θ) which is often not appropriate. We develop a rigorous non-parametric Bayesian approach using a Dirichlet process mixture model, with slice sampling to address the multi-modality typical within 14C calibration. Our approach simultaneously calibrates the set of 14C determinations and provides a predictive estimate for the underlying calendar age of a future sample. We show, in a simulation study, the improvement in calendar age estimation when jointly calibrating related samples using our approach, compared with calibration of each 14C determination independently. We also illustrate the use of the predictive calendar age estimate to provide insight on activity levels over time using three real-life case studies.

Estimation of entropy and extropy based on right censored data: A Bayesian non-parametric approach

Abstract Entropy and extropy are central measures in information theory. In this paper, Bayesian non-parametric estimators to entropy and extropy with possibly right censored data are proposed. The approach uses the beta-Stacy process and the difference operator. Examples are presented to illustrate the performance of the estimators.

A dependent Bayesian Dirichlet process model for source apportionment of particle number size distribution.

The relationship between particle exposure and health risks has been well established in recent years. Particulate matter (PM) is made up of different components coming from several sources, which might have different level of toxicity. Hence, identifying these sources is an important task in order to implement effective policies to improve air quality and population health. The problem of identifying sources of particulate pollution has already been studied in the literature. However, current methods require an a priori specification of the number of sources and do not include information on covariates in the source allocations. Here, we propose a novel Bayesian nonparametric approach to overcome these limitations. In particular, we model source contribution using a Dirichlet process as a prior for source profiles, which allows us to estimate the number of components that contribute to particle concentration rather than fixing this number beforehand. To better characterize them we also include meteorological variables (wind speed and direction) as covariates within the allocation process via a flexible Gaussian kernel. We apply the model to apportion particle number size distribution measured near London Gatwick Airport (UK) in 2019. When analyzing this data, we are able to identify the most common PM sources, as well as new sources that have not been identified with the commonly used methods.

A general modeling framework for open wildlife populations based on the Polya tree prior.

Wildlife monitoring for open populations can be performed using a number of different survey methods. Each survey method gives rise to a type of data and, in the last five decades, a large number of associated statistical models have been developed for analyzing these data. Although these models have been parameterized and fitted using different approaches, they have all been designed to either model the pattern with which individuals enter and/or exit the population, or to estimate the population size by accounting for the corresponding observation process, or both. However, existing approaches rely on a predefined model structure and complexity, either by assuming that parameters linked to the entry and exit pattern (EEP) are specific to sampling occasions, or by employing parametric curves to describe the EEP. Instead, we propose a novel Bayesian nonparametric framework for modeling EEPs based on the Polya tree (PT) prior for densities. Our Bayesian nonparametric approach avoids overfitting when inferring EEPs, while simultaneously allowing more flexibility than is possible using parametric curves. Finally, we introduce the replicate PT prior for defining classes of models for these data allowing us to impose constraints on the EEPs, when required. We demonstrate our new approach using capture-recapture, count, and ring-recovery data for two different casestudies.

Bayesian Survival Tree Ensembles with Submodel Shrinkage

We consider Bayesian nonparametric estimation of a survival time subject to right-censoring in the presence of potentially high-dimensional predictors. We argue that several approaches, such as random survival forests and existing Bayesian nonparametric approaches, possess several drawbacks, including: computational difficulties; lack of known theoretical properties; and ineffectiveness at filtering out irrelevant predictors. We propose two models based on the Bayesian additive regression trees (BART) framework. The first, Modulated BART (MBART), is fully-nonparametric and models the failure time as the first occurrence of a non-homogeneous Poisson process. The second, CoxBART, uses a Bayesian implementation of Cox’s partial likelihood. These models are adapted to high-dimensional predictors, have default prior specifications, and require simple modifications of existing BART methods to implement. We show the effectiveness of these methods on simulated and benchmark datasets. We also establish that, for a simplified variant of MBART, the posterior distribution contracts at a near-minimax optimal rate in a high-dimensional sparse asymptotic regime.

Ordered community detection in directed networks.

We develop a method to infer community structure in directed networks where the groups are ordered in a latent one-dimensional hierarchy that determines the preferred edge direction. Our nonparametric Bayesian approach is based on a modification of the stochastic block model (SBM), which can take advantage of rank alignment and coherence to produce parsimonious descriptions of networks that combine ordered hierarchies with arbitrary mixing patterns between groups. Since our model also includes directed degree correction, we can use it to distinguish nonlocal hierarchical structure from local in- and out-degree imbalance-thus, removing a source of conflation present in most ranking methods. We also demonstrate how we can reliably compare with the results obtained with the unordered SBM variant to determine whether a hierarchical ordering is statistically warranted in the first place. We illustrate the application of our method on a wide variety of empirical networks across several domains.

Towards smart monitoring of systems: an integrated non-parametric Bayesian KDE and LSTM approach for anomaly detection of rotating machinery under uncertainties

The Bayesian inference metric is derived from the normality assumption of data, and is widely used in engineering applications. Owing to data scarcity and uncertainty, the assumption is usually violated, leading to inaccurate results in anomaly detection of large rotating machinery. This paper proposes a novel non-parametric Bayesian evaluation metric based on kernel density estimation of data to avoid the normality assumption. Based on kernel density estimation, a non-parametric Bayesian evaluation metric is mathematically derived from both null and alternative hypothesis tests to improve its accuracy and generality without any distribution assumption. It provides a quantitative indicator for assessing the status of a rotating machines under data uncertainties. A comparison with the traditional method is conducted to demonstrate the effectiveness and feasibility of the proposed methodology in terms of normal and non-normal distributions of data. A general Bayesian evaluation procedure is proposed for the anomaly detection of rotating machinery. Sensor data collected from a real-world steam turbine were used to illustrate the effectiveness of the proposed method.

Towards predicting liquid fuel physicochemical properties using molecular dynamics guided machine learning models

Accurate determination of fuel properties of complex mixtures over a wide range of pressure and temperature conditions is essential to utilizing alternative fuels. The present work aims to construct cheap-to-compute machine learning (ML) models to act as closure equations for predicting the physical properties of alternative fuels. Those models can be trained using the database from MD simulations and/or experimental measurements in a data-fusion-fidelity approach. Here, Gaussian Process (GP) and probabilistic generative models are adopted. GP is a popular non-parametric Bayesian approach to build surrogate models mainly due to its capacity to handle the aleatory and epistemic uncertainties. Generative models have shown the ability of deep neural networks employed with the same intent. In this work, ML analysis is focused on two particular properties, the fuel density and diffusion, but it can also be extended to other physicochemical properties. This study explores the versatility of the ML models to handle multi-fidelity data. The results show that ML models can predict accurately the fuel properties of a wide range of pressure and temperature conditions.

Nonparametric Bayesian modelling of longitudinally integrated covariance functions on spheres

Taking into account axial symmetry in the covariance function of a Gaussian random field is essential when the purpose is modelling data defined over a large portion of the sphere representing our planet. Axially symmetric covariance functions admit a convoluted spectral representation that makes modelling and inference difficult. This motivates the interest in devising alternative strategies to attain axial symmetry, an appealing option being longitudinal integration of isotropic random fields on the sphere. This paper provides a comprehensive theoretical framework to model longitudinal integration on spheres through a nonparametric Bayesian approach. Longitudinally integrated covariances are treated as random objects, where the randomness is implied by the randomised spectrum associated with the covariance function. After investigating the topological support induced by our construction, we give the posterior distribution a thorough inspection. A Bayesian nonparametric model for the analysis of data defined on the sphere is described and implemented, its performance investigated by means of the analysis of both simulated and real data sets.

Towards healthy school neighbourhoods: A baseline analysis in Greater London.

Creating healthy environments around schools is important to promote healthy childhood development and is a critical component of public health. In this paper we present a tool to characterize exposure to multiple urban environment features within 400m (5-10min walking distance) of schools in Greater London. We modelled joint exposure to air pollution (NO2 and PM2.5), access to public greenspace, food environment, and road safety for 2,929 schools, employing a Bayesian non-parametric approach based on the Dirichlet Process Mixture modelling. We identified 12 latent clusters of schools with similar exposure profiles and observed some spatial clustering patterns. Socioeconomic and ethnicity disparities were manifested with respect to exposure profiles. Specifically, three clusters (containing 645 schools) showed the highest joint exposure to air pollution, poor food environment, and unsafe roads and were characterized with high deprivation. The neighbourhood of the most deprived cluster of schools had a median of 2.5ha greenspace, 29.0µg/m3 of NO2, 19.3µg/m3 of PM2.5, 20 fast food retailers, and five child pedestrian crashes over a three-year period. The neighbourhood of the least deprived cluster of schools had a median of 21.8ha greenspace, 15.6µg/m3 of NO2, 15.1µg/m3 of PM2.5, 2 fast food retailers, and one child pedestrian crash over a three-year period. To have a school-level understanding of exposure levels, we then benchmarked schools based on the probability of exceeding the median exposure to various features of interest. Our study accounts for multiple exposures, enabling us to highlight spatial distribution of exposure profile clusters, and to identify predominant exposure to urban environment features for each cluster of schools. Our findings can help relevant stakeholders, such as schools and public health authorities, to compare schools based on their exposure levels, prioritize interventions, and design local policies that target the schools most in need.

Bayesian nonparametric inference for the overlap coefficient: With an application to disease diagnosis.

Diagnostic tests play an important role in medical research and clinical practice. The ultimate goal of a diagnostic test is to distinguish between diseased and nondiseased individuals and before a test is routinely used in practice, it is a pivotal requirement that its ability to discriminate between these two states is thoroughly assessed. The overlap coefficient, which is defined as the proportion of overlap area between two probability density functions, has gained popularity as a summary measure of diagnostic accuracy. We propose two Bayesian nonparametric estimators, based on Dirichlet process mixtures, for estimating the overlap coefficient. We further introduce the covariate‐specific overlap coefficient and develop a Bayesian nonparametric approach based on Dirichlet process mixtures of additive normal models for estimating it. A simulation study is conducted to assess the empirical performance of our proposed estimators. Two illustrations are provided: one concerned with the search for biomarkers of ovarian cancer and another one aimed to assess the age‐specific accuracy of glucose as a biomarker of diabetes.

Abstract 1224: UMIBB: A novel nonparametric Bayesian method improves robustness and sensitivity of analysis in pooled CRISPR-Cas9 screens leveraging unique molecular identifiers

Abstract CRISPR-based functional genomics screens are a powerful tool for identifying synthetically lethal cancer drug targets. Current strategies for analyzing pooled CRISPR screens usually rely on signals from single guide RNAs (sgRNA) with differential relative abundance between two experimental conditions. However, conventional approaches are susceptible to false positives and false negatives driven by outlier cell clones, since the sgRNA abundance does not account for the heterogeneous phenotypes resulting from different editing outcomes of the same sgRNA. To overcome this, we added DNA barcodes to each sgRNA to create unique molecular identifiers (UMIs) for CRISPR libraries and developed a companion analytical platform that enables robust, industry-scale CRISPR screens. Here, we present UMIBB, a novel nonparametric Bayesian approach for analyzing UMI-CRISPR data. The number of UMIs with normalized count depletion or enrichment compared to the control experimental condition for each sgRNA is modeled by a beta-binomial distribution. The gene level statistics are derived by combining z-scores of the sgRNAs level posterior probabilities weighted by the number of UMIs in each sgRNA. This approach minimizes the impact of outlier cell clones on statistics and prioritizes genes with consistent count differentials across multiple UMIs in each gene. To assess the power of UMIBB, we benchmarked it on a low coverage (200X) genome-scale negative-selection screen, comparing with results from a high coverage (1000X) screen. These screens were conducted on KRAS mutant cancer celllines (A549) treated with trametinib or vehicle control. Despite the high noise level usually observed in lower coverage screens, our method was able to uncover most of the validated sensitizer genes for trametinib and achieved the highest sensitivity compared to conventional methods. Furthermore, we applied UMIBB on a genome-scale positive-selection screen and successfully identified novel genes (RAD18 and UBE2K) as key mediators of USP1 dependency in BRCA1 mutant cell lines. Our studies demonstrate that UMIBB is highly robust against false positives due to clonal heterogeneity and is more likely to identify true genetic interactions. Citation Format: Ashley Choi, Samuel Meier, Silvia Fenoglio, Tianshu Feng, Justin Engel, Binzhang Shen, Shangtao Liu, Teng Teng, Tenzing Khendu, Alan Huang, Jannik Andersen, Xuewen Pan, Yi Yu. UMIBB: A novel nonparametric Bayesian method improves robustness and sensitivity of analysis in pooled CRISPR-Cas9 screens leveraging unique molecular identifiers [abstract]. In: Proceedings of the American Association for Cancer Research Annual Meeting 2022; 2022 Apr 8-13. Philadelphia (PA): AACR; Cancer Res 2022;82(12_Suppl):Abstract nr 1224.