1. |
- Bodnar, Olha, senior lecturer, 1979-, et al.
(author)
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Bayesian estimation in multivariate inter-laboratory studies with unknown covariance matrices
- 2023
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In: Metrologia. - : IOP Publishing Ltd. - 0026-1394 .- 1681-7575. ; 60:5
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Journal article (peer-reviewed)abstract
- In the paper we present Bayesian inference procedures for the parameters of multivariate random effects model, which is used as a quantitative tool for performing multivariate key comparisons and multivariate inter-laboratory studies. The developed new approach does not require that the reported covariance matrices of participating laboratories are known and, as such, it can be used when they are estimated from the measurement results. The Bayesian inference procedures are based on samples generated from the derived posterior distribution when the Berger and Bernardo reference prior and the Jeffreys prior are assigned to the model parameter. Three numerical algorithms for the construction of Markov chains are provided and implemented in the CCAUV.V-K1 key comparisons. All three approaches yield similar Bayesian estimators with wider credible intervals when the Berger and Bernardo reference prior is used. Also, the Bayesian estimators for the elements of the inter-laboratory covariance matrix are larger under this prior than for the Jeffreys prior. Finally, the constructed joint credible sets for the components of the overall mean vector indicate the presence of linear dependence between them which cannot be captured when only univariate key comparisons are performed.
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2. |
- Bodnar, Olha, senior lecturer, 1979-, et al.
(author)
-
Bayesian estimation in multivariate inter-laboratory studies with unknown covariance matrices
- 2023
-
In: Metrologia. - : IOP Publishing Ltd. - 0026-1394 .- 1681-7575. ; 60:5
-
Journal article (peer-reviewed)abstract
- In the paper we present Bayesian inference procedures for the parameters of multivariate random effects model, which is used as a quantitative tool for performing multivariate key comparisons and multivariate inter-laboratory studies. The developed new approach does not require that the reported covariance matrices of participating laboratories are known and, as such, it can be used when they are estimated from the measurement results. The Bayesian inference procedures are based on samples generated from the derived posterior distribution when the Berger and Bernardo reference prior and the Jeffreys prior are assigned to the model parameter. Three numerical algorithms for the construction of Markov chains are provided and implemented in the CCAUV.V-K1 key comparisons. All three approaches yield similar Bayesian estimators with wider credible intervals when the Berger and Bernardo reference prior is used. Also, the Bayesian estimators for the elements of the inter-laboratory covariance matrix are larger under this prior than for the Jeffreys prior. Finally, the constructed joint credible sets for the components of the overall mean vector indicate the presence of linear dependence between them which cannot be captured when only univariate key comparisons are performed.
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3. |
- Bodnar, Olha, senior lecturer, 1979-, et al.
(author)
-
Constructing Bayesian tangency portfolios under short-selling restrictions
- 2024
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In: Finance Research Letters. - : Elsevier. - 1544-6123 .- 1544-6131. ; 62
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Journal article (peer-reviewed)abstract
- We address the challenge of constructing tangency portfolios in the context of short-selling restrictions. Utilizing Bayesian techniques, we reparameterize the asset return model, enabling direct determination of priors for the tangency portfolio weights. This facilitates the integration of non-negative weight constraints into an investor's prior beliefs, resulting in a posterior distribution focused exclusively on non-negative values. Portfolio weight estimators are subsequently derived via the Markov Chain Monte Carlo (MCMC) methodology. Our novel Bayesian approach is empirically illustrated using the most significant stocks in the S&P 500 index. The method showcases promising results in terms of risk-adjusted returns and interpretability.
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4. |
- Bodnar, Olha, senior lecturer, 1979-, et al.
(author)
-
Constructing Bayesian tangency portfolios under short-selling restrictions
- 2024
-
In: Finance Research Letters. - : Elsevier. - 1544-6123 .- 1544-6131. ; 62
-
Journal article (peer-reviewed)abstract
- We address the challenge of constructing tangency portfolios in the context of short-selling restrictions. Utilizing Bayesian techniques, we reparameterize the asset return model, enabling direct determination of priors for the tangency portfolio weights. This facilitates the integration of non-negative weight constraints into an investor’s prior beliefs, resulting in a posterior distribution focused exclusively on non-negative values. Portfolio weight estimators are subsequently derived via the Markov Chain Monte Carlo (MCMC) methodology. Our novel Bayesian approach is empirically illustrated using the most significant stocks in the S&P 500 index. The method showcases promising results in terms of risk-adjusted returns and interpretability.
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5. |
- Bodnar, Olha, senior lecturer, 1979-, et al.
(author)
-
Gibbs sampler approach for objective Bayesian inference in elliptical multivariate meta-analysis random effects model
- 2024
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In: Computational Statistics & Data Analysis. - : Elsevier. - 0167-9473 .- 1872-7352. ; 197
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Journal article (peer-reviewed)abstract
- Bayesian inference procedures for the parameters of the multivariate random effects model are derived under the assumption of an elliptically contoured distribution when the Berger and Bernardo reference and the Jeffreys priors are assigned to the model parameters. A new numerical algorithm for drawing samples from the posterior distribution is developed, which is based on the hybrid Gibbs sampler. The new approach is compared to the two Metropolis -Hastings algorithms previously derived in the literature via an extensive simulation study. The findings are applied to a Bayesian multivariate meta -analysis, conducted using the results of ten studies on the effectiveness of a treatment for hypertension. The analysis investigates the treatment effects on systolic and diastolic blood pressure. The second empirical illustration deals with measurement data from the CCAUV.V-K1 key comparison, aiming to compare measurement results of sinusoidal linear accelerometers at four frequencies.
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6. |
- Bodnar, Olha, et al.
(author)
-
Incorporating different sources of information for Bayesian optimal portfolio selection
- 2024
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In: Journal of business & economic statistics. - 0735-0015 .- 1537-2707.
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Journal article (other academic/artistic)abstract
- This paper introduces Bayesian inference procedures for tangency portfolios, with a primary focus on deriving a new conjugate prior for portfolioweights. This approach not only enables direct inference about the weightsbut also seamlessly integrates additional information into the prior specification. Specifically, it automatically incorporates high-frequency returns and amarket condition metric (MCM), exemplified by the CBOE Volatility Index(VIX) and Economic Policy Uncertainty Index (EPU), significantly enhancing the decision-making process for optimal portfolio construction. While theJeffreys prior is also acknowledged, emphasis is placed on the advantages andpractical applications of the conjugate prior. An extensive empirical studyreveals that our method, leveraging this conjugate prior, consistently outperforms existing trading strategies in the majority of examined cases.
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7. |
- Bodnar, Olha, senior lecturer, 1979-, et al.
(author)
-
Objective Bayesian Meta-Analysis Based on Generalized Marginal Multivariate Random Effects Model
- 2024
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In: Bayesian Analysis. - : International Society for Bayesian Analysis. - 1936-0975 .- 1931-6690. ; 19:2, s. 531-564
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Journal article (peer-reviewed)abstract
- Objective Bayesian inference procedures are derived for the parameters of the multivariate random effects model generalized to elliptically contoured distributions. The posterior for the overall mean vector and the between-study covariance matrix is deduced by assigning two noninformative priors to the model parameter, namely the Berger and Bernardo reference prior and the Jeffreys prior, whose analytical expressions are obtained under weak distributional assumptions. It is shown that the only condition needed for the posterior to be proper is that the sample size is larger than the dimension of the data-generating model, inde-pendently of the class of elliptically contoured distributions used in the definition of the generalized multivariate random effects model. The theoretical findings of the paper are applied to real data consisting of ten studies about the effectiveness of hypertension treatment for reducing blood pressure where the treatment effects on both the systolic blood pressure and diastolic blood pressure are investigated.
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8. |
- Bodnar, Olha, et al.
(author)
-
Objective Bayesian Meta-Analysis Based on Generalized Marginal Multivariate Random Effects Model
- 2024
-
In: Bayesian Analysis. - 1936-0975 .- 1931-6690. ; 19:2, s. 531-564
-
Journal article (peer-reviewed)abstract
- Objective Bayesian inference procedures are derived for the parameters of the multivariate random effects model generalized to elliptically contoured distributions. The posterior for the overall mean vector and the between -study covariance matrix is deduced by assigning two noninformative priors to the model parameter, namely the Berger and Bernardo reference prior and the Jeffreys prior, whose analytical expressions are obtained under weak distributional assumptions. It is shown that the only condition needed for the posterior to be proper is that the sample size is larger than the dimension of the data -generating model, independently of the class of elliptically contoured distributions used in the definition of the generalized multivariate random effects model. The theoretical findings of the paper are applied to real data consisting of ten studies about the effectiveness of hypertension treatment for reducing blood pressure where the treatment effects on both the systolic blood pressure and diastolic blood pressure are investigated. MSC2020 subject classifications: Primary 62F15, 62H10; secondary 62H12.
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9. |
- Bodnar, Olga, et al.
(author)
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Practical aspects of Bayesian multivariate meta-analysis : [Практичні аспекти Байєсівського багатовимірного мета-аналізу]
- 2022
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In: Ukrainian Metrological Journal. - : National Scientific Centre Institute of Metrology. - 2306-7039 .- 2522-1345. ; 2022:4, s. 7-11
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Journal article (peer-reviewed)abstract
- Multivariate meta-analysis is a mostly used approach when multivariate results of several studies are pooled together. The multivariate model of random effects provides a tool to perform the multivariate meta-analysis in practice. In this paper, we discuss Bayesian inference procedures derived for the multivariate model of random effects when the model parameters are endowed with two non-informative priors: the Berger-Bernardo reference prior and the Jeffreys prior. Moreover, two Metropolis-Hastings algorithms are presented, and their convergence properties are analysed via simulations.
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