Student-t Distribution Research Articles

Multivariate Gaussian and Student-t process regression for multi-output prediction

Gaussian process model for vector-valued function has been shown to be useful for multi-output prediction. The existing method for this model is to reformulate the matrix-variate Gaussian distribution as a multivariate normal distribution. Although it is effective in many cases, reformulation is not always workable and is difficult to apply to other distributions because not all matrix-variate distributions can be transformed to respective multivariate distributions, such as the case for matrix-variate Student-t distribution. In this paper, we propose a unified framework which is used not only to introduce a novel multivariate Student-t process regression model (MV-TPR) for multi-output prediction, but also to reformulate the multivariate Gaussian process regression (MV-GPR) that overcomes some limitations of the existing methods. Both MV-GPR and MV-TPR have closed-form expressions for the marginal likelihoods and predictive distributions under this unified framework and thus can adopt the same optimization approaches as used in the conventional GPR. The usefulness of the proposed methods is illustrated through several simulated and real-data examples. In particular, we verify empirically that MV-TPR has superiority for the datasets considered, including air quality prediction and bike rent prediction. At last, the proposed methods are shown to produce profitable investment strategies in the stock markets.

Maximum likelihood estimation of high-dimensional Student-[formula omitted] copulas

This paper suggests a simple iterative and robust maximum likelihood estimation method for the parameters of a high-dimensional Student t-distribution that is substantially faster than direct maximum likelihood approaches.

Geogrid installation damage caused by recycled construction and demolition waste

Using recycled construction and demolition waste (RCDW) in geosynthetic reinforced soil (GRS) structures presents attractive environmental and economic aspects. However, bearing in mind installation damage can be responsible for significant changes in geosynthetic tensile-strain behavior, the damage caused by the RCDW must be assessed and quantified. This study aims to investigate the occurrence of mechanical damage during the installation of geogrids with RCDW backfill material using an in-field test facility. In order to understand the mechanisms related to the damage, the influences of the dropping height and compaction method were investigated. Statistical analysis using the Student's t-distribution was carried out to validate the occurrence of damage and calculate reduction factors for geogrids’ tensile strengths. Results revealed that dropping processes reduced the geogrid ultimate tensile strengths, but the compaction methods caused the highest reductions. The reduction factor values encourage the design of GRS structures with RCDW, an interesting option to satisfy the technical and economic aspects required for these structures in agreement with the environmental concerns.

Efficacy of antiviral treatment in cytomegalovirus detected ulcerative colitis: meta-analysis of available data

Aim: This meta-analysis aimed to pool available data regarding the efficacy of ganciclovir treatment among cytomegalovirus-detected ulcerative colitis patients.Methods: We screened PubMed, Ovid, Web of Science and Cochrane databases for relevant studies, and four investigators independently evaluated the studies for eligibility. The primary outcome was surgical resection or death from ulcerative colitis. The data were then pooled via DerSimonian–Laird estimator and Mantel–Haenszel (MH) method, two points added for continuity correction and random-effects model fitted in the Bayesian framework. We first constructed a Bugs model with Student t-distribution as prior for between-study heterogeneity. The model was fitted by Gibbs sampler (JAGS) to produce a marginal posterior distribution.Results: Our screening identified 15 eligible studies for final data synthesis and combined data from 191 ganciclovir-treated and 166 non-treated patients. Effect estimates from the fixed-effects meta-analysis model did not encourage ganciclovir treatment (OR, 1.43; 95% CIs [0–95, 2.16]), with a negligible unaccounted heterogeneity (I2 = 0%). The Bayesian random-effects model generated high-density credible intervals, suggesting a high probability, that future studies will also not encourage ganciclovir treatment (mu, 1.028; 95% credible intervals [0.054, 2.238]; 80% credible intervals [0.401, 1.703]) which indicates that future studies will favor non-treatment of ulcerative colitis with ganciclovir.Conclusions: Data produced in this study do not encourage ganciclovir treatment for UC patients. However, studies included in this analysis were observational, and thus, inherited severe selection bias. We suggest randomized controlled studies be conducted to make firm recommendations in this context.

Quality Of Life And Stigma Among People Living With HIV/AIDS In Iran.

BackgroundStigma against HIV profoundly affects the quality of life (QOL) of people living with HIV/AIDS (PLWHA). We aimed to assess the factors associated with QOL in PLWHA in Iran, specifically HIV-related stigma, sociodemographic and clinical characteristics.MethodsTwo hundred PLWHA participated in this cross-sectional study. Data were collected using sociodemographic, stigma, and WHO-QOL-BREF questionnaires. Correlations, ANOVAs, and Student’s t-distribution tests were performed as bivariate analyses. We employed stepwise multiple linear regression analysis to explore the main factors associated with QOL domains.ResultsSix domains of QOL were negatively correlated with three domains of stigma (p<0.001 for all). Stepwise multiple linear regression revealed that, after adjusting for confounders, lack of healthcare insurance, having no basic knowledge of HIV/AIDs prior to diagnosis, low monthly income of participants and family, and stigma (blaming and distancing, discrimination, and fear) were associated with low mean score of different domains of QOL.ConclusionOur findings indicated that increasing HIV/AIDS-related stigma decreases QOL in PLWHA in Iran. Attention toward decreasing stigma, improving healthcare plan, and cultivating economic condition should be given high priority to ensure improvement in total QOL and corresponding domains in PLWHA’s life.

A Novel Kullback–Leibler Divergence Minimization-Based Adaptive Student's t-Filter

In this paper, in order to improve the Student's t-matching accuracy, a novel Kullback-Leibler divergence (KLD) minimization-based matching method is firstly proposed by minimizing the upper bound of the KLD between the true Student's t-density and the approximate Student's t-density. To improve the Student's t-modelling accuracy, a novel KLD minimization-based adaptive method is then proposed to estimate the scale matrices of Student's t-distributions, in which the modified evidence lower bound is maximized. A novel KLD minimization-based adaptive Student's t-filter is derived via combining the proposed Student's t-matching technique and the adaptive method. A manoeuvring target tracking example is provided to demonstrate the effectiveness and potential of the proposed filter.

Bayesian estimation of a multivariate TAR model when the noise process follows a Student-t distribution

In this paper, we introduce a Bayesian methodology for the estimation of non-structural parameters (autoregressive matrices, covariance matrices and degrees of freedom) of a multivariate TAR model (MTAR) when noise process follows a multivariate Student-t distribution. For this, the use of non-informative prior distributions is proposed to obtain the full conditional distributions. MCMC methods are used to obtain samples of such distributions. The performance of the estimation is evaluated by means simulations. Finally, the model is applied to the returns data from the Bovespa, Colcap and Standard and Poor indexes.

Comparing the Forecasting of Cryptocurrencies by Bayesian Time-Varying Volatility Models

This paper studies the forecasting ability of cryptocurrency time series. This study is about the four most capitalised cryptocurrencies: Bitcoin, Ethereum, Litecoin and Ripple. Different Bayesian models are compared, including models with constant and time-varying volatility, such as stochastic volatility and GARCH. Moreover, some cryptopredictors are included in the analysis, such as S&amp;P 500 and Nikkei 225. In this paper, the results show that stochastic volatility is significantly outperforming the benchmark of VAR in both point and density forecasting. Using a different type of distribution, for the errors of the stochastic volatility, the student-t distribution is shown to outperform the standard normal approach.

Caracterización epidemiológica de pacientes con enfermedad cerebral vascular aguda en un hospital de Chile en base a registros de grupos relacionados al diagnóstico

Stroke is the leading cause of death and disability in Chile. To analyze the epidemiological characteristics of hospitalized patients with a diagnosis of stroke in our hospital unit (Complejo Asistencial Víctor Ríos Ruiz). We performed an observational, cross-sectional study. We included patients who were discharged from our hospital with a diagnosis of stroke between 2014 and 2017. We extracted data on stroke-related ICD codes, demographic variables, types of stroke, case fatality rates, and hospital stay. Quantitative variables were expressed as averages with standard deviation (± SD), and categorical variables were expressed as absolute and relative frequencies. Differences were analyzed using Student t-distribution and ANOVA. We defined a p-value of < 0.05 as statistically significant. In total, 1856 patients were discharged of which 58.6% were male, with an average age of 66.9 (± 13.9) years, and an average stay of 10.4 (± 16.7) days. In the female population, the average age was 69.9 (± 16), and the average hospitalization was 11.1 (± 16.5) days. 55.5% of stroke cases was ischemic, and 17.4% was hemorrhagic. The main risk factors were hypertension (72%) and type 2 diabetes (33%). We found an overall in-hospital case fatality rate of 10.6%. Both the case fatality rate and prolonged in-hospital stay were associated with subarachnoid hemorrhage and hemorrhagic stroke (p < 0.05). Prevalence of stroke is similar in both men and women. Hypertension was the leading risk factor associated with acute stroke. Although ischemic stroke was the most frequent diagnosis, both subarachnoid hemorrhage and hemorrhagic stroke were related to an increased case fatality rate and a more extended hospital stay.

Modeling Heteroscedasticity in the Presence of Serial Correlations in Discrete-time Stochastic Series: A GARCH-in-Mean Approach

Background: In modeling heteroscedasticity of returns, it is often assumed that the series are uncorrelated. In practice, such series with small time periods between observations can be observed to contain significant serial correlations, hence the motivation for this research.&#x0D; Aim: The aim of this research is to assess the existence of serial correlations in the return series of Zenith Bank Plc, which is targeted at identifying their effects on the parameter estimates of heteroscedastic models.&#x0D; Materials and Methods: The data were obtained from the Nigerian Stock Exchange spanning from January 3, 2006, to November 24, 2016, having 2690 observations. The hybridized Autoregressive Integrated Moving Average-Generalized Autoregressive Conditional Heteroscedasticity (ARIMA-GARCH-type) models such as Autoregressive Integrated Moving Average-Generalized Autoregressive Conditional Heteroscedasticity (ARIMA-GARCH), Autoregressive Integrated Moving Average-Exponential Generalized Autoregressive Conditional Heteroscedasticity (ARIMA-EGARCH) and the Autoregressive Integrated Moving Average-Glosten, Jagannathan and Runkle Generalized Autoregressive Conditional Heteroscedastic (ARIMA-GJRGARCH) under normal and student-t distributions were employed to model the conditional variance while the GARCH-in-Mean-GARCH-type model corresponding to the selected ARIMA-GARCH-type model was applied to appraise the possible existence of serial correlations.&#x0D; Results: The findings of this study showed that heteroscedasticity exists and appeared to be adequately captured by ARIMA(2,1,1)-EGARCH(1,1) model under student-t distribution but failed to account for the presence of serial correlations in the series. Meanwhile, its counterpart, GARCH-in-Mean-EGARCH(1,1) model under student-t distribution sufficiently appraised the existence of serial correlations.&#x0D; Conclusion: One remarkable implication is that the estimates of the parameters of ARIMA-GARCH-type model are likely to be biased when the presence of serial correlations is ignored. Also, the application of GARCH-in-Mean-GARCH-type model possibly provides the feedback mechanism or interaction between the variance and mean equations.

Student-t policy in reinforcement learning to acquire global optimum of robot control

This paper proposes an actor-critic algorithm with a policy parameterized by student-t distribution, named student-t policy, to enhance learning performance, mainly in terms of reachability on global optimum for tasks to be learned. The actor-critic algorithm is one of the policy-gradient methods in reinforcement learning, and is proved to learn the policy converging on one of the local optima. To avoid the local optima, an exploration ability to escape it and a conservative learning not to be trapped in it are deemed to be empirically effective. The conventional policy parameterized by a normal distribution, however, fundamentally lacks these abilities. The state-of-the-art methods can somewhat but not perfectly compensate for them. Conversely, heavy-tailed distribution, including student-t distribution, possesses an excellent exploration ability, which is called Levy flight for modeling efficient feed detection of animals. Another property of the heavy tail is its robustness to outliers. Namely, conservative learning is performed to not be trapped in the local optima even when it takes extreme actions. These desired properties of the student-t policy enhance the possibility of the agents reaching the global optimum. Indeed, the student-t policy outperforms the conventional policy in four types of simulations, two of which are difficult to learn faster without sufficient exploration and the others have the local optima.

Registration of vascular structures using a hybrid mixture model.

Morphological changes to anatomy resulting from invasive surgical procedures or pathology, typically alter the surrounding vasculature. This makes it useful as a descriptor for feature-driven image registration in various clinical applications. However, registration of vasculature remains challenging, as vessels often differ in size and shape, and may even miss branches, due to surgical interventions or pathological changes. Furthermore, existing vessel registration methods are typically designed for a specific application. To address this limitation, we propose a generic vessel registration approach useful for a variety of clinical applications, involving different anatomical regions. A probabilistic registration framework based on a hybrid mixture model, with a refinement mechanism to identify missing branches (denoted as HdMM+) during vasculature matching, is introduced. Vascular structures are represented as 6-dimensional hybrid point sets comprising spatial positions and centerline orientations, using Student's t-distributions to model the former and Watson distributions for the latter. The proposed framework is evaluated for intraoperative brain shift compensation, and monitoring changes in pulmonary vasculature resulting from chronic lung disease. Registration accuracy is validated using both synthetic and patient data. Our results demonstrate, HdMM+ is able to reduce more than [Formula: see text] of the initial error for both applications, and outperforms the state-of-the-art point-based registration methods such as coherent point drift and Student's t-distribution mixture model, in terms of mean surface distance, modified Hausdorff distance, Dice and Jaccard scores. The proposed registration framework models complex vascular structures using a hybrid representation of vessel centerlines, and accommodates intricate variations in vascular morphology. Furthermore, it is generic and flexible in its design, enabling its use in a variety of clinical applications.

Understanding Distributional Ambiguity via Non-robust Chance Constraint

This paper provides a non-robust interpretation of the distributionally robust optimization (DRO) problem by relating the distributional uncertainties to the chance probabilities. Our analysis allows a decision-maker to interpret the size of the ambiguity set, which is often lack of business meaning, through the chance parameters constraining the objective function. We first show that, for general ϕ-divergences, a DRO problem is asymptotically equivalent to a class of mean-deviation problems. These mean-deviation problems are not subject to uncertain distributions, and the ambiguity radius in the original DRO problem now plays the role of controlling the risk preference of the decision-maker. We then demonstrate that a DRO problem can be cast as a chance-constrained optimization (CCO) problem when a boundedness constraint is added to the decision variables. Without the boundedness constraint, the CCO problem is shown to perform uniformly better than the DRO problem, irrespective of the radius of the ambiguity set, the choice of the divergence measure, or the tail heaviness of the center distribution. Thanks to our high-order expansion result, a notable feature of our analysis is that it applies to divergence measures that accommodate well heavy tail distributions such as the student t-distribution and the lognormal distribution, besides the widely-used Kullback-Leibler (KL) divergence, which requires the distribution of the objective function to be exponentially bounded. Using the portfolio selection problem as an example, our comprehensive testings on multivariate heavy-tail datasets, both synthetic and real-world, shows that this business-interpretation approach is indeed useful and insightful.

Late Reverberation Cancellation Using Bayesian Estimation of Multi-Channel Linear Predictors and Student's t-Source Prior

Multi-channel linear prediction MCLP can model the late reverberation in the short-time Fourier transform domain using a delayed linear predictor and the prediction residual is taken as the desired early reflection component. Traditionally, a Gaussian source model with time-dependent precision inverse of variance is considered for the desired signal. In this paper, we propose a Student's t-distribution model for the desired signal, which is realized as a Gaussian source with a Gamma distributed precision. Further, since the choice of a proper MCLP order is critical, we also incorporate a Gaussian distribution prior for the prediction coefficients and a higher order. We consider a batch estimation scenario and develop variational Bayes expectation maximization VBEM algorithm for joint posterior inference and hyper-parameter estimation. This has lead to more accurate and robust estimation of the late reverb component and hence its cancellation, benefitting the desired residual signal estimation. Along with these stochastic models, we formulate single channel output MISO and multi channel output MIMO schemes using shared priors for the desired signal precision and the estimated MCLP coefficients at each microphone. Experiments using real room impulse responses show improved late reverberation suppression with the proposed VBEM approach over the traditional methods, for different room conditions. Additionally, we achieve a sparse coefficient vector for the MCLP avoiding the criticality of manually choosing the model order. The MIMO formulation is easily extended to include spatial filtering of the enhanced signals, which further improves the estimation of the desired signal.

Joint target detection and tracking with heavy-tailed noises

This paper investigates the problem of simultaneous target detection and tracking with heavy-tailed noises under Bernoulli filtering framework. By exploiting the Student-t distributions to formulate the outlier-corrupted process noise and measurement noise, a novel target tracking algorithm named the Student-t mixture Bernoulli filter is proposed. Under linear assumptions on target dynamic model, sensor measurement model and birth process, closed-form recursions that propagate the parameters of Bernoulli random finite set are derived. The validity of the proposed algorithm is verified by numerical simulations.

Which Factors are Risk Factors in Asset Pricing? A Model Scan Framework

A key question for understanding the cross-section of expected returns of equities is the following: which factors, from a given collection of factors, are risk factors, equivalently, which factors are in the stochastic discount factor (SDF)? Though the SDF is unobserved, assumptions about which factors (from the available set of factors) are in the SDF restricts the joint distribution of factors in specific ways, as a consequence of the economic theory of asset pricing. A different starting collection of factors that go into the SDF leads to a different set of restrictions on the joint distribution of factors. The conditional distribution of equity returns has the same restricted form, regardless of what is assumed about the factors in the SDF, as long as the factors are traded, and hence the distribution of asset returns is irrelevant for isolating the risk-factors. The restricted factors models are distinct (nonnested) and do not arise by omitting or including a variable from a full model, thus precluding analysis by standard statistical variable selection methods, such as those based on the lasso and its variants. Instead, we develop what we call a Bayesian model scan strategy in which each factor is allowed to enter or not enter the SDF and the resulting restricted models (of which there are 114,674 in our empirical study) are simultaneously confronted with the data. We use a Student-t distribution for the factors, and model-specific independent Student-t distribution for the location parameters, a training sample to fix prior locations, and a creative way to arrive at the joint distribution of several other model-specific parameters from a single prior distribution. This allows our method to be essentially a scaleable and tuned-black-box method that can be applied across our large model space with little to no user-intervention. The model marginal likelihoods, and implied posterior model probabilities, are compared with the prior probability of 1/114,674 of each model to find the best-supported model, and thus the factors most likely to be in the SDF. We provide detailed simulation evidence about the high finite-sample accuracy of the method. Our empirical study with 13 leading factors reveals that the highest marginal likelihood model is a Student-t distributed factor model with 5 degrees of freedom and 8 risk factors.

Nanosatellite attitude estimation using Kalman-type filters with non-Gaussian noise

In order to control the orientation of a satellite, it is important to estimate the attitude accurately. Time series estimation is especially important in micro and nanosatellites, whose sensors are usually low-cost and have higher noise levels than high end sensors. Also, the algorithms should be able to run on systems with very restricted computer power. In this work, we evaluate five Kalman-type filtering algorithms for attitude estimation with 3-axis magnetometer and sun sensor measurements. The Kalman-type filters are selected so that each of them is designed to mitigate one error source for the unscented Kalman filter that is used as baseline. We investigate the distribution of the magnetometer noises and show that the Student's t-distribution is a better model for them than the Gaussian distribution. We consider filter responses in four operation modes: steady state, recovery from incorrect initial state, short-term sensor noise increment, and long-term increment. We find that a Kalman-type filter designed for Student's t sensor noises has the best combination of accuracy and computational speed for these problems, which leads to a conclusion that one can achieve more improvements in estimation accuracy by using a filter that can work with heavy tailed noise than by using a nonlinearity minimizing filter that assumes Gaussian noise.

Modeling of Returns Volatility using GARCH(1,1) Model under Tukey Transformations

This study proposed two new classes of GARCH(1,1) model by applying the Tukeytransformations to the returns and to the lagged variance. The behavior of return volatility was investigated on the basis of models with normal and Student-t distributions for return error. The competing models were estimated by using the Excel Solver and Matlab tools. The empirical analysis is based on simulated data, daily exchange rates of the IDR/USD, and daily stock indices of FTSE100 and TOPIX. This study recommends the use of Excel Solver for finance academics and practitioners working on volatility using GARCH(1,1) models. Our empirical findings conclude that GARCH(1,1) models under Tukey transformations should be considered in risk management decisions since the models are more appropriate than standard for describing returns and volatility of financial time series and its stylized facts including fat tails and mean reverting. The Tukey transformed returns imply a shorter volatility half-life, and thus this study suggests that investors should invest the observed assets in a shorter time period to obtain higher returns.

CREATION AND STANDARDIZATION OF “THE INTERSUBJECTNESS DIAGNOSTIC SURVEY”

Конструкт інтерсуб’єктності стосується таких особливостей взаємодії людей, які орієнтовані на розкриття потенціалу людини, розвиток рівня особистої суб’єктності, баланс емпатії та самореалізації у спілкуванні. Процес створення та стандартизації «Методики діагностики інтерсуб’єктності» тривав півтора роки (з серпня 2017 року по лютий 2019 року). Досліджуваною вибіркою стали 518 україномовних осіб юнацького віку з різних місць проживання та навчання (Ніжин, Київ, Суми, Чернігів, Сновськ, с. Пакуль). Альфа Кронбаха становить α=0,831, що є добрим рівнем внутрішньої узгодженості та надійності методики. Методика показала достатню ретестову надійність (коефіцієнт кореляції Спірмена r=0,516, р≤0,01). Наявність значущих кореляційних зв’язків за всіма шкалами методик, які співставлялися з «Методикою дослідження інтерсуб’єктності», є свідченням її конструктної та конвергентної валідності. У процесі факторного аналізу пунктів методики було виділено чотири фактори: «Розуміння людей та особисте натхнення»; «Спілкування і взаємодія»; «Врахування суб’єктної позиції іншого»; «Чути інших та бути почутим». За допомогою z-оцінок були обраховані тестові норми і виділені низький, середній та високий рівні інтерсуб’єктності. &nbsp

Robust Identification of Nonlinear Systems With Missing Observations: The Case of State-Space Model Structure

This paper investigates the robust identification of nonlinear systems in state-space setting with output measurements contaminated with outliers and part of output measurements missing at random. The problems of outliers and missing observations are often encountered in practical industrial processes and are taken into consideration comprehensively in this work. The robust Student's t-based observation model is built to model the output measurements with stochastic outliers, and the impact of outliers imposed on nonlinear system identification can be suppressed through inference of the degree of freedom in Student's t-distribution. The proposed robust nonlinear system identification method with an incomplete dataset is derived with the expectation–maximization (EM) algorithm, and the particle filter is employed to numerically approximate the Q-function of the EM algorithm. A numerical example and a chemical process are utilized to demonstrate the superiority of the proposed strategy.