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Abstract: Abstract In clinical trials of longitudinal continuous outcomes, reference based imputation (RBI) has commonly been applied to handle missing outcome data in settings where the estimand incorporates the effects of intercurrent events, e.g. treatment discontinuation. RBI was originally developed in the multiple imputation framework, however recently conditional mean imputation (CMI) combined with the jackknife estimator of the standard error was proposed as a way to obtain deterministic treatment effect estimates and correct frequentist inference. For both multiple and CMI, a mixed model for repeated measures (MMRM) is often used for the imputation model, but this can be computationally intensive to fit to multiple data sets (e.g. the jackknife samples) and lead to convergence issues with complex MMRM models with many parameters. Therefore, a step-wise approach based on sequential linear regression (SLR) of the outcomes at each visit was developed for the imputation model in the multiple imputation framework, but similar developments in the CMI framework are lacking. In this article, we fill this gap in the literature by proposing a SLR approach to implement RBI in the CMI framework, and justify its validity using theoretical results and simulations. We also illustrate our proposal on a real data application. PubDate: 2023-12-03
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Abstract: Abstract Without writing a single line of code by a human, an example Monte Carlo simulation-based application for stochastic dependence modeling with copulas is developed through pair programming involving a human partner and a large language model (LLM) fine-tuned for conversations. This process encompasses interacting with ChatGPT using both natural language and mathematical formalism. Under the careful supervision of a human expert, this interaction facilitated the creation of functioning code in MATLAB, Python, and R. The code performs a variety of tasks including sampling from a given copula model, evaluating the model’s density, conducting maximum likelihood estimation, optimizing for parallel computing on CPUs and GPUs, and visualizing the computed results. In contrast to other emerging studies that assess the accuracy of LLMs like ChatGPT on tasks from a selected area, this work rather investigates ways how to achieve a successful solution of a standard statistical task in a collaboration of a human expert and artificial intelligence (AI). Particularly, through careful prompt engineering, we separate successful solutions generated by ChatGPT from unsuccessful ones, resulting in a comprehensive list of related pros and cons. It is demonstrated that if the typical pitfalls are avoided, we can substantially benefit from collaborating with an AI partner. For example, we show that if ChatGPT is not able to provide a correct solution due to a lack of or incorrect knowledge, the human-expert can feed it with the correct knowledge, e.g., in the form of mathematical theorems and formulas, and make it to apply the gained knowledge in order to provide a correct solution. Such ability presents an attractive opportunity to achieve a programmed solution even for users with rather limited knowledge of programming techniques. PubDate: 2023-12-01
Please help us test our new pre-print finding feature by giving the pre-print link a rating. A 5 star rating indicates the linked pre-print has the exact same content as the published article.
Please help us test our new pre-print finding feature by giving the pre-print link a rating. A 5 star rating indicates the linked pre-print has the exact same content as the published article.
Abstract: Abstract The Poisson multinomial distribution (PMD) describes the distribution of the sum of n independent but non-identically distributed random vectors, in which each random vector is of length m with 0/1 valued elements and only one of its elements can take value 1 with a certain probability. Those probabilities are different for the m elements across the n random vectors, and form an \(n \times m\) matrix with row sum equals to 1. We call this \(n\times m\) matrix the success probability matrix (SPM). Each SPM uniquely defines a \({ \text {PMD}}\) . The \({ \text {PMD}}\) is useful in many areas such as, voting theory, ecological inference, and machine learning. The distribution functions of \({ \text {PMD}}\) , however, are usually difficult to compute and there is no efficient algorithm available for computing it. In this paper, we develop efficient methods to compute the probability mass function (pmf) for the PMD using multivariate Fourier transform, normal approximation, and simulations. We study the accuracy and efficiency of those methods and give recommendations for which methods to use under various scenarios. We also illustrate the use of the \({ \text {PMD}}\) via three applications, namely, in ecological inference, uncertainty quantification in classification, and voting probability calculation. We build an R package that implements the proposed methods, and illustrate the package with examples. This paper has online supplementary materials. PubDate: 2023-12-01
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Abstract: Abstract Bayesian multilevel models—also known as hierarchical or mixed models—are used in situations in which the aim is to model the random effect of groups or levels. In this paper, we conduct a simulation study to compare the predictive ability of 1-level Bayesian multilevel logistic regression models with that of 2-level Bayesian multilevel logistic regression models by using the prior Scaled Beta2 and inverse-gamma distributions to model the standard deviation in the 2-level. Then, these models are employed to estimate the correct answers in two questionnaires administered to university students throughout the first academic semester of 2018. The results show that 2-level models have a better predictive ability and provide more precise probability intervals than 1-level models, particularly when the prior Scaled Beta2 distribution is used to model the standard deviation in the second level. Moreover, the probability intervals of 1-level Bayesian multilevel logistic regression models proved to be more precise when Scaled Beta2 distributions, rather than an inverse-gamma distribution, are employed to model the standard deviation or when 1-level Bayesian multilevel logistic regression models, are used. PubDate: 2023-12-01
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Abstract: Abstract The Bayesian inference is widely used in many scientific and engineering problems, especially in the linear inverse problems in infinite-dimensional setting where the unknowns are functions. In such problems, choosing an appropriate prior distribution is an important task. Especially when the function to infer has much detail information, such as many sharp jumps, corners, and the discontinuous and nonsmooth oscillation, the so-called total variation-Gaussian (TG) prior is proposed in function space to address it. However, the TG prior is easy to lead the blocky (staircase) effect in numerical results. In this work, we present a fractional order-TG (FTG) hybrid prior to deal with such problems, where the fractional order total variation (FTV) term is used to capture the detail information of the unknowns and simultaneously uses the Gaussian measure to ensure that it results in a well-defined posterior measure. For the numerical implementations of linear inverse problems in function spaces, we also propose an efficient independence sampler based on a transport map, which uses a proposal distribution derived from a diagonal map, and the acceptance probability associated to the proposal is independent of discretization dimensionality. And in order to take full advantage of the transport map, the hierarchical Bayesian framework is applied to flexibly determine the regularization parameter. Finally we provide some numerical examples to demonstrate the performance of the FTG prior and the efficiency and robustness of the proposed independence sampler method. PubDate: 2023-12-01
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Abstract: Abstract The elastic net plays an important role in regularization regressions. We develop a new hybrid Gibbs sampler for the fully Bayesian elastic net, in which we make use of the exchange algorithm to draw the penalized parameter from its full conditional posterior with an intractable normalizing constant. A great advantage of the proposed sampler is that it is exact and/or time-saving. Moreover, we consider a novel algorithm to sample the standard deviation of the model error from its full conditional that includes the auxiliary vector no longer. We also incorporate a generalised move step in our approach to improve the convergence further. The performance of the proposed method is demonstrated by four simulated examples and the prostate cancer data, and compared with that of the existing methods. PubDate: 2023-12-01
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Abstract: Abstract Sparse Markov models (SMMs) provide a parsimonious representation for higher-order Markov models. We present a computationally efficient method for fitting SMMs using a collapsed Gibbs sampler, the GSDPMM. We prove the consistency of the GSDPMM in fitting SMMs. In simulations, the GSDPMM was found to perform as well or better than existing methods for fitting SMMs. We apply the GSDPMM method to fit SMMs to patterns of wind speeds and DNA sequences. PubDate: 2023-12-01
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Abstract: Abstract Housing is of primary importance for immigrants in New York City. This study analyzed the housing conditions of and price changes for residents in New York City from the NYCHVS survey over the past 30 years. First, a house condition index is defined through dimension reduction approach with a supervised framework. In addition, spatio-temporal information is leveraged to build a two-stage model to predict rent. Data visualization is utilized to show immigrant preferences interactively and provide information for both researchers and new residents to the city. PubDate: 2023-12-01
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Abstract: Abstract Motivated by data measuring progression of leishmaniosis in a cohort of US dogs, we develop a Bayesian longitudinal model with autoregressive errors to jointly analyze ordinal and continuous outcomes. Multivariate methods can borrow strength across responses and may produce improved longitudinal forecasts of disease progression over univariate methods. We explore the performance of our proposed model under simulation, and demonstrate that it has improved prediction accuracy over traditional Bayesian hierarchical models. We further identify an appropriate model selection criterion. We show that our method holds promise for use in the clinical setting, particularly when ordinal outcomes are measured alongside other variables types that may aid clinical decision making. This approach is particularly applicable when multiple, imperfect measures of disease progression are available. PubDate: 2023-12-01
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Abstract: Abstract The physical condition of an occupant’s home represents a significant factor in determining the dweller’s overall quality of life. This paper provides a statistical framework for measuring housing quality in an urban area through a standardized index. This index is constructed using principal component analysis, incorporating demographic, geographic, and economic factors from the New York City Housing and Vacancy Survey. This metric allows for investigating differences in housing quality based upon ownership status. Analysis of the index demonstrates that renters face more housing quality issues than owners. Several of the index’s input variables driving these differences were found to exhibit varying effects on housing quality over time, possibly due to events such as the 2008 financial crisis. Implementing this novel statistical framework, housing quality indices can be constructed for other cities to examine housing disparities and inform policies aimed at improving quality of life for urban residents. PubDate: 2023-12-01
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Abstract: Abstract The least absolute shrinkage and selection operator (LASSO) and its variants are widely used for sparse signal recovery. However, the determination of the regularization factor requires cross-validation strategy, which may obtain a sub-optimal solution. Motivated by the self-regularization nature of sparse Bayesian learning (SBL) approach and the framework of generalized LASSO, we propose a new hierarchical Bayesian model using automatic-weighting Laplace priors in this paper. In the proposed hierarchical Bayesian model, the posterior distributions of all the parameters can be approximated using variational Bayesian inference, resulting in closed-form solutions for all parameters updating. Moreover, the space alternating variational estimation strategy is used to avoid matrix inversion, and a fast algorithm (SAVE-WLap-SBL) is proposed. Comparing to existed SBL methods, the proposed method encourages the sparsity of signals more efficiently. Numerical experiments on synthetic and real data illustrate the benefit of these advances. PubDate: 2023-12-01
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Abstract: Abstract We propose a new nonparametric regression approach that combines deep neural networks with support vector quantile regression models. The nature of deep neural networks enables complex nonlinear regression quantiles to be estimated more accurately. Because deep learning models have a complicated structure, the proposed method can easily fit both smooth and non-smooth data sets. For this reason, we can effectively model data sets with truncated points or locally different smoothness in which spline-based smoothing methods often fail. Stepwise fitting is used to increase computing speed when fitting multiple quantiles. This produces stable fits, especially when observations are scarce near the target quantile. In addition, we employ certain constraints to prevent the fitted quantiles from crossing. The benefits of the proposed method are more apparent when the errors are heteroscedastic, although quantile regression does not require homogeneous errors. We illustrate the flexibility of the proposed method using simulated data sets and six real data examples with univariate and multivariate input variables. PubDate: 2023-12-01
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Abstract: Abstract We introduce a new algorithm to compute the difference between values of the \(\log \Gamma\) -function in close points, where \(\Gamma\) denotes Euler’s gamma function. As a consequence, we obtain a way of computing the Dirichlet-multinomial log-likelihood function which is more accurate, has a better computational complexity and a wider range of application than the previously known ones. PubDate: 2023-12-01
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Abstract: Abstract We explore the quality of life of immigrants in New York City through housing and neighborhood conditions by creating a happiness metric to measure a household’s quality of life. Utilizing data provided by the New York City Housing and Vacancy Survey, the New York City Police Department, the New York City Department of Education, the New York City Department of Health and Mental Hygiene, along with reports from Happy City and the New Economics Foundation, a happiness score was assigned to each sub-borough in New York City. This happiness score evaluated five main domains: work, place, community, education, and health. As a result of this analysis, we discovered higher happiness scores were associated with lower percentages of immigrant households. PubDate: 2023-12-01
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Abstract: Abstract Given the costliness of HIV drug therapy research, it is important not only to maximize true positive rate (TPR) by identifying which genetic markers are related to drug resistance, but also to minimize false discovery rate (FDR) by reducing the number of incorrect markers unrelated to drug resistance. In this study, we propose a multiple testing procedure that unifies key concepts in computational statistics, namely Model-free Knockoffs, Bayesian variable selection, and the local false discovery rate. We develop an algorithm that utilizes the augmented data-Knockoff matrix and implement Bayesian Lasso. We then identify signals using test statistics based on Markov Chain Monte Carlo outputs and local false discovery rate. We test our proposed methods against non-bayesian methods such as Benjamini–Hochberg (BHq) and Lasso regression in terms TPR and FDR. Using numerical studies, we show the proposed method yields lower FDR compared to BHq and Lasso for certain cases, such as for low and equi-dimensional cases. We also discuss an application to an HIV-1 data set, which aims to be applied analyzing genetic markers linked to drug resistant HIV in the Philippines in future work. PubDate: 2023-12-01
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Abstract: Abstract It is the concern of policymakers every year in New York City to consider whether or not the enacted rent control policy has a positive effect on the rental market. In order to measure the efficacy of the rent control policy, we aim to study the change in housing quality of people who live in rent controlled homes compared to those in non-rent controlled homes. A housing quality index metric was created in order to study how housing quality changes over time and its relationship to rent control. The impact of rent control on housing quality is analyzed, thus assessing one measure of policy effectiveness. The analysis indicates that rent controlled homes are associated with higher damage rates than non-rent controlled homes, perhaps indicating that the inverse of the intended effect is occurring. PubDate: 2023-12-01
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Abstract: Abstract In many applications, the presence of interactions or even mild non-linearities can affect inference and predictions. For that reason, we suggest the use of a class of models laying between statistics and machine learning and we propose a learning procedure. The models combine a linear part and a tree component that is selected via an evolutionary algorithm, and they can be adopted for any kinds of response, such as, for instance, continuous, categorical, ordinal responses, and survival times. They are inherently interpretable but more flexible than standard regression models, as they easily capture non-linear and interaction effects. The proposed genetic-like learning algorithm allows avoiding a greedy search of the tree component. In a simulation study, we show that the proposed approach has a performance comparable with other machine learning algorithms, with a substantial gain in interpretability and transparency, and we illustrate the method on a real data set. PubDate: 2023-12-01
Please help us test our new pre-print finding feature by giving the pre-print link a rating. A 5 star rating indicates the linked pre-print has the exact same content as the published article.
Please help us test our new pre-print finding feature by giving the pre-print link a rating. A 5 star rating indicates the linked pre-print has the exact same content as the published article.
Abstract: Abstract The relationship between housing and immigration has become relevant in the U.S., especially in a highly populated metropolis such as New York City. Determining whether immigration status affects housing variables such as home ownership, rent, or housing cost could help understand the quality of life of NYC residents. Graphical exploration and spatial dependence tests of housing and immigration variables provide some insights about their relationships. Our exploration takes place at the borough and the sub-borough level. PubDate: 2023-09-29
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