Pub Date : 2020-06-16DOI: 10.5772/intechopen.88822
Junshan Shen, Catherine C Liu
Random effects models have been widely used to analyze correlated data sets, and Bayesian techniques have emerged as a powerful tool to fit the models. How-ever, there has been scarce literature that systematically reviews and summarizes the recent advances of Bayesian analyses of random effects models. This chapter reviews the use of the Dirichlet process mixture (DPM) prior to approximate the distribution of random errors within the general semiparametric random effects models with parametric random effects for longitudinal data setting and failure time setting separately. In a survival setting with clusters, we propose a new class of nonparametric random effects models which is motivated from the accelerated failure models. We employ a beta process prior to tact clustering and estimation simultaneously. We analyze a new data set integrated from Alzheimer ’ s disease (AD) study to illustrate the presented model and methods.
{"title":"Bayesian Analysis for Random Effects Models","authors":"Junshan Shen, Catherine C Liu","doi":"10.5772/intechopen.88822","DOIUrl":"https://doi.org/10.5772/intechopen.88822","url":null,"abstract":"Random effects models have been widely used to analyze correlated data sets, and Bayesian techniques have emerged as a powerful tool to fit the models. How-ever, there has been scarce literature that systematically reviews and summarizes the recent advances of Bayesian analyses of random effects models. This chapter reviews the use of the Dirichlet process mixture (DPM) prior to approximate the distribution of random errors within the general semiparametric random effects models with parametric random effects for longitudinal data setting and failure time setting separately. In a survival setting with clusters, we propose a new class of nonparametric random effects models which is motivated from the accelerated failure models. We employ a beta process prior to tact clustering and estimation simultaneously. We analyze a new data set integrated from Alzheimer ’ s disease (AD) study to illustrate the presented model and methods.","PeriodicalId":306321,"journal":{"name":"Bayesian Inference on Complicated Data","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2020-06-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125138346","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-05-14DOI: 10.5772/intechopen.91171
Shahid Naseem
Cloud-based healthcare data are a form of distributed data over the internet. The internet has become the most vulnerable part of critical healthcare infrastructures. Healthcare data are considered to be sensitive information, which can reveal a lot about a patient. For healthcare data, apart from confidentiality, privacy and protection of data are very sensitive issues. Proactive measures such as early warning are required to reduce the risk of patient ’ s data violation. This chapter investigates the ability of Patient Bayesian Inference (PBI) for network scenario analysis with violation of patient data to produce early warning. The Bayesian inference allows modeling the uncertainties that come with the problem of dealing with missing data, allows integrating data from remote nodes, and explicitly indicates depen-dence and independence. The use of constraint-based adaptive boost algorithm can demonstrate the patient ’ s Bayesian inference performance in the real-world datasets from healthcare data.
{"title":"Patient Bayesian Inference: Cloud-Based Healthcare Data Analysis Using Constraint-Based Adaptive Boost Algorithm","authors":"Shahid Naseem","doi":"10.5772/intechopen.91171","DOIUrl":"https://doi.org/10.5772/intechopen.91171","url":null,"abstract":"Cloud-based healthcare data are a form of distributed data over the internet. The internet has become the most vulnerable part of critical healthcare infrastructures. Healthcare data are considered to be sensitive information, which can reveal a lot about a patient. For healthcare data, apart from confidentiality, privacy and protection of data are very sensitive issues. Proactive measures such as early warning are required to reduce the risk of patient ’ s data violation. This chapter investigates the ability of Patient Bayesian Inference (PBI) for network scenario analysis with violation of patient data to produce early warning. The Bayesian inference allows modeling the uncertainties that come with the problem of dealing with missing data, allows integrating data from remote nodes, and explicitly indicates depen-dence and independence. The use of constraint-based adaptive boost algorithm can demonstrate the patient ’ s Bayesian inference performance in the real-world datasets from healthcare data.","PeriodicalId":306321,"journal":{"name":"Bayesian Inference on Complicated Data","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2020-05-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128758713","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-04-14DOI: 10.5772/intechopen.91451
Michelle Y. Wang, Trevor Park
Unlike in the past, the modern Bayesian analyst has many options for approxi-mating intractable posterior distributions. This chapter briefly summarizes the class of posterior sampling methods known as Markov chain Monte Carlo, a type of dependent sampling strategy. Varieties of algorithms exist for constructing chains, and we review some of them here. Such methods are quite flexible and are now used routinely, even for relatively complicated statistical models. In addition, extensions of the algorithms have been developed for various goals. General-purpose software is currently also available to automate the construction of samplers, freeing the analyst to focus on model formulation and inference.
{"title":"A Brief Tour of Bayesian Sampling Methods","authors":"Michelle Y. Wang, Trevor Park","doi":"10.5772/intechopen.91451","DOIUrl":"https://doi.org/10.5772/intechopen.91451","url":null,"abstract":"Unlike in the past, the modern Bayesian analyst has many options for approxi-mating intractable posterior distributions. This chapter briefly summarizes the class of posterior sampling methods known as Markov chain Monte Carlo, a type of dependent sampling strategy. Varieties of algorithms exist for constructing chains, and we review some of them here. Such methods are quite flexible and are now used routinely, even for relatively complicated statistical models. In addition, extensions of the algorithms have been developed for various goals. General-purpose software is currently also available to automate the construction of samplers, freeing the analyst to focus on model formulation and inference.","PeriodicalId":306321,"journal":{"name":"Bayesian Inference on Complicated Data","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2020-04-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125425244","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2019-11-13DOI: 10.5772/intechopen.88619
Hongsheng Dai
Perfect Monte Carlo sampling refers to sampling random realizations exactly from the target distributions (without any statistical error). Although many different methods have been developed and various applications have been implemented in the area of perfect Monte Carlo sampling, it is mostly referred by researchers to coupling from the past (CFTP) which can correct the statistical errors for the Monte Carlo samples generated by Markov chain Monte Carlo (MCMC) algorithms. This paper provides a brief review on the recent developments and applications in CFTP and other perfect Monte Carlo sampling methods.
{"title":"A Review on the Exact Monte Carlo Simulation","authors":"Hongsheng Dai","doi":"10.5772/intechopen.88619","DOIUrl":"https://doi.org/10.5772/intechopen.88619","url":null,"abstract":"Perfect Monte Carlo sampling refers to sampling random realizations exactly from the target distributions (without any statistical error). Although many different methods have been developed and various applications have been implemented in the area of perfect Monte Carlo sampling, it is mostly referred by researchers to coupling from the past (CFTP) which can correct the statistical errors for the Monte Carlo samples generated by Markov chain Monte Carlo (MCMC) algorithms. This paper provides a brief review on the recent developments and applications in CFTP and other perfect Monte Carlo sampling methods.","PeriodicalId":306321,"journal":{"name":"Bayesian Inference on Complicated Data","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2019-11-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132871510","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2019-09-21DOI: 10.5772/intechopen.88994
Fatemeh Ghaderinezhad, Christophe Ley
A key question in Bayesian analysis is the effect of the prior on the posterior, and how we can measure this effect. Will the posterior distributions derived with distinct priors become very similar if more and more data are gathered? It has been proved formally that, under certain regularity conditions, the impact of the prior is waning as the sample size increases. From a practical viewpoint it is more important to know what happens at finite sample size n. In this chapter, we shall explain how we tackle this crucial question from an innovative approach. To this end, we shall review some notions from probability theory such as the Wasserstein distance and the popular Stein's method, and explain how we use these a priori unrelated concepts in order to measure the impact of priors. Examples will illustrate our findings, including conjugate priors and the Jeffreys prior.
{"title":"On the Impact of the Choice of the Prior in Bayesian Statistics","authors":"Fatemeh Ghaderinezhad, Christophe Ley","doi":"10.5772/intechopen.88994","DOIUrl":"https://doi.org/10.5772/intechopen.88994","url":null,"abstract":"A key question in Bayesian analysis is the effect of the prior on the posterior, and how we can measure this effect. Will the posterior distributions derived with distinct priors become very similar if more and more data are gathered? It has been proved formally that, under certain regularity conditions, the impact of the prior is waning as the sample size increases. From a practical viewpoint it is more important to know what happens at finite sample size n. In this chapter, we shall explain how we tackle this crucial question from an innovative approach. To this end, we shall review some notions from probability theory such as the Wasserstein distance and the popular Stein's method, and explain how we use these a priori unrelated concepts in order to measure the impact of priors. Examples will illustrate our findings, including conjugate priors and the Jeffreys prior.","PeriodicalId":306321,"journal":{"name":"Bayesian Inference on Complicated Data","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2019-09-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122494930","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2019-08-28DOI: 10.5772/INTECHOPEN.88799
Xi Chen, J. Xuan
Gene regulatory networks (GRN) have been studied by computational scientists and biologists over 20 years to gain a fine map of gene functions. With large-scale genomic and epigenetic data generated under diverse cells, tissues, and diseases, the integrative analysis of multi-omics data plays a key role in identifying casual genes in human disease development. Bayesian inference (or integration) has been successfully applied to inferring GRNs. Learning a posterior distribution than making a single-value prediction of model parameter makes Bayesian inference a more robust approach to identify GRN from noisy biomedical observations. Moreover, given multi-omics data as input and a large number of model parameters to estimate, the automatic preference of Bayesian inference for simple models that sufficiently explain data without unnecessary complexity ensures fast convergence to reliable results. In this chapter, we introduced GRN modeling using hierarchical Bayesian network and then used Gibbs sampling to identify network variables. We applied this model to breast cancer data and identified genes relevant to breast cancer recurrence. In the end, we discussed the potential of Bayesian inference as well as Bayesian deep learning for large-scale and complex GRN inference.
{"title":"Bayesian Inference of Gene Regulatory Network","authors":"Xi Chen, J. Xuan","doi":"10.5772/INTECHOPEN.88799","DOIUrl":"https://doi.org/10.5772/INTECHOPEN.88799","url":null,"abstract":"Gene regulatory networks (GRN) have been studied by computational scientists and biologists over 20 years to gain a fine map of gene functions. With large-scale genomic and epigenetic data generated under diverse cells, tissues, and diseases, the integrative analysis of multi-omics data plays a key role in identifying casual genes in human disease development. Bayesian inference (or integration) has been successfully applied to inferring GRNs. Learning a posterior distribution than making a single-value prediction of model parameter makes Bayesian inference a more robust approach to identify GRN from noisy biomedical observations. Moreover, given multi-omics data as input and a large number of model parameters to estimate, the automatic preference of Bayesian inference for simple models that sufficiently explain data without unnecessary complexity ensures fast convergence to reliable results. In this chapter, we introduced GRN modeling using hierarchical Bayesian network and then used Gibbs sampling to identify network variables. We applied this model to breast cancer data and identified genes relevant to breast cancer recurrence. In the end, we discussed the potential of Bayesian inference as well as Bayesian deep learning for large-scale and complex GRN inference.","PeriodicalId":306321,"journal":{"name":"Bayesian Inference on Complicated Data","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2019-08-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122398362","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2019-08-12DOI: 10.5772/INTECHOPEN.88587
Ying-Ying Zhang
In this chapter, we have investigated six loss functions. In particular, the squared error loss function and the weighted squared error loss function that penalize overestimation and underestimation equally are recommended for the unrestricted parameter space (cid:1) ∞ ; ∞ ð Þ ; Stein ’ s loss function and the power-power loss function, which penalize gross overestimation and gross underestimation equally, are recommended for the positive restricted parameter space 0 ; ∞ ð Þ ; the power-log loss function and Zhang ’ s loss function, which penalize gross overestimation and gross underestimation equally, are recommended for 0 ; 1 ð Þ . Among the six Bayesian estimators that minimize the corresponding posterior expected losses (PELs), there exist three strings of inequalities. However, a string of inequalities among the six smallest PELs does not exist. Moreover, we summarize three hierarchical models where the unknown parameter of interest belongs to 0 ; ∞ ð Þ , that is, the hierarchical normal and inverse gamma model, the hierarchical Poisson and gamma model, and the hierarchical normal and normal-inverse-gamma model. In addition, we summarize two hierarchical models where the unknown parameter of interest belongs to 0 ; 1 ð Þ , that is, the beta-binomial model and the beta-negative binomial model. For empirical Bayesian analysis of the unknown parameter of interest of the hierarchical models, we use two common methods to obtain the estimators of the hyperparameters, that is, the moment method and the maximum likelihood estimator (MLE) method.
{"title":"The Bayesian Posterior Estimators under Six Loss Functions for Unrestricted and Restricted Parameter Spaces","authors":"Ying-Ying Zhang","doi":"10.5772/INTECHOPEN.88587","DOIUrl":"https://doi.org/10.5772/INTECHOPEN.88587","url":null,"abstract":"In this chapter, we have investigated six loss functions. In particular, the squared error loss function and the weighted squared error loss function that penalize overestimation and underestimation equally are recommended for the unrestricted parameter space (cid:1) ∞ ; ∞ ð Þ ; Stein ’ s loss function and the power-power loss function, which penalize gross overestimation and gross underestimation equally, are recommended for the positive restricted parameter space 0 ; ∞ ð Þ ; the power-log loss function and Zhang ’ s loss function, which penalize gross overestimation and gross underestimation equally, are recommended for 0 ; 1 ð Þ . Among the six Bayesian estimators that minimize the corresponding posterior expected losses (PELs), there exist three strings of inequalities. However, a string of inequalities among the six smallest PELs does not exist. Moreover, we summarize three hierarchical models where the unknown parameter of interest belongs to 0 ; ∞ ð Þ , that is, the hierarchical normal and inverse gamma model, the hierarchical Poisson and gamma model, and the hierarchical normal and normal-inverse-gamma model. In addition, we summarize two hierarchical models where the unknown parameter of interest belongs to 0 ; 1 ð Þ , that is, the beta-binomial model and the beta-negative binomial model. For empirical Bayesian analysis of the unknown parameter of interest of the hierarchical models, we use two common methods to obtain the estimators of the hyperparameters, that is, the moment method and the maximum likelihood estimator (MLE) method.","PeriodicalId":306321,"journal":{"name":"Bayesian Inference on Complicated Data","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2019-08-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115922621","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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