{"title":"Dependent percolation on Z2","authors":"B. D. de Lima, V. Sidoravicius, M. Vares","doi":"10.1214/23-bjps575","DOIUrl":"https://doi.org/10.1214/23-bjps575","url":null,"abstract":"","PeriodicalId":51242,"journal":{"name":"Brazilian Journal of Probability and Statistics","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2023-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45519426","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Alex de la Cruz Huayanay, Jorge L. Bazán, Carlos A. Ribeiro Diniz
{"title":"Longitudinal binary response models using alternative links for medical data","authors":"Alex de la Cruz Huayanay, Jorge L. Bazán, Carlos A. Ribeiro Diniz","doi":"10.1214/23-bjps572","DOIUrl":"https://doi.org/10.1214/23-bjps572","url":null,"abstract":"","PeriodicalId":51242,"journal":{"name":"Brazilian Journal of Probability and Statistics","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2023-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47573500","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"On the asymptotic distribution of sample autocovariance differences of long-memory processes","authors":"M. Zevallos","doi":"10.1214/23-bjps569","DOIUrl":"https://doi.org/10.1214/23-bjps569","url":null,"abstract":"","PeriodicalId":51242,"journal":{"name":"Brazilian Journal of Probability and Statistics","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2023-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45817297","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Maximum likelihood estimation for the reflected stochastic linear system with a large signal","authors":"Xuekang Zhang, H. Shu","doi":"10.1214/23-bjps571","DOIUrl":"https://doi.org/10.1214/23-bjps571","url":null,"abstract":"","PeriodicalId":51242,"journal":{"name":"Brazilian Journal of Probability and Statistics","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2023-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47721772","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"A new distance-based distribution: Detecting concentration in directional data","authors":"Saul A. Souza, G. Amaral, A. Nascimento","doi":"10.1214/23-bjps563","DOIUrl":"https://doi.org/10.1214/23-bjps563","url":null,"abstract":"","PeriodicalId":51242,"journal":{"name":"Brazilian Journal of Probability and Statistics","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2023-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41697167","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Jorge Luis Bazán, Sandra Elizabeth Flores Ari, C. Azevedo, D. Dey
. In 2010, the Samejima-Bolfarine-Bazán (SBB) Item Response Theory (IRT) models were introduced by Bolfarine and Bazán (2010) under a Bayesian approach. These models extend the regular Bayesian One and Two Parameter Logistic IRT models by incorporating a parameter accounting for asymmetry of the Item Characteristic Curve (ICC) which is named the complexity of the item. It includes the Logistic Positive Exponent (LPE) IRT model formulated initially by (Samejima, 2000) and the Reflection of the LPE (RLPE). In the present work, new properties of the SBB models are developed including a random effect for testlet structures with a Bayesian inference through a Markov chain Monte Carlo (MCMC) algorithm which includes the parameter estimation and model comparison. The asymmetric behavior of the Item Characteristic Curve (ICC) is detected using a marginal item information function and a mixture structure of the related prior distribution. Two simulation studies are developed to analyze the sensitiveness of the penalized parameter in the asymmetric behavior of the ICC and to evaluate the parameter recovery of the proposed model. A real data set, with a testlet structure and empirical evidence of asymmetric behavior of the ICCs, is used to apply the models.
{"title":"Revisiting the Samejima–Bolfarine–Bazán IRT models: New features and extensions","authors":"Jorge Luis Bazán, Sandra Elizabeth Flores Ari, C. Azevedo, D. Dey","doi":"10.1214/22-bjps558","DOIUrl":"https://doi.org/10.1214/22-bjps558","url":null,"abstract":". In 2010, the Samejima-Bolfarine-Bazán (SBB) Item Response Theory (IRT) models were introduced by Bolfarine and Bazán (2010) under a Bayesian approach. These models extend the regular Bayesian One and Two Parameter Logistic IRT models by incorporating a parameter accounting for asymmetry of the Item Characteristic Curve (ICC) which is named the complexity of the item. It includes the Logistic Positive Exponent (LPE) IRT model formulated initially by (Samejima, 2000) and the Reflection of the LPE (RLPE). In the present work, new properties of the SBB models are developed including a random effect for testlet structures with a Bayesian inference through a Markov chain Monte Carlo (MCMC) algorithm which includes the parameter estimation and model comparison. The asymmetric behavior of the Item Characteristic Curve (ICC) is detected using a marginal item information function and a mixture structure of the related prior distribution. Two simulation studies are developed to analyze the sensitiveness of the penalized parameter in the asymmetric behavior of the ICC and to evaluate the parameter recovery of the proposed model. A real data set, with a testlet structure and empirical evidence of asymmetric behavior of the ICCs, is used to apply the models.","PeriodicalId":51242,"journal":{"name":"Brazilian Journal of Probability and Statistics","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2023-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48099145","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
R. P. de Oliveira, Marcos Vinicius de Oliveira Peres, J. Achcar, Edson Z Martinez
. The present study introduces a new bivariate distribution based on the Sushila distribution to model bivariate lifetime data in presence of a cure fraction, right- censored data and covariates. The new bivariate probability distribution was obtained using a methodology used in the reliability theory based on fatal shocks, usually used to build new bivariate models. Additionally, the cure rate was introduced in the model based on a generalization of standard mixture models extensively used for the univariate lifetime case. The inferences of interest for the model parameters are obtained under a Bayesian approach using MCMC (Markov Chain Monte Carlo) simulation methods to generate samples of the joint posterior distribution for all parameters of the model. A simulation study was developed to study the inferential properties of the new methodology.The proposed methodology also was applied to analyze a set of real medical data obtained from a retrospective cohort study that aimed to assess specific clinical conditions that affect the lives of patients with diabetic retinopathy. For the discrimination of the proposed model with other usual models used in the analysis of bivariate survival data, some Bayesian techniques of model discrimination were used and the model validation was verified from usual Cox-Snell residuals, which allowed us to identify the adequacy of the proposed bivariate cure rate model.
{"title":"A new class of bivariate Sushila distributions in presence of right-censored and cure fraction","authors":"R. P. de Oliveira, Marcos Vinicius de Oliveira Peres, J. Achcar, Edson Z Martinez","doi":"10.1214/22-bjps560","DOIUrl":"https://doi.org/10.1214/22-bjps560","url":null,"abstract":". The present study introduces a new bivariate distribution based on the Sushila distribution to model bivariate lifetime data in presence of a cure fraction, right- censored data and covariates. The new bivariate probability distribution was obtained using a methodology used in the reliability theory based on fatal shocks, usually used to build new bivariate models. Additionally, the cure rate was introduced in the model based on a generalization of standard mixture models extensively used for the univariate lifetime case. The inferences of interest for the model parameters are obtained under a Bayesian approach using MCMC (Markov Chain Monte Carlo) simulation methods to generate samples of the joint posterior distribution for all parameters of the model. A simulation study was developed to study the inferential properties of the new methodology.The proposed methodology also was applied to analyze a set of real medical data obtained from a retrospective cohort study that aimed to assess specific clinical conditions that affect the lives of patients with diabetic retinopathy. For the discrimination of the proposed model with other usual models used in the analysis of bivariate survival data, some Bayesian techniques of model discrimination were used and the model validation was verified from usual Cox-Snell residuals, which allowed us to identify the adequacy of the proposed bivariate cure rate model.","PeriodicalId":51242,"journal":{"name":"Brazilian Journal of Probability and Statistics","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2023-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42005169","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
: Suppose that X n is a sample of size n with log likelihood nl ( θ ), where θ is an unknown parameter in R p having a prior distribution ξ ( θ ). We need not assume that the sample values are independent or even stationary. Let (cid:98) θ be the maximum likelihood estimate (MLE). We show that θ | X n is asymptotically normal with mean (cid:98) θ and covariance − n − 1 l (cid:5) , (cid:5) (cid:16)(cid:98) θ (cid:17) − 1 , where l (cid:5) , (cid:5) ( θ ) = ∂ 2 l ( θ ) /∂θ∂θ ′ . In contrast (cid:98) θ | θ is asymptotically normal with mean θ and covariance n − 1 [ I ( θ )] − 1 , where I ( θ ) = − E (cid:104) l (cid:5) , (cid:5) (cid:16)(cid:98) θ (cid:17) | θ (cid:105) is Fisher’s information. So, frequentist inference conditional on θ cannot be used to approximate Bayesian inference, except for exponential families. However, under mild conditions − l (cid:5) , (cid:5) (cid:16)(cid:98) θ (cid:17) | θ → I ( θ ) in probability. So, Bayesian inference (that is, conditional on X n ) can be used to approximate frequentist inference. For t ( θ ) any smooth function, we obtain posterior cumulant expansions, posterior Edgeworth-Cornish-Fisher (ECF) expansions and posterior tilted Edgeworth expansions for L t ( θ ) | X n , as well as confidence regions for t ( θ ) | X n of high accuracy. We also give expansions for the Bayes estimate (estimator) of t ( θ ) about t (cid:16)(cid:98) θ (cid:17) , and for the maximum a posteriori estimate about (cid:98) θ , as well as their relative efficiencies with respect to squared error loss.
{"title":"Expansions for posterior distributions","authors":"C. Withers, S. Nadarajah","doi":"10.1214/22-bjps561","DOIUrl":"https://doi.org/10.1214/22-bjps561","url":null,"abstract":": Suppose that X n is a sample of size n with log likelihood nl ( θ ), where θ is an unknown parameter in R p having a prior distribution ξ ( θ ). We need not assume that the sample values are independent or even stationary. Let (cid:98) θ be the maximum likelihood estimate (MLE). We show that θ | X n is asymptotically normal with mean (cid:98) θ and covariance − n − 1 l (cid:5) , (cid:5) (cid:16)(cid:98) θ (cid:17) − 1 , where l (cid:5) , (cid:5) ( θ ) = ∂ 2 l ( θ ) /∂θ∂θ ′ . In contrast (cid:98) θ | θ is asymptotically normal with mean θ and covariance n − 1 [ I ( θ )] − 1 , where I ( θ ) = − E (cid:104) l (cid:5) , (cid:5) (cid:16)(cid:98) θ (cid:17) | θ (cid:105) is Fisher’s information. So, frequentist inference conditional on θ cannot be used to approximate Bayesian inference, except for exponential families. However, under mild conditions − l (cid:5) , (cid:5) (cid:16)(cid:98) θ (cid:17) | θ → I ( θ ) in probability. So, Bayesian inference (that is, conditional on X n ) can be used to approximate frequentist inference. For t ( θ ) any smooth function, we obtain posterior cumulant expansions, posterior Edgeworth-Cornish-Fisher (ECF) expansions and posterior tilted Edgeworth expansions for L t ( θ ) | X n , as well as confidence regions for t ( θ ) | X n of high accuracy. We also give expansions for the Bayes estimate (estimator) of t ( θ ) about t (cid:16)(cid:98) θ (cid:17) , and for the maximum a posteriori estimate about (cid:98) θ , as well as their relative efficiencies with respect to squared error loss.","PeriodicalId":51242,"journal":{"name":"Brazilian Journal of Probability and Statistics","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2023-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44239360","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
J. S. Vasconcelos, E. M. Ortega, R. Vila, V. Cancho
{"title":"An extension of the partially linear Rice regression model for bimodal and correlated data","authors":"J. S. Vasconcelos, E. M. Ortega, R. Vila, V. Cancho","doi":"10.1214/23-bjps566","DOIUrl":"https://doi.org/10.1214/23-bjps566","url":null,"abstract":"","PeriodicalId":51242,"journal":{"name":"Brazilian Journal of Probability and Statistics","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2023-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46290807","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"A two-step estimation procedure for locally stationary ARMA processes with tempered stable innovations","authors":"S. Chou-Chen, P. Morettin","doi":"10.1214/23-bjps565","DOIUrl":"https://doi.org/10.1214/23-bjps565","url":null,"abstract":"","PeriodicalId":51242,"journal":{"name":"Brazilian Journal of Probability and Statistics","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2023-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47303426","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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