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Priors in R-INLA
Published in Virgilio Gómez-Rubio, Bayesian Inference with INLA, 2020
The half-t is also a truncated distribution at zero. In this case, a Student’s t distribution with ν degrees of freedom. The resulting density function is
Non-parametric estimation of the population size using the empirical probability generating function
Published in Dankmar Böhning, Peter G.M. van der Heijden, John Bunge, Capture-Recapture Methods for the Social and Medical Sciences, 2017
For the second data set (3.0 Gy) the maximum of is attained at the right limit of the interval [0, 1 ], that is s* = 1. The sample mean and variance of the truncated distribution are and . Therefore, according to (11.15), . In this example the total number of blood lymphocytes is N = 500, lying to the left of the estimated 95% CI. The estimated proportion of zeros is , while the observed proportion is p0 = 0.4260. Note that does not provide a lower bound of N. It happens because the distribution of the data does not belong to the LC-class. There is a detailed discussion in Pujol et al. [238] concerning the underdispersion of these data sets. Figure 11.5 shows that the estimated -epgf is convex while the observed log-epgf is not.
Candidate-gene association analysis for a continuous phenotype with a spike at zero using parent-offspring trios
Published in Journal of Applied Statistics, 2020
Nadja Klein, Andrew Entwistle, Albert Rosenberger, Thomas Kneib, Heike Bickeböller
There is a lot of literature on various types of a non-negative variable with a probability mass at zero and a continuous distribution for the positive values with a wide variety of area applications. We do not attempt to give a review of that literature and only want to highlight a few points. Hurdle models have a distribution for the zero-values and a truncated distribution for non-zero observations with no probability mass assigned to zero for non-zero observations. In contrast, the inflated models allow zeros from both parts. We do believe that this difference is very relevant for count data, but not for distributions that have zero probability for exactly this zero-value in the continuous part. Of cause some data with detection limits might reveal censoring, which we will not discuss further.
Bayesian truncated beta nonlinear mixed-effects models
Published in Journal of Applied Statistics, 2018
Carolina Costa Mota Paraíba, Natalia Bochkina, Carlos Alberto Ribeiro Diniz
In [13], a Bayesian mixed-effects approach was proposed for the well-known and widely applicable beta regression model [12]. Although the model is primarily suitable for response variables in the unit interval 12], transforming the response variable may unable the interpretation of model parameters with regard to the original variable. Furthermore, in [8], the author considers it to be more accurate to state that truncation is a property of the distribution which gives rise to the observed data and [22] suggests that in order to take truncation into consideration, we should assume a truncated distribution.
Spirometry reference equations for an adult Middle Eastern population
Published in Expert Review of Respiratory Medicine, 2019
Walid Al-Qerem, Alaa M. Hammad, Ezeddin S. Gassar, Rania A. Al-Qirim, Jonathan Ling
T test was used to compare spirometric and anthropometric values between the two sexes, if normality was not assumed, Mann Whitney U test was used. Generalised Additive Models for Location Scale and Shape (GAMLSS) as applied to formulate Global Lung Initiative 2012 (GLI 2012) equations [15] were used. GAMLSS uses different distributions that can be adjusted for variability, skewness and kurtoses, also a different link function between the mean of the outcome and the predictor can be used. Models used include Box-Cox-Cole-Green (BCCG) distribution, normal distribution and Box-Cox power exponential (BCPE) to adjust for skewness and/or kurtosis. BCCG was chosen because it is suitable for all data distributions with the mean >0, variability >0, and skewness = (-Infinty,+Infinity) [16]. Identity link was used to model equations that contains an additive relation between age and height, while the log function was used to model equations that multiplies age with height [17]. A truncated distribution for FEV1/FVC was used as the endpoint of FEV1/FVC is 100. The different models that were tested to evaluate the most suitable model for the data are detailed in Table 1. Age and height were grouped by bin widths of 2 years and 5 cm as in accordance with GLI 2012 methodology [15]. The most suitable model was determined by examining Schwarz Bayesian Criterion (SBC) and degree of freedom (df). Quanjer et al. suggested that it is preferable to choose the model with the lowest SBC at the expense of df as long as df is up to 10 [15]. Goodness of fit of the model was also evaluated by examining the centiles, standard residuals and by studying the worm plots.