ترغب بنشر مسار تعليمي؟ اضغط هنا

Two-stage Circular-circular Regression with Zero-inflation: Application to Medical Sciences

64   0   0.0 ( 0 )
 نشر من قبل Prajamitra Bhuyan Dr.
 تاريخ النشر 2019
  مجال البحث الاحصاء الرياضي
والبحث باللغة English




اسأل ChatGPT حول البحث

This paper considers the modeling of zero-inflated circular measurements concerning real case studies from medical sciences. Circular-circular regression models have been discussed in the statistical literature and illustrated with various real-life applications. However, there are no models to deal with zero-inflated response as well as a covariate simultaneously. The Mobius transformation based two-stage circular-circular regression model is proposed, and the Bayesian estimation of the model parameters is suggested using the MCMC algorithm. Simulation results show the superiority of the performance of the proposed method over the existing competitors. The method is applied to analyse real datasets on astigmatism due to cataract surgery and abnormal gait related to orthopaedic impairment. The methodology proposed can assist in efficient decision making during treatment or post-operative care.



قيم البحث

اقرأ أيضاً

We introduce a new approach to a linear-circular regression problem that relates multiple linear predictors to a circular response. We follow a modeling approach of a wrapped normal distribution that describes angular variables and angular distributi ons and advances it for a linear-circular regression analysis. Some previous works model a circular variable as projection of a bivariate Gaussian random vector on the unit square, and the statistical inference of the resulting model involves complicated sampling steps. The proposed model treats circular responses as the result of the modulo operation on unobserved linear responses. The resulting model is a mixture of multiple linear-linear regression models. We present two EM algorithms for maximum likelihood estimation of the mixture model, one for a parametric model and another for a non-parametric model. The estimation algorithms provide a great trade-off between computation and estimation accuracy, which was numerically shown using five numerical examples. The proposed approach was applied to a problem of estimating wind directions that typically exhibit complex patterns with large variation and circularity.
Occupancy models are used in statistical ecology to estimate species dispersion. The two components of an occupancy model are the detection and occupancy probabilities, with the main interest being in the occupancy probabilities. We show that for t he homogeneous occupancy model there is an orthogonal transformation of the parameters that gives a natural two-stage inference procedure based on a conditional likelihood. We then extend this to a partial likelihood that gives explicit estimators of the model parameters. By allowing the separate modelling of the detection and occupancy probabilities, the extension of the two-stage approach to more general models has the potential to simplify the computational routines used there.
We establish verifiable conditions under which Metropolis Hastings (MH) algorithms with position-dependent proposal covariance matrix will or will not have geometric rate of convergence. Some of the diffusions based MH algorithms like Metropolis adju sted Langevin algorithms (MALA) and Pre-conditioned MALA (PCMALA) have position independent proposal variance. Whereas, for other variants of MALA like manifold MALA (MMALA), the proposal covariance matrix changes in every iteration. Thus, we provide conditions for geometric ergodicity of different variations of Langevin algorithms. These conditions are verified in the context of conditional simulation from the two most popular generalized linear mixed models (GLMMs), namely the binomial GLMM with logit link and the Poisson GLMM with log link. Empirical comparison in the framework of some spatial GLMMs shows that computationally less expensive PCMALA with an appropriately chosen pre-conditioning matrix may outperform MMALA.
In this paper, we study the asymptotic variance of sample path averages for inhomogeneous Markov chains that evolve alternatingly according to two different $pi$-reversible Markov transition kernels $P$ and $Q$. More specifically, our main result all ows us to compare directly the asymptotic variances of two inhomogeneous Markov chains associated with different kernels $P_i$ and $Q_i$, $iin{0,1}$, as soon as the kernels of each pair $(P_0,P_1)$ and $(Q_0,Q_1)$ can be ordered in the sense of lag-one autocovariance. As an important application, we use this result for comparing different data-augmentation-type Metropolis-Hastings algorithms. In particular, we compare some pseudo-marginal algorithms and propose a novel exact algorithm, referred to as the random refreshment algorithm, which is more efficient, in terms of asymptotic variance, than the Grouped Independence Metropolis-Hastings algorithm and has a computational complexity that does not exceed that of the Monte Carlo Within Metropolis algorithm.
We consider perfect simulation algorithms for locally stable point processes based on dominated coupling from the past, and apply these methods in two different contexts. A new version of the algorithm is developed which is feasible for processes whi ch are neither purely attractive nor purely repulsive. Such processes include multiscale area-interaction processes, which are capable of modelling point patterns whose clustering structure varies across scales. The other topic considered is nonparametric regression using wavelets, where we use a suitable area-interaction process on the discrete space of indices of wavelet coefficients to model the notion that if one wavelet coefficient is non-zero then it is more likely that neighbouring coefficients will be also. A method based on perfect simulation within this model shows promising results compared to the standard methods which threshold coefficients independently.
التعليقات
جاري جلب التعليقات جاري جلب التعليقات
mircosoft-partner

هل ترغب بارسال اشعارات عن اخر التحديثات في شمرا-اكاديميا