Supplementary material for Independent Component Models for Replicated Point Processes
نویسنده
چکیده
1 Estimation 1.1 EM algorithm We derive the EM algorithm for Uks withGamma( k; ) distributions, so S = Pp k=1 Uk isGamma( ; ) with = Pp k=1 k andW = U=S is Dirichlet( 1; : : : ; p), and S andW are independent. With a slight abuse of notation we are going to identify xB = ft1; : : : ; tmg with (m; t) from now on. The joint density of (m; t) and the latent variables (y; s;w) is f(m; t;y; s;w) = f(t j m;y)f(m j s)f(y j w)f(s)f(w) = f m Y
منابع مشابه
TESTING FOR AUTOCORRELATION IN UNEQUALLY REPLICATED FUNCTIONAL MEASUREMENT ERROR MODELS
In the ordinary linear models, regressing the residuals against lagged values has been suggested as an approach to test the hypothesis of zero autocorrelation among residuals. In this paper we extend these results to the both equally and unequally replicated functionally measurement error models. We consider the equally and unequally replicated cases separately, because in the first case the re...
متن کاملSupplementary Materials for Learning to Recognize Discontiguous Entities
This is the supplementary material for “Learning to Recognize Discontiguous Entities” [Muis and Lu, 2016]. This material gives more details in the experiment setup, the ambiguity of each model, and compare the models from theoretical point of view.
متن کاملIndividualness and Determinantal Point Processes for Pedestrian Detection: Supplementary Material
In this supplementary material, we describe experimental results which were not included in the paper due to the page limitation. Comparisons of NMS, QUBO, and the proposed method are provided in Section 1. A sensitivity analysis of parameters is reported in Section 2. Section 3 shows the effectiveness of the proposed quality and similarity term design by comparing it to other models. Fig. 1. D...
متن کاملA robust wavelet based profile monitoring and change point detection using S-estimator and clustering
Some quality characteristics are well defined when treated as response variables and are related to some independent variables. This relationship is called a profile. Parametric models, such as linear models, may be used to model profiles. However, in practical applications due to the complexity of many processes it is not usually possible to model a process using parametric models.In these cas...
متن کاملProperties of Spatial Cox Process Models
Probabilistic properties of Cox processes of relevance for statistical modeling and inference are studied. Particularly, we study the most important classes of Cox processes, including log Gaussian Cox processes, shot noise Cox processes, and permanent Cox processes. We consider moment properties and point process operations such as thinning, displacements, and superpositioning. We also discuss...
متن کامل