اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدOn equivalence of the LKJ distribution and the restricted Wishart distribution
69
0
0.0
(
0
)
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
In this paper, we want to show the Restricted Wishart distribution is equivalent to the LKJ distribution, which is one way to specify a uniform distribution from the space of positive definite correlation matrices. Based on this theorem, we propose a new method to generate random correlation matrices from the LKJ distribution. This new method is faster than the original onion method for generating random matrices, especially in the low dimension ($T<120$) situation.
قيم البحث
اقرأ أيضاً
Message passing on a factor graph is a powerful paradigm for the coding of approximate inference algorithms for arbitrarily graphical large models. The notion of a factor graph fragment allows for compartmentalization of algebra and computer code. We
show that the Inverse G-Wishart family of distributions enables fundamental variational message passing factor graph fragments to be expressed elegantly and succinctly. Such fragments arise in models for which approximate inference concerning covariance matrix or variance parameters is made, and are ubiquitous in contemporary statistics and machine learning.
There exist a large literature on the application of $q$-statistics to the out-of-equilibrium non-ergodic systems in which some degree of strong correlations exists. Here we study the distribution of first return times to zero, $P_R(0,t)$, of a rando
m walk on the set of integers ${0,1,2,...,L}$ with a position dependent transition probability given by $|n/L|^a$. We find that for all values of $ain[0,2]$ $P_R(0,t)$ can be fitted by $q$-exponentials, but only for $a=1$ is $P_R(0,t)$ given exactly by a $q$-exponential in the limit $Lrightarrowinfty$. This is a remarkable result since the exact analytical solution of the corresponding continuum model represents $P_R(0,t)$ as a sum of Bessel functions with a smooth dependence on $a$ from which we are unable to identify $a=1$ as of special significance. However, from the high precision numerical iteration of the discrete Master Equation, we do verify that only for $a=1$ is $P_R(0,t)$ exactly a $q$-exponential and that a tiny departure from this parameter value makes the distribution deviate from $q$-exponential. Further research is certainly required to identify the reason for this result and also the applicability of $q$-statistics and its domain.
We propose the exact calculation of the probability density function (PDF) and cumulative distribution function (CDF) of mutual information (MI) for a two-user MIMO MAC network over block Rayleigh fading channels. So far the PDF and CDF have been num
erically evaluated since MI depends on the quotient of two Wishart matrices, and no closed-form for this quotient was available. We derive exact results for the PDF and CDF of extreme (the smallest/the largest) eigenvalues. Based on the results of quotient ensemble the exact calculation for PDF and CDF of mutual information is presented via Laplace transform approach and by direct integration of joint PDF of quotient ensembles eigenvalues. Furthermore, our derivations also provide the parameters to apply the Gaussian approximation method, which is comparatively easier to implement. We show that approximation matches the exact results remarkably well for outage probability, i.e. CDF, above 10%. However, the approximation could also be used for 1% outage probability with a relatively small error. We apply the derived expressions to analyze the effects of adding receiving antennas on the receivers performance. By supposing no channel knowledge at transmitters and successive decoding at receiver, the capacity of the first user increases and outage probability decreases with extra antennas, as expected.
We consider the problem of computing the joint distribution of order statistics of stochastically independent random variables in one- and two-group models. While recursive formulas for evaluating the joint cumulative distribution function of such or
der statistics exist in the literature for a longer time, their numerical implementation remains a challenging task. We tackle this task by presenting novel generalizations of known recursions which we utilize to obtain exact results (calculated in rational arithmetic) as well as faithfully rounded results. Finally, some applications in stepwise multiple hypothesis testing are discussed.
This paper is concerned with making Bayesian inference from data that are assumed to be drawn from a Bingham distribution. A barrier to the Bayesian approach is the parameter-dependent normalising constant of the Bingham distribution, which, even whe
n it can be evaluated or accurately approximated, would have to be calculated at each iteration of an MCMC scheme, thereby greatly increasing the computational burden. We propose a method which enables exact (in Monte Carlo sense) Bayesian inference for the unknown parameters of the Bingham distribution by completely avoiding the need to evaluate this constant. We apply the method to simulated and real data, and illustrate that it is simpler to implement, faster, and performs better than an alternative algorithm that has recently been proposed in the literature.
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
