Finding predictors of upper level of a variable

I am analyzing data on a health variable and its relation to age, gender, height etc. I am more interested in 90th percentile of the health variable, which can be called upper limit of ‘normal’. How will this analysis be different from regular analysis where one is trying to find out factors predicting the value … Read more

What test should I use with a dichotomous dependent variable and a continuous independent variable for agreement analysis?

I’m conducting a study in which I’m testing interrater agreement on a new radiologic technique to the pathological evaluation (gold standard). I’ve got 58 patients and 15 raters. Raters have been asked to evaluate the degree of cancer invasion (‘Deep’ vs. ‘Superficial’) and have also reported how certain they are in their assessment, using a … Read more

Not able to understand KL decomposition

The bias-variance decomposition usually applies to regression data. We would like to obtain similar decomposition for classification, when the prediction is given as a probability distribution over C classes. Let P=[P1,…,PC] be the ground truth class distribution associated to a particular input pattern. Assume the random estimator of class probabilities ˉP=[ˉP1,…,ˉPC] for the same input … Read more

Conditional Gaussian Distribution

I am trying to study this paper on Linear Gaussian Models. I’m a little stuck on the following result for finding the conditional of a Gaussian: In the paper it states this is done ‘simply by linear matrix projection’, could anyone possibly provide me with a starting point or some hints so I can try … Read more

Expectation of ratio between product of gaussian r.v.’s and generalized gamma r.v

Given Z=[z11z12⋯z1Pz21z22⋯z2Pz31z32⋯z3P⋮⋮⋱⋮zM1zM2⋯zMP]=[z1z2⋯zP] where the zmp are i.i.d. ∀ m,p with distribution zmp∼CN(0,c) and zi represents each of the columns of Z∼CN(0M×P,cMIP). Other necessary definition is given by ZHZ=[zH1zH2⋮zHP][z1z2⋯zP]=[zH1z1zH1z2⋯zH1zPzH2z1zH2z2⋯zH2zP⋮⋮⋱⋮zHPz1zHPz2⋯zHPzP] Next we define the following ratio: ZHZTr(ZHZ)2=ZHZ(zH1z1+zH2z2+⋯+zHPzP)2 where Tr is the Trace operator. It is important to note that the elements of the main diagonal of ZHZ, namely … Read more

Distribution of $\frac{X_{1}}{X_{1}^{2}+X_{2}^{2}}$, where $(X_1,X_2)$ is bivariate normal?

What is the distribution of $\frac{X_{1}}{X_{1}^{2}+X_{2}^{2}}$ when $(X_1,X_2)$ has a bivariate normal distribution? Answer AttributionSource : Link , Question Author : Jingjings , Answer Author : Community

For y=x+ϵy=x+\epsilon, how can we obtain the SD of xx when y>ty\gt t

Given that x∼N(0,σ2=h2)ϵ∼N(0,σ2=(1−h2))y=x+ϵ Then y is essentially a bivariate normal distribution with ∑=(0000) (thank you whuber) If we select the top t% of y as cases, then we can obtain the mean and variance of y for case and control as follow <- function(t){ require(truncnorm) case.mean <- dnorm(qnorm(t))/t case.var <- vtruncnorm(a=qnorm(t, lower.tail=F), b=Inf, mean=0, … Read more

Subsample to follow a normal distribution

I have a problem, that sounds very simple in theory but I fail to implement a good solution. Let my data be a sample of a continuous variable that that follows a normal distribution (m1,v1), associated with some other variables for each point. I want to get a subsample of this data where this variable … Read more

Large deviations results for cosine of two samples from Normal?

I’m looking for large-deviations style results for cosine of two independent samples drawn from N(0,Σ) . IE, q=⟨X,Y⟩‖ More specifically, are there any interesting bounds on the probability of this value being large in terms of properties of \mathcal \Sigma ? Intuitively it seems this value should be small when \Sigma has small condition number. … Read more

Chisquared distribution test in R

I’m reading the paper by Lourme A. et al (2016) and try to plot the Fig.2 from this paper. The question regarding to programming of confidence areas and my example in R is here. 4.1.2. Confidence areas Let u=(u1,…,ud)⊤ be a random vector with uniform margins on (0,1) and let y=(y1,…,yd)⊤∈Rd be defined by: yj=G(uj), … Read more