Test if one Poisson process’s rate is smaller than a given value

Suppose N(t) is a Poisson process with rates λ. Suppose I’ve been observing it for t∈[0,T] and recorded events. How can I test the null hypothesis λ<λ0, where λ0 is a given value? An obvious solution is to derive MLE of rates ˆλ and compare with λ0. But I don’t know how to calculate the … Read more

Independence of points from same underlying function

I have a function y=sin(x) I sample the points xi={0,0.1,0.2,0.3,0.4,0.5,0.6,0.7,0.8,0.9,1} and yi=sin(xi)+ϵ  ϵ∼iid Normal Now given only the set {xi,yi} I want to uncover the underlying functional form f(x) given as y=f(x)+ϵ    ϵ∼iid Normal My question is : ARE yi‘s independent ? My intuition is that y1 and y2 are not independent. This is because given a new x … Read more

Are there any quantitative metrics for how representative a sample is?

I’m interested in selecting a sample that is representative of a population. Additionally, I want to be able to quantitatively measure the representativeness of a sample. For example, is there a way to determine, for a sample size n, where n is some fraction of the population size x, how representative the sample is? Can … Read more

Centrality measures and interpretation

I am new to graph theory and I have some questioning. First of all, how can I determine the significant of two different degree centrality means and two different closeness centrality means? For example, I have a network of international organizations which are public or private, but I don’t know how to determine if the … Read more

Significance Testing with Model Error

My set up is the following: I have a group of people, initially whose gender I do not know. I predict the gender of each individual with a gender prediction model and put them into Male and Female group. I know the accuracy/error of this model. My test statistic is % of people that like … Read more

How do I test for differences in cost per acquisition (CPA) in an A/B test?

How would I go about testing for differences in cost per acquisition (CPA) in an A/B test? I’m a huge novice and am unsure if I would use some kind of t-test or chi-square test (or neither) to compare the proportion of cost per acquisition in group A to cost per acquisition in group B. … Read more