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Unanswered Questions

50,648 questions with no upvoted or accepted answers
34
votes
0answers
2k views

Probability inequalities

I am looking for some probability inequalities for sums of unbounded random variables. I would really appreciate it if anyone can provide me some thoughts. My problem is to find an exponential upper ...
28
votes
0answers
1k views

Link Anomaly Detection in Temporal Network

I came across this paper that uses link anomaly detection to predict trending topics, and I found it incredibly intriguing: The paper is "Discovering Emerging Topics in Social Streams via Link Anomaly ...
25
votes
1answer
490 views

Jaynes' $A_p$ distribution

In Jaynes' book "Probability Theory: The Logic of Science", Jaynes has a chapter (Ch 18) entitled "The $A_p$ distribution and rule of succession" in which he introduces the idea of $A_p$ distributions,...
22
votes
0answers
320 views

Did Deborah Mayo refute Birnbaum's proof of the likelihood principle?

This is somewhat related to my previous question here: An example where the likelihood principle *really* matters? Apparently, Deborah Mayo published a paper in Statistical Science refuting Birnbaum'...
22
votes
1answer
10k views

The cross validation (CV) and the generalized cross validation (GCV) statistics

I have found possibly conflicting definitions for the cross validation (CV) statistic and for the generalized cross validation (GCV) statistic associated with a linear model $Y = X\boldsymbol\beta + \...
21
votes
1answer
545 views

Wavelet-domain gaussian processes: what is the covariance?

I've been reading Maraun et al, "Nonstationary Gaussian processes in wavelet domain: Synthesis, estimation, and significant testing" (2007) which defines a class of non-stationary GPs that can be ...
21
votes
0answers
533 views

Bound for Arithmetic Harmonic mean inequality for matrices?

NOTE: This question has originally been posted in MSE, but it did not generate any interest. It was first posted there, because the question itself is a pure matrix-algebra question. Nevertheless, ...
18
votes
0answers
987 views

How to create a multivariate Brownian Bridge

It is known, that a standard multivariate Brownian bridge $ y(\mathbf u) $ is a centered Gaussian process with covariance function $$ \mathbb E(y(\mathbf u) y(\mathbf v)) = \prod_{j=1}^d (u_j \wedge ...
17
votes
0answers
618 views

How does a Relevance Vector Machine (RVM) work?

Relevance Vector Machines (RVMs) are really interesting models when contrasted with the highly geometrical (and popular) SVMs. In the light of a question like How does a Support Vector Machine (SVM) ...
17
votes
0answers
382 views

Blind source separation of convex mixture?

Suppose I have $n$ independent sources, $X_1, X_2, ..., X_n$ and I observe $m$ convex mixtures: \begin{align} Y_1 &= a_{11}X_1 + a_{12}X_2 + \cdots + a_{1n}X_n\\ ...&\\ Y_m &= a_{m1}X_1 + ...
17
votes
1answer
973 views

$ARIMA(p,d,q)+X_t$, Simulation over Forecasting period

I have time series data and I used an $ARIMA(p,d,q)+X_t$ as the model to fit the data. The $X_t$ is an indicator random variable that is either 0 (when I don’t see a rare event) or 1 (when I see the ...
16
votes
0answers
449 views

Fitting custom distributions by MLE

My question relates to fitting custom distributions in R but I feel it has enough of a probability element to remain on CV. I have an interesting set of data which has the following characteristics: ...
16
votes
0answers
749 views

Diagnostic plot for assessing homogeneity of variance-covariance matrices

Is there a handy plot for comparing the variance-covariance matrices of two (or perhaps more) groups? An alternative to looking at lots of marginal plots, especially in the multivariate Normal case?
16
votes
1answer
650 views

Upper bounds for the copula density?

The Fréchet–Hoeffding upper bound applies to the copula distribution function and it is given by $$C(u_1,...,u_d)\leq \min\{u_1,..,u_d\}.$$ Is there a similar (in the sense that it depends on the ...
16
votes
0answers
490 views

Distribution of inverse Wishart to a power?

In a related question, I had asked about the norm induced by an inverse Wishart matrix. I am interested in generalizing that result somewhat. Let $A\sim\mathcal{W}_p\left(I,n\right)$, a Wishart matrix ...

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