Tagged Questions
2
votes
1answer
60 views
Pinsker's Inequality for Bayesian hypothesis testing
I am wondering if one can relate the KL divergence to the probability of error in a Bayesian binary hypothesis testing setting. That is, we have to decide between hypotheses $A$ and $B$ given ...
6
votes
1answer
361 views
Error exponent in hypothesis testing
In hypothesis testing, one must decide between two probability distributions $P_1(x)$ and $P_2(x)$ on a finite set $X$, after observing $n$ i.i.d. samples $x_1,...,x_n$ drawn from the unknown ...
6
votes
2answers
256 views
On error probability bounds in Bayesian hypothesis testing
In the Bayesian version of (binary) hypothesis testing one has to decide which of two hypotheses $A$ and $B$ holds true. The two hypotheses are given prior probability $p(A)$ and $p(B)$, summing up to ...
4
votes
3answers
358 views
Akaike Information Criterion and composite variables
Akaike information criterion is a measure for goodness of fit of a model that compensates for the number of parameters that were used to build that model.
Consider two linear models, one that is ...
1
vote
1answer
76 views
How does one express the decrease in minimal type II error bound for each observation added?
Problem: I have a "classifier" that uses some arbitrary hypothesis test on observations from one of two known probability distributions:
$P_0$ (null hypothesis $H_0$) is a zero-mean Gaussian ...
5
votes
2answers
932 views
Hypothesis testing and total variation distance vs. Kullback-Leibler divergence
In my research I have run into the following general problem: I have two distributions $P$ and $Q$ over the same domain, and a large (but finite) number of samples from those distributions. Samples ...
5
votes
3answers
2k views
Measure of similarity or distance between two symmetric covariance matrices
are there any measures of similarity or distance between two symmetric covariance matrices (both having the same dimension)?
I am thinking here of analogues to KL divergence of two probability ...
