Tagged Questions
1
vote
0answers
30 views
Likelihood ratio test for a random variable following the Gamma Distribution
Assuming we have a random variable $X\sim \operatorname{Gamma}\left(\alpha,\beta \right )$:$\frac{1}{\Gamma (\alpha )\beta ^{\alpha}}x^{\alpha-1}e^{\frac{-x}{\beta }}$
I'd like to test the ...
2
votes
0answers
41 views
Understanding Sequential Probability Ratio Test (SPRT) Likelihood Ratio
I am a software developer looking to develop an alternative for the simple hypothesis testing scheme described here. In short, the test works as follows:
Two URLs are compared for their ability to ...
3
votes
0answers
112 views
Likelihood ratio test: $f(x)=2x$ vs $f(x)=3x^2$: $2n$ degrees of freedom?
Suppose $X_1, . . . , X_n$ are i.i.d. with pdf $f(ยท)$.
We want to test the hypotheses
\begin{align}
H_0 &: f(x) = 2x , \;\, \text{ for } 0 \le x \le 1, \text{ against}, \\
H_1 &: f(x) = 3x^2 , ...
0
votes
0answers
40 views
Comparing tests for staging cancer
I am comparing 4 different tests for the evaluation/identification of cancer. One is a continuous variable yielding cut-off values based on both the mean and the median of 5 consecutive measurements ...
4
votes
2answers
203 views
Can I use a likelihood ratio test when the error distributions differ?
This question might sound simple, but in fact I am absolutely unsure whether it is allowed to use an LRT for model comparison when the error distributions differ.
For example, can I compare a model ...
1
vote
1answer
269 views
Finding the p-value
I am a little stuck on the following question.
Skulls were excavated from a dig. The sex of each skull was determined by anatomical appreciation. For Sites A, the data was Male=162, Female=110.
a) ...
2
votes
1answer
191 views
How to choose between z and t in 2 sample (non-paired) tests?
I understand that in the one sample case, z is employed where population variance is known and t for where it is unknown.
In the two sample case: we are trying to test $H_0: \mu_x=\mu_y$ against ...
1
vote
1answer
359 views
How to interpret this criterion of logistic regression result
I run a backward variable selection logistic regression and find out the SAS program selected 12 variables and give me the output like this:
It is funny that my configuration of the SAS ...
1
vote
1answer
113 views
What is the outline for the procedure of model selection, with different models based on likelihood functions?
I have two basic models $M_1$ and $M_2$. They each have a likelihood function;
$L_{M_1} = f(\mathbf{X}|\mathbf{\theta_1})$ and $L_{M_2} = f(\mathbf{X}|\mathbf{\theta_2})$ (here $\mathbf{X}$ is the ...
2
votes
2answers
343 views
Practical definition of a UMP test?
I'm trying to make sense of these two statements about UMP (uniformly most powerful) tests:
If $g(t\mid\theta)~$ is a UMP then $~g(t\mid\theta_1)>k g(t\mid\theta_0)~\forall~t\in C$ and ...
2
votes
1answer
340 views
Likelihood ratio test vs. $\chi^2$/Z-test for comparing binomial datasets
When does/can one use the likelihood ratio significance test instead of Fisher's exact test or its Pearson $\chi^2$ approximation for comparing two binomial datasets?
Given two binomial datasets ...
10
votes
2answers
444 views
Has anyone solved PTLOS exercise 4.1?
This an exercise given in Probability Theory: The Logic of Science by Edwin Jaynes, 2003. There is a partial solution here. I have worked out a more general partial solution, and was wondering if ...
