The Likelihood Ratio Test

The likelihood ratio test maximizes the probability of correctly deciding hypothesis H_1 is true for any given probability of deciding H_0 is false when the hypotheses are both simple. Example showing the likelihood ratio test for a known signal in noise is a matched filter.

[@nhuphan6969]

I don't think I can understand LRT just with one video like this!!! Amazing video! Thank you for doing this. Your writing is so neat as well ! Thanks again.

[@hihihi5367]

Wow! Thanks for the video, I was struggling making sense of what my instructors were trying to explain during lecture, but this video made everything extremely clear. Thank you!!

[@fakhtehsiavoshi9818]

It was fantastic I can't believe I understand this topic finally after one week. You helped me a lot. Thanks.

[@allsignalprocessing]

Sorry for the slow reply. Normally you would vary the threshold to get the ROC, and if the pdfs of your test statistic under each hypothesis are unknown, then you can use simulations - run a large number of random simulations when each hypoth is true and then use that one set with your varying threshold to find the fraction of each exceeding the threshold to get the ROC. Be careful near the endpoints though as getting those probabilities with simulation is tricky.

[@umehabiba2666]

Likelyhood ratio and generalized likelyhood ratio are same or not?

[@hayaeman6583]

Excuse me... How type one error effect likelihood ratio test?.. Can you plz tell me

[@allsignalprocessing]

yes, L and L' are different symbols for the likelihood ratio. L' is NOT the derivative of L.

[@RickCorp]

You are using prime as a notation and not a derivative?

[@copernicus99]

Nice lecture. Could you please direct me to a site which will calculate d-prime from the hit and false alarm rates? Thanks.

[@rohanghige]

Such a nice explaination. I am becoming fan of your teaching.. :)

[@HaVuong2023]

I like your teaching. Thanks

[@hebaomar7535]

thank you for great explanation , can you send me the executable code for this explanation

[@ozairkamal1022]

Variable Parameter Standard Error
Intercept 0.34 0.29
Travel Time (in Minutes) -0.039 0.01
Travel Costs (In €) -0.175 0.02
Observations 500
Null Log-Likelihood (𝑙𝑛L0) -510
Final Log-Likelihood (𝑙𝑛L1) -500
a) Write down the logistic regression equation.
b) Interpret the estimated coefficients.
c) What is the probability of car use, if he needs 10 Minutes to go to
work and the cost for this is one Euro?
d) Perform a Likelihood-Ratio test (=0.01) in order to decide on the
overall goodness of the model.
e) For additional points: How can you interpret the ratio of the
coefficient of travel time to the coefficient of travel cost
NOTE: THIS QUESTION IS LOGESTIC REGRESSION
please "Barry van veen" can you solve this question for me. i'm a student and day after tomorrow i've to submit my homework and i dont know how to solve this question especially part D and E

[@jmsescribano]

Ja

[@samsayn5170]

what a jerk

[@jiamingxie4781]

Very nice explanations!

[@boostan66]

Very well explained!

[@Ms151084]

how come I cannot play this video?

[@ispeakfactslol]

Thank you sir.

[@alhazen93]

thank u, very good explanation

[@thisSreal]

Great Teaching :-) !!!

[@TheOneT1]

Thank you sir

[@ltbd78]

Thank you