You have no idea how your video is literally saving my semester ! I've just started a Master in Finance and we all have to take advanced stats. We've already spent 3 weeks talking about exponential families and no student in class understands what the heck is going on (the Professor is terrible at explaining). Your lecture makes it so much easier to understand this topic. I wish we could have you as a statistics Professor ! Thank you a million times for your video(s)❤
Thanks for answering all my questions. I need to understand every detail of a problem, so thanks for being so accommodating. At 47:39, there is not an h(x). That is okay?
Rather than saying there isn't an h(x), I would say h(x)=1, which is fine. It doesn't have to be a non-trivial function of x. Happy to answer any questions! Honestly, I never expected anyone other than my students to view these, so it's neat to see other folks working through them.
@@stephencarden3717 , again, thanks so much for your help. I'm going to McGill in the fall for a PhD in biostatistics after being a statistician for ten years, and I'm refreshing my memory with abstract statistics. This class has been invaluable!
There's two reasons. The theoretical reason is that If is treated as a parameter then θ is a vector containing both and , then we can't separate out the functions h(x) and c(θ), and the whole framework of exponential families doesn't apply. But I find the practical reason more enlightening. In Mathematical Statistics II, you shift perspective and use observed data to estimate unknown parameters. Binomials are used to model the number of successes in iid Bernoulli() trials. Most famously, when sampling and observing a qualitative variable, the true proportion p of being in the category of interest is unknown, but the sample size is known. There's a need to estimate p, but there's no need to estimate the sample size n... it's whatever the researcher decided to use. So there's a fundamental difference in practice in how we think about n and p, and that's why we treat it as a fixed value not included in θ in this example.Now, it's possible to construct a scenario in which both and are unknown, and I do a single example of how to perform a joint estimation when I teach Math Stat II (off the top of my head I think it's in Casella & Berger). But that's not the typical case, and for the usual scenario it's fine to treat p as fixed but unknown and n as fixed and known.
You have no idea how your video is literally saving my semester !
I've just started a Master in Finance and we all have to take advanced stats.
We've already spent 3 weeks talking about exponential families and no student in class understands what the heck is going on (the Professor is terrible at explaining).
Your lecture makes it so much easier to understand this topic.
I wish we could have you as a statistics Professor !
Thank you a million times for your video(s)❤
Glad it helped! It's a tricky topic to begin with, and made worse by texts using varying definitions. Thanks for dropping a comment!
Thanks for answering all my questions. I need to understand every detail of a problem, so thanks for being so accommodating. At 47:39, there is not an h(x). That is okay?
Rather than saying there isn't an h(x), I would say h(x)=1, which is fine. It doesn't have to be a non-trivial function of x.
Happy to answer any questions! Honestly, I never expected anyone other than my students to view these, so it's neat to see other folks working through them.
@@stephencarden3717 , again, thanks so much for your help. I'm going to McGill in the fall for a PhD in biostatistics after being a statistician for ten years, and I'm refreshing my memory with abstract statistics. This class has been invaluable!
15:15, why aren't we treating n as a variable parameter as we normally do?
There's two reasons. The theoretical reason is that If is treated as a parameter then θ is a vector containing both and , then we can't separate out the functions h(x) and c(θ), and the whole framework of exponential families doesn't apply.
But I find the practical reason more enlightening. In Mathematical Statistics II, you shift perspective and use observed data to estimate unknown parameters. Binomials are used to model the number of successes in iid Bernoulli() trials. Most famously, when sampling and observing a qualitative variable, the true proportion p of being in the category of interest is unknown, but the sample size is known. There's a need to estimate p, but there's no need to estimate the sample size n... it's whatever the researcher decided to use. So there's a fundamental difference in practice in how we think about n and p, and that's why we treat it as a fixed value not included in θ in this example.Now, it's possible to construct a scenario in which both and are unknown, and I do a single example of how to perform a joint estimation when I teach Math Stat II (off the top of my head I think it's in Casella & Berger). But that's not the typical case, and for the usual scenario it's fine to treat p as fixed but unknown and n as fixed and known.
@@stephencarden3717 , ooooohhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhh