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 16h comment I want to show$X : ((0,1],\mathcal B,\lambda)\to \mathbb R$ is random variable If $F$ is strictly increasing, can you solve it? If you can do that,you can get the answer in general by modifying your original answer. Dec5 comment Stats is not maths? @whuber I don't think that analogy is totally fair, because saying that statistics is "an inverse of probability" actually captures what statisticians are doing - given random data generated from a process, we attempt to learn things about that process. I don't see how this is that far away from what a practicing statistician is doing (e.g. I'm given data from a clinical trial and I wish to generalize the effect of a drug to the whole population). Dec5 comment Stats is not maths? @whuber could you elaborate on why you feel that regarding statistics as an "inverse of probability theory in some sense" is uninformed? I feel that it captures the high-level difference in motivations fairly well, in that in statistics we are given data and are tasked with getting at the generating mechanism while probability focuses on a given generating mechanism and asks questions about such as what data to expect from it. Insofar as statistics is a mathematical discipline this seems reasonable. Nov29 comment Do ensemble techniques increase VC-dimension? Well, just thinking about the definition of VC-dimension, do you think (say) boosted decision stumps can shatter a larger number of points than a single decision stump? Nov25 comment Can Kaplan Meier method be used to estimate left-censored data? Assuming nonnegative, can't you just invert the observations and apply the KM estimator to that? It is my guess is that this is equivalent to deriving and using the KM estimator for left censored data, but I'm not sure. Nov7 comment What is the computational complexity of the EM algorithm? You can do the computational cost per iteration, though. Of course, for a given problem there might be different ways of implementing the same EM procedure with different computational complexities. Nov6 comment p-value of hypothesis “a home court advantage exists” I also do not see why we can't just test $p_H > p_A$ where $p_H$ is the probability that the home team won and $p_A$ the probability the away team won. If we have a random sample of games with different teams, why isn't this test equivalent to a home advantage? Isn't that the definition of a home advantage? Nov4 comment Is it possible to interpret the bootstrap from a Bayesian perspective? If I recall, they make this argument, bootstrap a NN, and proceed to get creamed by a fully Bayesian NN by Radford Neal. I think that says something, not sure what though. Oct31 comment Why semi/nonparametric models? Wolfram also agrees with me. See here. Or just google "Neural network nonparametric" and look over the tons of papers that come up. Oct31 comment Why semi/nonparametric models? Are you arguing that neither Wasserman nor Vapnik would consider ANNs to be nonparametric techniques? I'm confident enough that I would bet money that both would agree with me. Wasserman because he devotes most of his book to estimating arbitrary mean functions and densities - which Neural nets can do within a statistical framework - and Vapnik because he uses ANNs as a constant comparison to his SVM which I know he explicitly labels as nonparametric. Oct30 comment Why semi/nonparametric models? Never mentioned Brownian bridges, no idea where you got that from. What I'm saying is that estimating an arbitrary real valued function is a nonparametric problem regardless of what your goals are - see this, or this, for example - and since ANNs with topology as a free parameter can solve this problem, it should be regarded as a nonparametric method. Oct30 comment Why semi/nonparametric models? I don't see what conducting inference has to do with a problem being nonparametric. If I want estimate an arbitrary function on $[0, 1]$, this is by all definitions I've read a nonparametric problem. I mean, if you want you can have as strict a definition of "nonparametric" as you like, but I think these days people are much looser with the term. Incidentally, Cox models and rank tests didn't even make it into Wasserman's "All of Nonparametric Statistics." Oct30 comment Why semi/nonparametric models? "Nonparametric" doesn't typically mean "I have no parameters." Even in the simplest case of $X_1, \ldots, X_n \sim F$ where $F$ is an unspecified cdf, $F$ is just a parameter in the (infinite-dimensional) space of cdfs. A common definition of a nonparametric problem is one with an infinite-dimensional parameter space, and a method is nonparametric if it can estimate anything in that space. Then, the class of ANNs (with network topology a free parameter) fits this definition for nonparametric function estimation. Oct30 comment Why semi/nonparametric models? The ML models can be formalized as nonparametric using sieves (which to an extent is similar to how they are used) I think, combined with universal approximation I'd say nonparametric is a fine label. Oct30 comment Why semi/nonparametric models? Bayesian nonparametric has nonparametric right there in the name (formally, we put a prior on the space of cdfs which has large support) and is used for inference all the time. To simulate we can just draw the measure from the posterior. OP is also likely from ML given that he is using Statistical Learning Theory lingo. Oct30 comment Why semi/nonparametric models? Now that you've edited, it's apparent this is about Bayesian nonparametrics, rather than the other 90% of nonparametrics. Associated with each BNP model is usually some story about the data similar to a parametric model, and they tend to do well when the story they tell makes sense. For a success story, just look at HDP; variations on HDP are very close to state-of-the-art for topic modeling. Oct30 comment Why semi/nonparametric models? This is a very classical perspective. Personally, I'd be fine with calling RBMs or ANNs "nonparametric" but you certainly can simulate from them. Ditto for Bayesian nonparametric methods. Oct30 comment Why semi/nonparametric models? I don't know why this is tagged with Bayesian - most research in nonparametric methods is frequentist. And isn't the success of the SVM an argument that we can do nonparametric stuff with provable empirical risk bounds? Neural nets are also, in spirit, nonparametric models (universal approximation theorem) with some clever regularization schemes, and these are state-of-the-art for many problems. Oct30 comment Understanding Sufficient Statistics If $X_1, \ldots, X_n \sim N(\mu, 1)$ then $\bar X$ is sufficient for $\mu$. Does it make sense to write $f(x_1, \ldots, x_n, \bar x)$? It only makes sense if the density is defined on $\mathbb R^n$ rather than $\mathbb R^{n+1}$. You can't just appeal to your definition of conditional probability, because these are density functions; they don't have sets as their arguments. Oct30 comment Understanding Sufficient Statistics Are these random variables discrete? Otherwise the first equality does not necessarily make sense. Typically $(X_1, \ldots, X_n \mid \hat \Theta)$ will not admit an $n$-dimensional density, nor will $(X_1, \ldots, X_n, \hat \Theta)$ admit an $n+1$-dimensional density.