# sesqu

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 Feb15 comment Poisson distribution and statistical significance As in Aniko's answer, you need to use 129 for the first parameter to ppois, since $F(X\ge 130)=F(X>129)$. Feb12 comment Compression theory, practice, for time series with values in a space of distributions (say of a real random variable) Sure, if your model family is, say, an equal mix of multinomials $N(\vec {data}, \vec 1)$, you will have to store all data, since that is your parameter. In this case, you will have to compress the data according to some prior. However, unless your model assumes subsequent time points are independent (and it doesn't, or you wouldn't have specified time series), you can still take advantage of the dependence to refine the prior for $X_t|data_t,X_{t-1}$. Feb12 comment Compression theory, practice, for time series with values in a space of distributions (say of a real random variable) @robin You said you have a forecast, which implies a model for a random variable. That model comprises a family of distributions for the variable and a function to identify the distribution you predict from the data. The parameter is the processed data that identifies the predictive distribution - without one, there would be no variability in your predictions. Feb12 revised Compression theory, practice, for time series with values in a space of distributions (say of a real random variable) added 1 characters in body Feb12 answered Compression theory, practice, for time series with values in a space of distributions (say of a real random variable) Feb5 comment What, precisely, is a confidence interval? @probabilityislogic - yes. If probability is redefined, one can no longer use the inductive and abductive justifications for various distributions. Distributions like the binomial need to be re-derived within this belief system, and it's my understanding that this is done merely by grafting the necessary axioms onto the system, under the pseudonym "rationality". These axioms are intrinsic to the nondeterministic interpretation. Feb5 comment What, precisely, is a confidence interval? @probabilityislogic - the question I attempted to pose is the nature of $p$. What is this known thing your faith in $k$ is so specifically conditional on? Why is it conditional on $p$ in that particular manner? Feb5 comment What, precisely, is a confidence interval? @probabilityislogic - if probability is defined as state of mind, we lose derived results (except maybe as conjugate posteriors from a description length perspective). Consider the binomial distribution - if the probability $P(K=k|p,N)$ is defined as belief, what is the $p$ parameter of that belief? Not a probability. The binomial would have to be seen as the limiting case of a beta-binomial. While such complications may prove manageable, I don't think the rational belief can be. As for the other worlds behaving similarly: that is explicit in the conditional iid assumption always made. Feb4 revised How to find the best input value for this simple problem? added 202 characters in body; deleted 1 characters in body Feb4 answered How to find the best input value for this simple problem? Feb4 comment What, precisely, is a confidence interval? Is (1) really the commonly accepted definition of classical probability? I find it circular, and use a different one myself. Specifically, the long-run proportion is a random variable, and only approaches the probability in probability. The definition I use is a many-worlds interpretation, in which probability is the proportion of relevant possible futures. My understanding is that quantum physics isn't at war with this interpretation, but that's difficult to ascertain with coevolutionary fields. Jan29 comment What is the hardest statistical concept to grasp? This was the question I found most distracting after statistics 101. I would encounter many distributions with no motivation for them beyond "properties" that were relevant to topics at hand. It took unacceptably long to find out what any represented. Jan29 comment What is the hardest statistical concept to grasp? @Carlos I suspect the prevalence of $2\pi$ is mostly due to the use of the $\ell^2$ metric, leading to n-spheres. In the same vein, I would expect it's $e$ whose prevalence is due to analysis. Jan19 answered How to prove that Elo rating or Page ranking have a meaning for my set? Jan7 awarded Supporter Jan6 awarded Commentator Jan6 comment Estimating a distribution based on three percentiles Good observation. In this case, the usual quadratic polynomial fails to work, but there are infinitely many quadratic splines to choose from (think Bézier) that should not have the same problem (though some might still require domain cropping). Similarly, it should be possible to find a suitable monotonic cubic spline. I am aware of spline algorithms that guarantee monotonicity, but am unable to find one just now, so I have to leave the matter at "pick something you like that works as cdf". Jan6 awarded Editor Jan6 answered Estimating a distribution based on three percentiles Jan5 answered How to identify outliers in server uptime performance data?