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Interesting philosophical issues arise with very small Poisson rates. Also with the choosing of appropriate prior distributions for Bayesian analysis of low rates. Hypthetical particle. Suppose I'm looking for evidence of a theoretically predicted, but never observed G-particle. After 50 runs of my particle collider, I have seen no traces of the kind G-...


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When including an interaction in a regression, you should always center (= x - μ) to maintain interpretability of the main effects (by centering, main effects are calculated for the mean value of x). Whether you divide by sd is up to you. The standardising by sd is usually done to make regression estimates directly comparable. A side effect is that it ...


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Visual summary There no evidence more compelling than a simple visual summary of your data: Both figures show count vs distance, but the one on the right has a logarithmic y-axis. There is a clear trend towards lower particle counts further from the road curb, which I assume is also what you would expect. Which of these plots is better depends on your ...


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What you want is a model that relates the expected distance $E[D]$ to the count $C$. If you thought the three samples functioned differently, you could estimate three separate regression models of the form $E[D|C,S=s']=\beta_{s'0}+\beta_{s'1}C$, where $S$ is the sample variable and $s'$ is one of the samples (i.e., a, f, m). This would give you three ...


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It's a bit nuanced. You could pull out the big guns and use a poisson regression # example sample of counts (n = 50, 'true' mean = 5) set.seed(25) d <- rpois(50, 5) model = glm(d~1, family = poisson) exp(confint(model)) >>> 2.5 % 97.5 % 4.143126 5.348048 Or you could use the normal approximation since, as $\lambda$ gets big ...


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your data suggests not on;y a mean shift but a change in variance AND an anomaly at the last point. What you need to do is to identify a SARIMA model https://autobox.com/pdfs/ARIMA%20FLOW%20CHART.pdf and include any and all latent deterministic structure . Consider http://docplayer.net/12080848-Outliers-level-shifts-and-variance-changes-in-time-series.html ...


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