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Bayesian Estimation Of The Intensity Function Of A Non-Homogeneous Poisson Process, James Jensen
Bayesian Estimation Of The Intensity Function Of A Non-Homogeneous Poisson Process, James Jensen
Theses
In this paper we explore Bayesian inference and its application to the problem of estimating the intensity function of a non-homogeneous Poisson process. These processes model the behavior of phenomena in which one or more events, known as arrivals, occur independently of one another over a certain period of time. We are concerned with the number of events occurring during particular time intervals across several realizations of the process. We show that given sufficient data, we are able to construct a piecewise-constant function which accurately estimates the mean rates on particular intervals. Further, we show that as we reduce these …
On Misuses Of The Kolmogorov–Smirnov Test For One-Sample Goodness-Of-Fit, Anthony Zeimbekakis
On Misuses Of The Kolmogorov–Smirnov Test For One-Sample Goodness-Of-Fit, Anthony Zeimbekakis
Honors Scholar Theses
The Kolmogorov–Smirnov (KS) test is one of the most popular goodness-of-fit tests for comparing a sample with a hypothesized parametric distribution. Nevertheless, it has often been misused. The standard one-sample KS test applies to independent, continuous data with a hypothesized distribution that is completely specified. It is not uncommon, however, to see in the literature that it was applied to dependent, discrete, or rounded data, with hypothesized distributions containing estimated parameters. For example, it has been "discovered" multiple times that the test is too conservative when the parameters are estimated. We demonstrate misuses of the one-sample KS test in three …