First, a quick review of intervals. We define the following four cases: • The closed interval [a, b] = {t : a ≤ t ≤ b}; The half-open interval (a, b] = {t : a < t ≤ b}; • The half-open interval [a, b) = {t : a ≤ t < b}; The open interval (a, b) = {t : a < t < b}. If a or b is ±∞, use a half-open or open interval. Never write (even implicitly) “t = ∞”–this is uncouth! Now let x(t) be a continuou...

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A number of studies in perception, attention, and memory employ signal detection theory (SDT) to assess the accuracy of an observer's detection or discrimination performance. Some of the problems that students have with understanding and using SDT are associated with the calculations needed to obtain SDT parameters and predictions. All of these calculations, plus the simulation of SDT processes...

How often are we wise after the event? With the benefit of hindsight we see that we should have paid attention to something but at the time it seemed irrelevant. It may not even have been brought to the attention of the responsible executive as it was considered trivial. We may not have even seen the relevant data, even if we saw it then we may not have paid it much attention. Even if we or our...

What do inferring what a person is thinking or feeling, judging a defendant's guilt, and navigating a dimly lit room have in common? They involve perceptual uncertainty (e.g., a scowling face might indicate anger or concentration, for which different responses are appropriate) and behavioral risk (e.g., a cost to making the wrong response). Signal detection theory describes these types of decis...

We extend the Bayesian method of Gregory and Loredo (1992) for the detection of a periodic signal of unknown shape and period, to the case where the noise sampling distribution is independent Gaussian. The analysis readily handles nonuniformily sampled data and allows for an unknown noise variance. The method is applied to the radio astronomy data for the interesting X-ray binary system LS I +6...

This paper does not present finished work but discusses a current problem faced by the EMEA in detecting when a new safety problem with a marketed pharmaceutical product is emerging. This detection is based on analysis of a very large database of spontaneous reports by healthcare professionals. The mixture of complexity but also known structure within the data appear to call for a combination o...

Signal Detection Theory (often abridged as SDT) is used to analyze data coming from experiments where the task is to categorize ambiguous stimuli which can be generated either by a known process (called the signal) or be obtained by chance (called the noise in the SDT framework). For example a radar operator must decide if what she sees on the radar screen indicates the presence of a plane (the...

The paper addresses a problem of tracking multiple number of frequencies using Regularized Autoregressive (RAR) approximation. The RAR procedure allows to decrease approximation bias, comparing to other AR-based frequency detection methods, while still providing competitive variance of sample estimates. We show that the RAR estimates of multiple periodicities are consistent in probabilit...