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Because the underlying generative model is formulated in continuous time (with a discrete observation process) it can be applied to a wide variety of models specified with either ordinary or stochastic differential equations.
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Because studies made at the single cell level are not subject to the averaging effect characteristic of bulk-phase population-scale methods, they offer a level of discrete observation that is unavailable with traditional biological methods [3].
Although the predictors may change in continuous time, we only observed them at the discrete observation times and so do not express them as a function of time (t).
A longitudinal study involves time- discrete observation of time- continuous processes, where measurements of the variables of interest are taken at consecutive points in time.
It is more realistic and interesting to consider the parameter estimation for diffusion processes based on discrete observation, since the actual data may be obtained discretely.
The challenge, however, is that, a closed form expression for the transitional density between two consecutive discrete observation points is unavailable for the system in (4).
We demonstrate the existence and uniqueness of optimal observation schedules for discrete observation of the simple death process.
The cameras allowed for discrete observation of staff compared to direct "live" observation; however, the cameras were visible to staff, and all staff were made aware of the study in advance to provide consent, therefore Hawthorne effects still could have resulted in altered (i.e. artificially improved) behaviour [ 53].
In this situation, we have a sample of discrete observations and try to estimate parameters for the process of (8) generating the sample.
As the prediction scheme is based on time series analysis, which basically requires a series of discrete observations collected over time, the input could be either class-wise traffic flow or total vehicular flow aggregated into any desired uniform time interval.
The Viterbi algorithm works by calculating the most likely sequence of states based on a sequence of discrete observations.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com