Given a likelihood function, f(θ|D), where θ denotes parameter of interest and D denotes observed data, and prior distribution, p, on the parameter space, Θ, our statistical inference is based on posterior distribution of θ, p(θ|D)∝f(θ|D p.
Applying (5) the likelihood of replicate r=1,2,3 is (10) where y i r, R is the vector of observed data points i=1,…, T R for variables M, P, P v for replicate r under the red light experiment, y j r, C denotes observed data points j=1,…, T C for the corresponding control experiment and g is a product of Gamma densities.
The root mean square percent error (RMSPE) statistic [30] is used for Fig. 4: Open image in new window Fig. 4 Summary goodness-of-fit statistic (RMSPE) Open image in new window (15 where x is the variable of interest, N is the number of observations (years) and superscripts 0 and 1 denote observed and fitted measures respectively.
"Obs"and "Calc" denote observed displacements after the Geospatial Information Authority of Japan et al. (2012) and those calculated for the model given by Fig. 7 and Table 4, respectively.
Red lines denote volcanic craters; dots represent areas of volcanic cones; bold lines and dashed lines denote observed and estimated active faults, respectively; and the fine dashed lines denote the lineaments.
Large ellipses denote observed phase tensor ellipses, whereas small ones in the background denote synthetic ellipses at respective virtual sites, which were calculated from the 3-D resistivity model.
Take the example of a survival data with right censoring up to time T, where we observe m random failures out of n subjects and denote observed failure times as t 1, t 2, t 3, … t m.
BPCA assumes Y = { Y obs, Y mis}, where Y obs and Y mis denote observed part and the missing part.
In addition, we used the mean absolute percentage error (MAPE) and fitting effect diagram to assess forecast accuracy., where x t and denote observed and fitted values at time point t.
We explicitly allow for time-varying elements of (X k, U k ), k=1,2, and C12 by adding the subscript (t), use bold-face font to denote vectors, and use lower-case letters to denote observed and counterfactual values of random variables.
The first, the CUSUM (for "cumulative summation") algorithm, monitors the daily statistic S i which is defined by the recursive formula where X i denotes the observed daily count on day i, μ denotes the overall mean daily count estimated from the data, and k is an off-set parameter set by the user [ 17, 18].
