Smoothing a time-series with a Bayesian model

Smoothing a time-series with a Bayesian model Recently I looked at fitting a smoother to atime-series usingBayesian modelling.Now I will look at how you can control the smoothness by using more orless informative priors on the precision (1/variance) of the randomeffect. We will use the same dataset as the lastpost. To control the priors for an R-INLA model, weuse the hyper argument (not hyperactive, but hyper-parameters): library(INLA) f3 We can control the level of smoothing through param=c(theta1,0.01). Avalue of 1 (theta1) is a reasonable starting point (based on the INLAdocumentation).Lower values will result in a smoother fit. The pc.param stands for Penalized complexity parameters (you couldalso use a loggamma prior here). My understanding of penalizedcomplexity priors is that they shrinkthe parameter estimate towards a ‘base-model’ that is less flexible. Inthis case, we are shrinking the standard deviation (AKA the…
Original Post: Smoothing a time-series with a Bayesian model

Quantifying the magnitude of a population decline with Bayesian time-series modelling

Quantifying the magnitude of a population decline with Bayesian time-series modelling Population abundances tend to vary year to year. This variation can makeit make it hard detect a change and hard to quantify exactly what thatchange is. Bayesian time-series analysis can help us quantify a decline and putuncertainty bounds on it too. Here I will use the R-INLApackage to fit a time-series model to apopulation decline. For instance, take the pictured time-series. Quantifying change as thedifference between the first and last time-points is obviouslymisleading. Doing so would imply that abundance has declined by 77% fromthe historical value. Another approach would be to compare the average of the first and lastdecades. Doing so would yield a 72% decline. A better way might be to model the population trend over time and thenestimate our change from the model. An advantage of…
Original Post: Quantifying the magnitude of a population decline with Bayesian time-series modelling