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Bayesian Analysis of Latent Threshold Dynamic Models
, 2011
"... We describe a general approach to dynamic sparsity modelling in time series and statespace models. Timevarying parameters are linked to latent processes that are thresholded to induce zero values adaptively, providing dynamic variable inclusion/selection. We discuss Bayesian model estimation and p ..."
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We describe a general approach to dynamic sparsity modelling in time series and statespace models. Timevarying parameters are linked to latent processes that are thresholded to induce zero values adaptively, providing dynamic variable inclusion/selection. We discuss Bayesian model estimation and prediction in dynamic regressions, timevarying vector autoregressions and multivariate volatility models using latent thresholding. Substantive examples in macroeconomics and financial time series show the utility of this approach to dynamic parameter reduction and timevarying sparsity modelling in terms of statistical and economic interpretations as well as improved predictions.
with system input periods
, 2012
"... During the 1950s the Australian entomologist Alexander Nicholson studied a sheep pest, lucilia cuprina, (L cuprina), the sheepblowfly. In laboratory experiments blowfly populations were set up in cages. They were supplied with necessary food and water and every other day counts were made of the num ..."
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During the 1950s the Australian entomologist Alexander Nicholson studied a sheep pest, lucilia cuprina, (L cuprina), the sheepblowfly. In laboratory experiments blowfly populations were set up in cages. They were supplied with necessary food and water and every other day counts were made of the numbers in their various stages of development. The experiments went on for over a year. Various statistical studies have been carried out on their data. Sadly, the bulk of the data appears to be lost. Recently this author made the discovery of total population counts for ten Nicholson experiments. These data were in a collection of copies of index cards he made during a trip to Australia in 1977. In eight of the experiments the input food was varied cyclically in sawtooth fashion, each experiment having a different period of application. However, and what is the concern of this article, which data set went with which period of application remains unclear. In the present study use is made of periodograms, spectrograms and seasonal adjustment to seek a onetoone correspondence between series and period. The estimate constructed is consistent under smoothing and limiting conditions. It is time domain based, but confirmed by periodogram and
Snapshots of modern mathematics from Oberwolfach № 6/2013
"... phenomena Howel l Tong A friend of mine, an expert in statistical genomics, told me the following story: At a dinner party, an attractive lady asked him, “What do you do for a living? ” He replied, “I model. ” As my friend is a handsome man, the lady did not question his statement and continued, “ ..."
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phenomena Howel l Tong A friend of mine, an expert in statistical genomics, told me the following story: At a dinner party, an attractive lady asked him, “What do you do for a living? ” He replied, “I model. ” As my friend is a handsome man, the lady did not question his statement and continued, “What do you model? ” “Genes. ” She then looked at him up and down and said, “Mh, you must be very much in demand. ” “Yes, very much so, especially after I helped discover a new culprit gene for a common childhood disease. ” The lady looked puzzled. In this snapshot, I will give you an insight into Statistics, the field that fascinated my friend (and myself) so much. I will concentrate on phenomena that change over time, in other words, dynamical events. 1 1 Chaos and autoregressive models Consider the following doubling map, where n denotes an integer: We choose y0> 0, and define a series whose n th element is given by yn = 2yn−1 mod 1. (1) In words this means that we double the previous yvalue, throw away the integer part and keep only the decimal part∗. The map is also called a sawtooth map because it is equivalent to the iteration defined by the sawtooth function f(y) =