I know of a Schnute and Hilborn (1993) paper that might be helpful. It is titled "Analysis of contradictory data sources in fish stock assessment" and is in the Canadian Journal of Fisheries an Aquatic Sciences.
Here is the abstract:
Schnute, J.T., and R. Hilborn. 1993. Analysis of contradictory data sources in fish stock assessment. Can. J. Fish.
Aquat. Sci. 50: 1916-1923.
Fisheries stock assessments sometimes prove, in retrospect, to be wrong. Errors may be due to poor model
assumptions or to data that do not reflect the biological process of interest. We develop a method that formally
admits the possibility of such errors. Likelihood functions derived from this method indicate greater uncertainty in
parameter values than conventional likelihoods, whose derivations presume that models correctly describe the
observed data. The problem of uncertainty is particularly acute when more than one data source is available and
different data sets provide contradictory parameter estimates. Traditional methods of stock assessment involve
weighted averages of the contradictory data, and these generally produce parameter estimates intermediate to
those obtained from the data sets individually. We demonstrate that, when model or data errors are considered,
the most likely parameter values are not intermediary to conflicting values; instead, they occur at one of the
apparent extremes. We provide an example using contradictory trends in catch-per-unit-effort data for the Canadian
northern cod stock (1978-88).
Warren Schlechte
-----Original Message-----
From: Yuanlong Shao [mailto:[log in to unmask]]
Sent: Wednesday, August 10, 2011 10:58 PM
Subject: Is Multi-Modality a common experience?
Dear List Members,
I know that doing MCMC on mixture models
has the multi-modality issue due to permutation of labels.
But is this a common issue in models
that are not exactly mixtures? Such as those
models with multiple layers of random variables,
resulting in a non-convex posterior density surface.
If so, then what additional care do we commonly
need when making estimations from the samples
in Gibbs sampling? For mixtures we have various
ways to deal with label switching, but for a general
model with multi-modality, do we simply estimate
parameters by averaging the samples? Or is there
anyway to restrict the joint samples to be within
a major posterior density area?
Thanks!
Louis
--
Louis Yuanlong Shao
Department of Computer Science and Engineering
Ohio State University
http://www.shaoyuanlong.com
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