«Representing
each parameter as a probability distribution allows us to account for experimental uncertainty, and it also allows us to suss out which parameters are covarying.»
Not exact matches
There's no real progress in our evaluation of climate sensitivity, rather the demonstration that real progress will be very difficut to reach (worse even, the range should enlarge
as we include more and more
parameters for evaluation of f, so more and more uncertainty because each new
parameter will have its own distribution of
probability).
This model could be used
as a starting point in the development of a GCM parameterization of a the ice mixing - ratio
probability distribution function and cloud amount, if a means of diagnosing the depth of the saturated layer and the standard deviation of cloud depth from basic large - scale meterological
parameters could be determined.
In the model used by Groisman et al. (1999), the mean total precipitation is also proportional to the shape and scale
parameters of the gamma distribution
as well
as to the
probability of precipitation on any given day.
One can easily prove theoretically that the
probability that the credible interval based on the posterior CDF will contain the true
parameter value will always be exactly
as specified, if you average over true
parameter values drawn from the prior used to construct the posterior.
Sea ice conditions, such
as September extent, maps of sea ice
probability and first ice - free day, or any other sea ice
parameter based on early - season data.
Where genuine prior information exists, one can suppose that it is equivalent to a notional observation with a certain
probability density, from which a posterior density of the
parameter given that observationhas been calculated using Bayes» theorem with a noninformative «pre-prior», with the thus computed posterior density being employed
as the prior density (Hartigan, 1965).
That the «objective» Bayesian method using Jeffreys» prior will produce perfect
probability matching is most easily seen
as being due to the general fact that an analysis using the Jeffreys» prior is not affected by applying some monotonic transformation to the
parameter (and then interpreting the results
as transformed, of course).
A quick answer to your query: A confidence interval is intended to indicate the reliability of an estimate, in terms of the
probability that the true value of the
parameter being estimated falling below the lower confidence limit, inside the confidence interval, or above its upper limit,
as the case may be.