Sentences with phrase «prior distribution»

In addition, several approaches have been based on a uniform prior distribution of climate feedback.

There may be various arguments to support some particular prior distribution for the real dates, because those represent a quantity we do really have some prior information on.

But what prior distribution should we use — especially if we have no information to go on?

The default prior distribution is uniform with a very high upper bound.

The PDFs / likelihoods based on instrumental data are from Andronova and Schlesinger (2001), Forest et al. (2002; dashed line, considering anthropogenic forcings only), Forest et al. (2006; solid, anthropogenic and natural forcings), Gregory et al. (2002a), Knutti et al. (2002), Frame et al. (2005), and Forster and Gregory (2006), transformed to a uniform prior distribution in ECS using the method after Frame et al. (2005).

All of the pattern based techniques either limit the number of patterns used in the early period, or use prior distributions on the variance assigned to each one so that the regressions are well behaved when there are few data.

The problems with ECS distributions most often involve use of inappropriate prior distributions, so that the ECS distribution obtained does not properly reflect the error distributions of the underlying data.

Some studies have further attempted to use non-uniform prior distributions.

But with such a limited understanding of how the climate actually works, I (and Carl Hauser) prefer a more conservative prior distribution which allows for that possibility, assuming it actually is found through Bayesian analysis of the evidence collected later than 1959.

Sometimes the necessity of specifying prior distributions is seen as a drawback to Bayesian inference.

Forest et al. (2002, 2006) obtained narrower uncertainty ranges when using expert prior distributions (Table 9.3).

[For both α > 1 and β > 1, the beta prior distribution is concave downward and increasingly concentrated around its mean as the sum α + β increases.]

The commonly used uniform prior distributions for parameters have an effect akin to effecting a change of variables without using the Jacobian determinant conversion factor applicable to the functional relationship between the parameters and the observational data variables.

Frame et al. (2005) demonstrate that uncertainty ranges for sensitivity are dependent on the choices made about prior distributions of uncertain quantities before the observations are applied.

I have concentrated on the Bayesian inference involved in such studies, since they seem to me in many cases to use inappropriate prior distributions that heavily fatten the upper tail of the estimated PDF for S. I may write a future post concerning that issue, but in this post I want to deal with more basic statistical issues arising in what is, probably, the most important of the Bayesian studies whose PDFs for climate sensitivity were featured in AR4.

Flat prior distributions were defined for the nongenetic effects and effects at the single locus (− ∞, ∞), for the variance components (0, ∞), and for the allele frequencies (0,1).

Nevertheless, the IPCC concluded its discussion of the issue by simply stating that «uniform prior distributions for the target of the estimate [the climate sensitivity S] are used unless otherwise specified».

They find a climate feedback parameter of 2.3 ± 1.4 W m — 2 °C — 1, which corresponds to a 5 to 95 % ECS range of 1.0 °C to 4.1 °C if using a prior distribution that puts more emphasis on lower sensitivities as discussed above, and a wider range if the prior distribution is reformulated so that it is uniform in sensitivity (Table 9.3).

Frame et al. (2005) infer a 5 to 95 % uncertainty range for the ECS of 1.2 °C to 11.8 °C, using a uniform prior distribution that extends well beyond 10 °C sensitivity.

The final three rows list some studies using non-uniform prior distributions, while the other studies use uniform prior distributions of ECS, except for Gregory et al. (2002a) who implicitly use a uniform prior on transient climate response (see Frame et al., 2005), and Annan et al. (2005) who select a range based on sampling uncertain parameters in their model.

All PDFs shown are based on a uniform prior distribution of ECS and have been rescaled to integrate to unity for all positive sensitivities up to 10 °C to enable comparisons of results using different ranges of uniform prior distributions (this affects both median and upper 95th percentiles if original estimates were based on a wider uniform range).

Translating these results into ECS estimates is equivalent to using a prior distribution that favours smaller sensitivities, and hence tends to result in narrower ECS ranges (Frame et al., 2005).

If the unitholder dies and the units pass to heirs, their fair market value is determined to be the value as of the date of death, and the prior distributions are not taxed.

That income distribution payment reflects the income earned by the fund since the prior distribution was made.

If this latter happens there could be adverse tax effects for current AND prior shareholders, I believe in the form of tax recategorization of prior distributions.

«We generally pay the income as it is earned, so at each distribution period income received since the prior distribution period is paid.

The current attempt is to find a rational way to establish a prior distribution when little is known.

Theta is assumed to be a random quantity sampled from a prior distribution (a lot of people talk of theta and it as a prior, but we need to delve a little deeper) which is: pi (theta» lambda), where lambda is a vector of so called hyperparameters.