Interpreting posterior density about mixsiar HOT 3 CLOSED

Hi Adam,

The posterior densities are probability distributions for the proportion of each source. The values of the y-axis cannot be interpreted as probabilities--probabilities are measured over intervals by taking the integral (area under the curve). So yes, if the curve is higher there, then more area will be under the curve nearby. Yes, you're right that the width of the distributions are used to calculate the quantiles. The 95% credible interval is the middle portion of the distribution, with 2.5% of the area to the left and 2.5% of the area to the right.

Short answer: The y-axis units are pretty much meaningless in both scaled and unscaled plots. I scaled the posterior densities because in some situations the y-axis would be very high for one source (ex. when one source is known to be close to 0, the y-axis can be very high), and you couldn't see the other sources well. The scaled posterior densities are no longer true probability distributions, because they don't integrate to 1. But visually they are the same, in that 95% of the area under the curve shows you 95% probability.

To demonstrate, let's say we just fit the Wolves example in MixSIAR.

In the summary statistics, we see the following line for Region 2 Deer:

p.Region 2.Deer           0.594 0.083 0.431 0.457 0.540 0.594 0.651 0.727 0.753

Above, the 2.5% and 97.5% quantiles are given as 0.431 and 0.753. We can report the median as 0.59 with a 95% CI of (0.43, 0.75). The MCMC chain for Region 2 Deer diet proportion is mixsiar$jags.1$p.fac1[,2,1], and we can calculate the 95% CI limits with:

attach.jags(mixsiar$jags.1) # attach.jags(jags.1) if using mixsiar_script.r
median(p.fac1[,2,1])
quantile(p.fac1[,2,1],.025)
quantile(p.fac1[,2,1],.975)

If you wanted the probability that the Region 2 Deer diet proportion is greater than 0.7:

# Total num draws
(tot <- length(p.fac1[,2,1]))
# Num draws above 0.7
(above <- length(which(p.fac1[,2,1]>0.7)))
# Prob that the diet proportion is above 70%
(prob <- above/tot)

Or maybe we want the probability that Pack 4 eats more Deer than Pack 7:

                           Mean    SD  2.5%    5%   25%   50%   75%   95% 97.5%
p.Pack 4.Deer             0.466 0.051 0.362 0.379 0.435 0.469 0.503 0.543 0.555
p.Pack 7.Deer             0.369 0.046 0.266 0.284 0.342 0.374 0.401 0.432 0.442

prob.Deer.Pack4.Pack7 <- sum(p.fac2[,4,1] > p.fac2[,7,1])/dim(p.fac2)[1]
> prob.Deer.Pack4.Pack7
[1] 0.938

We can also get a complete posterior probability for the difference between Pack 4 and Pack 7 (i.e. is Pack4 - Pack7 greater than 0?)

p.Deer.Pack4.Pack7 <- p.fac2[,4,1] - p.fac2[,7,1]
hist(p.Deer.Pack4.Pack7,breaks=50,col="grey")
abline(v=0,col="red",lty=2,lwd=3)

See also: http://www.sumsar.net/blog/2014/10/probable-points-and-credible-intervals-part-one/

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Thanks for the quick reply Brian. That was extremely helpful.
-Adam

On Mon, Mar 2, 2015 at 2:46 PM, Brian Stock [email protected]
wrote:

Closed #21 #21.

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#21 (comment).

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Hi, I am trying to do this (MixSIAR v. 3.1.10.9000) but the console just says "could not find function "attach.jags"" and then the rest won't work. Or am I missing an additional package? or something else? Thanks in advance for your answer!

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