Ranking metric

[emittman]

We discussed ranking these models by the expected number of replacements over a fixed interval, say 10 years. This could be accomplished by sampling:

For every MCMC iteration, for every drive model, simulate $C(\theta^{(s)})$ the random number of units required to provide 10 years of service. The we do Monte Carlo integration, $1/S * \sum_{s=1}^{S} C(\theta^{(s)} \approx \int C(\theta) p(\theta|y) d \theta$. We can provide a ranking based on the mean and include a plot including error bars for this quantity.

[clewisbe]

Hey Eric, Yes, I think this could work. One thing I'm thinking about is how to simulate draws from the GLFP pdf. I think it might be difficult to implement the reverse CDF method with uniform draws. Maybe a rejection sampling algorithm?

[emittman]

An easy (not necessarily best) way is to draw z ~ bernoulli(pi) , x1 ~ weibull(mu1,sigma1), and x2 ~ weibull(mu2,sigma2). If z = 1, you take min(x1,x2), else take x2.

Also, I'm thinking that to get the expectation, what we really want to do is just compute E(1/lifetime) because this would be interpretable as expected "units per year", which makes sense as a cost function. We can easily just scale that to units per 10 years, if we want. Using the samples gives us the posterior predictive distribution of "units per year".

[clewisbe]

Hey Eric,

That makes sense! Plus, we would only have to do one draw per sample rather than aggregating times together to a fixed end point. I'm going to work on some paper stuff this morning. Clb

On May 24, 2017, at 4:24 PM, emittman notifications@github.com wrote:

An easy (not necessarily best) way is to draw z ~ bernoulli(pi) , x1 ~ weibull(mu1,sigma1), and x2 ~ weibull(mu2,sigma2). If z = 1, you take min(x1,x2), else take x2.

Also, I'm thinking that to get the expectation, what we really want to do is just compute E(1/lifetime) because this would be interpretable as expected "units per year", which makes sense as a cost function. We can easily just scale that to units per 10 years, if we want. Using the samples gives us the posterior predictive distribution of "units per year".

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