smith-garrett/firstpassagetools.jl

Tools for working with first-passage time distributions for continuous-time, discrete-state Markov processes

firstpassagetools.jl's Issues

Add tests for splitting probabilities

Not really used in fitting right now, but would be useful to test:

1. With a single condition: should sum to 1.0
2. With multiple conditions: each condition separately should sum to 1.0.

Add checks to ensure that `p_0` has number of dimensions as there are transient states

Create tutorial(s)

• Simple random walk from van Kampen (2007, Ch. XII)
• Parsing example
• Chemical example?
• Queuing example?

Remove vectorized versions of (log)pdf (etc.) functions

These are now deprecated in Distributions.jl and seem to be causing issues in testing/compiling with newer versions of Julia.

Trouble with autodifferentiation in Turing

MethodError: no method matching exponential!(::Matrix{ForwardDiff.Dual{ForwardDiff.Tag{DynamicPPL.DynamicPPLTag, Float64}, Float64, 2}}, ::ExponentialUtilities.ExpMethodHigham2005Base)

Rework `rescale!()` so that it works for both $T$ and $A$ matrices

pdf() sometimes returns very small negative values

Could be a numerical issue, but the numbers are often -1e-162. This causes issues in logpdf() when trying to fit models because log() doesn't take negative arguments unless they are explicitly of type Complex.

Implement conditional first-passage statistics

Interface: pdf(d::fpdistribution, x::Real, dims=...). The dims argument is either an integer or a collection/vector of integers referring to the absorbing states/the rows of the absorbing matrix A.

Demonstrate parameter recovery

Add test comparing Erlang distribution and an appropriate `fpdistribution`

Probably compare mean and variance, as well as pdf() evaluated at same points.

Register

@JuliaRegistrator register

Implement conditional statistics

CDF/quantile fns. need to know which transient states exit into which absorbing states in order to implement for systems with more than one absorbing state.

CDF_abs = 1 - (sum_{transient states exiting into abs} / splitting probability_abs)

Add test for `rescale!()`

Provide pre-calculated, rescaled $T$ and $A$ matrices and test equality.

Make notebooks all use consistent fitting/sampling methods

• AD backend
• Sampling algorithm (NUTS)
• Number of samples
• etc.

Fix local git mess-up/deleted files.

Revise to get rid of conditions interface

The idea of encoding multiple conditions (= multiple different transition rate matrices) seems to just be making things complicated. Better to just remove and make the user handle that manually in the @model internals.

TagBot trigger issue

This issue is used to trigger TagBot; feel free to unsubscribe.

If you haven't already, you should update your TagBot.yml to include issue comment triggers.
Please see this post on Discourse for instructions and more details.

If you'd like for me to do this for you, comment TagBot fix on this issue.
I'll open a PR within a few hours, please be patient!

Domain Error from logpdf & occasional incorrect T matrix errors

Error:

ERROR: DomainError with -4.5958295283709015e-27:
log will only return a complex result if called with a complex argument. Try log(Complex(x)).

This happens occasionally. Most recently, I've noticed it using ReverseDiff.jl while fitting fpdistribs in Turing. I suspect that this might be due to proposals being sampled that cause the entries in the T matrix to be very close to zero. When that gets fed to pdf(), it might lead to numerical overflow.

I think something similar happens when I get feedback from the fpdistribution() fn. that the T matrix is incorrect, i.e., the columns don't sum to zero.

Make sure documentation shows up, e.g., in auto-help in Pluto

Implement plotting of conditional PDFs/CDFs

Currently only plots, e.g., PDF of exit time.

Could implement function signature: plot(fp, conditional={true/false}

Need to resolve #34 first

Ensure that $p_0$ is always a probability distribution

This should probably be asserted when generating a fpdistribution.

Add test checking the output of the setup() function

Manually create a T and an A matrix, make sure that they are the same.

Reconsider rescaling in setup()

Currently, rescaling is done by multiplying the transition rates by the total number of states, transient + absorbing. It might be better to rescale by the number of transient states only, since this is what really contributes to first-passage times, i.e., the number of states you have to pass through (approx.) before you reach an absorbing state (which no longer contributes to FPT).

Add test that fails when the requirements of W-matrices aren't met

This is already asserted in the setup() function, but it might be a good idea to check it when creating an fpdistribution.

In addition to the rows of $T$ summing to 0, $$A = T \mathbf{1}$$.

Add tests for checking the format of CSV files

Input CSVs should have a standard, documented format. Test should check that correctly formatted CSVs work and that easy-to-make errors don't.

Implement hazard function

Consider using different approach to calculating time-dependent quantities

Currently using numerical solution of matrix exponential. Could also consider:

• Uniformization
• Erlangization (mandjes2022numerical)

Might be faster and/or better for automatic differentiation? More numerically stable?

Figure out why posterior sampling is biased

Simulation-based calibration is consistently showing that any sampling algorithm gives samples that are higher than where the true posterior should be.

Demonstrate model comparison with PSIS-LOO

Can be done in parameter recovery example. PSIS-LOO available as Turing.jl subpackage or maybe here.

Biased sampling from NUTS and SMC

Simulation-based calibration returns evidence of biased sampling for a simple, non-hierarchical model. PG(25) seems to work just fine, though.