# Simple BNPR Vignette In phylodyn: Statistical Tools for Phylodynamics

This vignette shows a simple and typical use of `phylodyn` and its main functions BNPR and BNPR_PS.

We start by loading the `phylodyn` package.

```set.seed(8675309)
library(phylodyn)
```

We need to set the true effective population size trajectory function. For this example, we choose a seasonal growth/collapse trajectory (already implemented in `phylodyn`).

```traj = logistic_traj
```

We set the end of the sampling interval and the number of samples we should expect.

```samp_end = 48
nsamps   = 500
```

We calculate the proportionality constant necessary to produce the correct expected number of samples. We then produce a set of samples by drawing from an inhomogeneous Poisson process with intensity proportional to the effective population size trajectory.

```Cprop      = nsamps/integrate(traj_beta, 0, samp_end, traj=traj, beta=1)\$value
samp_times = pref_sample(traj, c=Cprop, lim=c(0,samp_end), beta=1)
```

We simulate a genealogy based on our sample using the coalescent.

```gene = coalsim(samp_times = samp_times, n_sampled = rep(1, length(samp_times)),
traj = traj, lower_bound = 10)
```

We use BNPR and BNPR_PS to calculate approximate marginals (without and with a sampling model).

```res_BNPR    = BNPR(data = gene, lengthout = 100)
res_BNPR_PS = BNPR_PS(data = gene, lengthout = 100)
```

We plot the results.

```par(mfrow=c(1,2))
plot_BNPR(res_BNPR, traj = traj, main="BNPR", ylim = c(1, 700))
plot_BNPR(res_BNPR_PS, traj = traj, main="BNPR-PS", ylim = c(1, 700))
```

## References

1. J. A. Palacios and V. N. Minin. Integrated nested Laplace approximation for Bayesian nonparametric phylodynamics. In Proceedings of the Twenty-Eighth International Conference on Uncertainty in Artificial Intelligence, pages 726–735, 2012.

2. M. S. Gill, P. Lemey, N. R. Faria, A. Rambaut, B. Shapiro, and M. A. Suchard. Improving Bayesian population dynamics inference: a coalescent-based model for multiple loci. Molecular biology and evolution, 30(3):713–724, 2013.

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phylodyn documentation built on May 29, 2017, 1:28 p.m.