# KissABC 3.0

# Table of Contents

### Release Notes

- 3.0: Added SMC algorithm callable with
`smc`

for efficient Approximate bayesian computation, the speedup is 20X for reaching the same epsilon tolerance. Removed`AISChain`

return type in favour of`MonteCarloMeasurements`

particle, this change allows immediate use of the inference results for further processing.

## Usage guide

The ingredients you need to use Approximate Bayesian Computation:

- A simulation which depends on some parameters, able to generate datasets similar to your target dataset if parameters are tuned
- A prior distribution over such parameters
- A distance function to compare generated dataset to the true dataset

We will start with a simple example, we have a dataset generated according to an Normal distribution whose parameters are unknown

`tdata=randn(1000).*0.04.+2`

we are ofcourse able to simulate normal random numbers, so this constitutes our simulation

`sim((μ,σ)) = randn(1000) .* σ .+ μ`

The second ingredient is a prior over the parameters μ and σ

```
using KissABC
prior=Factored(Uniform(1,3), Truncated(Normal(0,0.1), 0, 100))
```

we have chosen a uniform distribution over the interval [1,3] for μ and a normal distribution truncated over ℝ⁺ for σ.

Now all that we need is a distance function to compare the true dataset to the simulated dataset, for this purpose comparing mean and variance is optimal,

```
function cost((μ,σ))
x=sim((μ,σ))
y=tdata
d1 = mean(x) - mean(y)
d2 = std(x) - std(y)
hypot(d1, d2 * 50)
end
```

Now we are all set, we can use `AIS`

which is an Affine Invariant MC algorithm via the `sample`

function, to simulate the posterior distribution for this model, inferring `μ`

and `σ`

```
approx_density = ApproxKernelizedPosterior(prior,cost,0.005)
res = sample(approx_density,AIS(10),1000,ntransitions=100)
```

the repl output is:

```
Sampling 100%|██████████████████████████████████████████████████| Time: 0:00:02
2-element Array{Particles{Float64,1000},1}:
2.0 ± 0.018
0.0395 ± 0.00093
```

We chose a tolerance on distances equal to `0.005`

, a number of particles equal to `10`

, we chose a number of steps per sample `ntransitions = 100`

and we acquired `1000`

samples.
For comparison let's extract some prior samples

`prsample=[rand(prior) for i in 1:5000] #some samples from the prior for comparison`

plotting prior and posterior side by side we get:

we can see that the algorithm has correctly inferred both parameters, this exact recipe will work for much more complicated models and simulations, with some tuning.

to this same problem we can perhaps even more easily apply `smc`

, a more advanced adaptive sequential monte carlo method

```
julia> smc(prior,cost)
(P = Particles{Float64,79}[2.0 ± 0.0062, 0.0401 ± 0.00081], W = 0.0127, ϵ = 0.011113205245491245)
```

to know how to tune the configuration defaults of `smc`

, consult the docs :)
for more example look at the `examples`

folder.