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Parameter

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# Dagger

*dagger* is a embedded domain-specific language for probabilistic programming in OCaml. Models are written in monadic style. Sampling from the posterior is performed using one of the following algorithms:

- Single-site Metropolis-Hastings, a.k.a. Lightweight Metropolis-Hastings
- Incrementalized single-site MH, similar to that implemented in Hakaru10

## Example

Let us consider the classical "sprinkler" example (drawn from Functional Programming for Modular Bayesian Inference).

Our lawn can become wet either because it rained or because the sprinkler is activated. We construct a simple model that encodes our belief that the lawn becomes wet knowing that it rained or not and the sprinkler state.

```
open Lmh_inference
open Infix
let model : bool t =
let open Infix in
let* rain = sample (Stats_dist.bernoulli ~bias:0.2) in
let* sprinkler = sample (Stats_dist.bernoulli ~bias:0.1) in
let prob_lawn_wet =
match (rain, sprinkler) with
| (true, true) -> 0.99
| (true, false) -> 0.7
| (false, true) -> 0.9
| (false, false) -> 0.01
in
let+ () = score prob_lawn_wet in
rain
```

Each execution trace is weighted by the density of the samples taken in that trace *and* by calls to the `score`

construct. The inference algorithm samples execution traces proportionally to their total weight. Scoring therefore amounts to a form of soft conditioning (and assigning a score of 0 to a trace amounts to rejecting that trace). Let us sample from the posterior implicitly defined by our `model`

.

```
let rng_state = RNG.make [| 0x1337; 0x533D |]
let nsamples = 100_000
let samples =
Lmh_inference.stream_samples model rng_state
|> Seq.take nsamples
let freq =
(samples
|> Seq.map (fun x -> if x then 1 else 0)
|> List.of_seq |> List.fold_left ( + ) 0 |> float_of_int)
/. float_of_int nsamples
```

The result is that the probability that it rains knowing that the lawn is wet is approximately equal to 0.64.

## Companion libraries

In the interest of modularity, sampleable distributions (such as `bernoulli`

) are defined in auxilliary libraries. Currently, we have:

`prbnmcn-dagger-gsl`

, which relies on the OCaml bindings to the GNU`gsl`

library. Note that`prbnmcn-dagger-gsl`

is licensed under the GNU GPL.`prbnmcn-dagger-stats`

, which relies on`prbnmcn-stats`

.

## API

`Dagger.Intf`

Module type definitions`Dagger.Lmh_inference`

Lightweight Metropolis-Hastings`Dagger.Lmh_incremental_inference`

Incremental lightweight Metropolis-Hastings`Dagger.Smc_inference`

Sequential Monte-Carlo`Dagger.Dist`

Distributions`Dagger.Resampling`

Resampling functions.