InitContext, part 3 - Introduce InitContext

[penelopeysm]

Part 1: Adding hasvalue and getvalue to AbstractPPL
Part 2: Removing hasvalue and getvalue from DynamicPPL

This is Part 3/N of splitting up #967.

---

This PR solely adds the code for a new leaf context, InitContext. Its behaviour is to always override existing values inside a VarInfo.

A long-held goal of mine is to split up contexts.jl and context_implementations.jl such that each context is in its own file. To this end, I've put all the InitContext-related code inside src/contexts/init.jl. This should, hopefully, also make reviewing easier.

InitContext comes in three forms:

1. PriorInit: Samples values from the prior;
2. UniformInit(min, max): Samples values from between min and max before invlinking them back into the support of the original distribution;
3. ParamsInit(params): Takes values from params, which can be a NamedTuple or a Dict. Also takes a fallback strategy, which is used in case the varname is not found in params.

PriorInit and UniformInit have almost one-to-one correspondence with SampleFromPrior and SampleFromUniform. I haven't removed them yet because a LOT of stuff depends on SampleFromPrior. We will eventually remove all of it but doing it in a single PR would make it way too big.

However, ParamsInit is new. Its purpose is to set fixed values in a VarInfo in a principled manner. Right now, there is a fair amount of code that does low-level VarInfo manipulation by reaching inside and modifying the underlying arrays, such as initialise_values!!, and setval_and_resample!. This is prone to bugs, and also leads to (for example) the VarInfo's logp being out of sync. (All of that code will be removed in subsequent PRs.)

ParamsInit accomplishes the same in a much cleaner way, although in some cases (specifically, when setting initial values for sampling) it may necessitate one extra model evaluation. Because initialisation is not meant to happen within a tight loop (by definition it happens once), I don't consider performance to be an important issue.

One might ask what's the difference between InitContext{ParamsInit}, ConditionContext, and FixedContext. Consider the model @model f() = x ~ Normal(). Evaluating this with each of the contexts gives the following behaviour:

	InitContext{ParamsInit}	ConditionContext	FixedContext
logpdf of x ~ Normal()	Prior	Likelihood	Ignored
x in VarInfo	Yes	No	No

In other words, InitContext behaves as if you had run the model and sampled a new value for x, but that value just so happened to be the one that you provided. In contrast, Condition and FixedContext fundamentally change the model that is being run in that x is no longer a parameter.

Closes #375.

[github-actions]

Benchmark Report for Commit ab3e8da

Computer Information

Julia Version 1.11.6
Commit 9615af0f269 (2025-07-09 12:58 UTC)
Build Info:
  Official https://julialang.org/ release
Platform Info:
  OS: Linux (x86_64-linux-gnu)
  CPU: 4 × AMD EPYC 7763 64-Core Processor
  WORD_SIZE: 64
  LLVM: libLLVM-16.0.6 (ORCJIT, znver3)
Threads: 1 default, 0 interactive, 1 GC (on 4 virtual cores)

Benchmark Results

|                 Model | Dimension |  AD Backend |      VarInfo Type | Linked | Eval Time / Ref Time | AD Time / Eval Time |
|-----------------------|-----------|-------------|-------------------|--------|----------------------|---------------------|
| Simple assume observe |         1 | forwarddiff |             typed |  false |                  8.6 |                 1.6 |
|           Smorgasbord |       201 | forwarddiff |             typed |  false |                647.5 |                42.6 |
|           Smorgasbord |       201 | forwarddiff | simple_namedtuple |   true |                418.3 |                52.7 |
|           Smorgasbord |       201 | forwarddiff |           untyped |   true |                999.2 |                34.3 |
|           Smorgasbord |       201 | forwarddiff |       simple_dict |   true |               6688.2 |                28.5 |
|           Smorgasbord |       201 | reversediff |             typed |   true |               1027.8 |                40.9 |
|           Smorgasbord |       201 |    mooncake |             typed |   true |               1024.5 |                 4.2 |
|    Loop univariate 1k |      1000 |    mooncake |             typed |   true |               5847.9 |                 3.8 |
|       Multivariate 1k |      1000 |    mooncake |             typed |   true |                988.6 |                 9.1 |
|   Loop univariate 10k |     10000 |    mooncake |             typed |   true |              65451.4 |                 3.5 |
|      Multivariate 10k |     10000 |    mooncake |             typed |   true |               8372.5 |                10.3 |
|               Dynamic |        10 |    mooncake |             typed |   true |                135.6 |                10.8 |
|              Submodel |         1 |    mooncake |             typed |   true |                 13.9 |                 4.5 |
|                   LDA |        12 | reversediff |             typed |   true |               1380.0 |                 2.6 |

[github-actions]

DynamicPPL.jl documentation for PR #981 is available at:
https://TuringLang.github.io/DynamicPPL.jl/previews/PR981/

[codecov]

Codecov Report

❌ Patch coverage is 88.70968% with 7 lines in your changes missing coverage. Please review.
✅ Project coverage is 82.41%. Comparing base (b1cdc2a) to head (fd78d42).

Files with missing lines	Patch %	Lines
src/contexts/init.jl	91.66%	4 Missing ⚠️
src/model.jl	72.72%	3 Missing ⚠️

Additional details and impacted files

@@             Coverage Diff              @@
##           breaking     #981      +/-   ##
============================================
+ Coverage     82.16%   82.41%   +0.25%     
============================================
  Files            38       39       +1     
  Lines          3935     3992      +57     
============================================
+ Hits           3233     3290      +57     
  Misses          702      702              

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[penelopeysm]

This code was shifted verbatim to src/model.jl to avoid circular dependencies between files.