src/jnesty/
├── __init__.py            # Public exports
├── jnesty.py              # NestedSampler class (user-facing API)
├── sampler.py             # Core NS loop (run_nested_sampling, two-phase)
├── internal_samplers.py   # Proposal strategies (InternalSampler + RWalkSampler + vmap_queue_refill)
├── bounding.py            # Bounding methods (Bound + UnitCube/Single/Multi)
├── multi_ellipsoid.py     # JIT-compiled multi-ellipsoid fitting
├── results.py             # Results class + format_results() + FITS I/O
├── plotting.py            # Dynesty-style plotting (built-in, no dynesty dependency)
└── utils.py               # Shared utilities (randsphere, logsubexp, mean_and_cov)

Data Flow

User code
  │
  ▼
NestedSampler (jnesty.py)          ← User-facing API
  │  __init__: configure parameters, auto-tune defaults
  │  run_nested(): build config, call core loop, format results
  │
  ▼
run_nested_sampling (sampler.py)   ← Core NS loop (two-phase)
  │
  │  Phase 1: Uniform rejection sampling
  │  │  _run_uniform_phase() with lax.while_loop
  │  │  Draws unit_cube_batch_size uniform points per iteration
  │  │  Switches when eff < min_eff% after min_ncall calls
  │  │  All JIT-compiled
  │  │
  │  Transition: Fit initial bound from Phase 1 live points
  │  │  bound_obj.fit(live_x)
  │  │  estimate_batch_size_from_memory() to cap batch_size
  │  │
  │  Phase 2: Random walk with adaptive bounds
  │  │  Legacy mode: lax.while_loop with batch parallel walks
  │  │  Queue mode: lax.while_loop with pre-filled candidate queue
  │  │  Per iteration:
  │  │    a. Find worst live point (loglstar)
  │  │    b. Retry loop: select start + ellipsoid, run walk until valid
  │  │    c. Adapt scale via Robbins-Munro (or at queue drain)
  │  │    d. Update live points and evidence
  │  │    e. Check convergence (delta_logZ < threshold)
  │  │  Chunked loop (multi-ellipsoid): periodic bound refit between chunks
  │  │
  │  Return WhileLoopNSResult
  │
  ▼
format_results (results.py)        ← Raw result → Results object
  │  Converts JAX arrays to numpy
  │  Computes trapezoidal weights
  │  Adds remaining live points (sorted by logL, Dynesty's add_live_points)
  │  Computes cumulative evidence trajectory
  │  Returns Results(dict)
  │
  ▼
Results object                      ← Dict wrapper with attribute access
     save_results() / load_results() for FITS I/O

Key Data Structures

WhileLoopNSConfig (sampler.py)

NamedTuple carrying all run configuration:

class WhileLoopNSConfig(NamedTuple):
    nlive: int = 500
    max_iterations: int = 10000
    delta_logZ_threshold: float = 0.01
    rwalk_K: int = 25
    rwalk_step_scale: float = 1.0
    target_acceptance: float = 0.5
    prior_bounds: Optional[jnp.ndarray] = None
    verbose: bool = True
    print_progress: bool = True
    bound: str = 'none'
    bound_update_interval: int = 0     # in likelihood calls
    max_ellipsoids: int = 20
    batch_size: int = 1                # parallel walks (legacy mode)
    queue_size: int = 0                # 0=legacy, >1=queue mode
    memory_frac: float = 0.9
    ncdim: int = None                  # clustered dimensions (defaults to ndim)
    unit_cube_batch_size: int = 200    # Phase 1 batch size
    min_eff: float = 10.0             # Phase 1 -> 2 efficiency threshold (%)
    min_ncall: int = None             # min calls before phase switch (default 2*nlive)

WhileLoopNSResult (sampler.py)

Raw output from the NS loop:

class WhileLoopNSResult(NamedTuple):
    logZ: float
    logZ_error: float
    H: float
    delta_logZ: float
    n_iterations: int
    runtime: float
    samples: jnp.ndarray          # (niter, ndim) dead point samples (physical)
    logL_samples: jnp.ndarray     # (niter,) dead log-likelihoods
    delta_logZ_trajectory: jnp.ndarray  # (niter,) convergence history
    scale_trajectory: jnp.ndarray       # (niter,) scale adaptation history
    acceptance_rate: float
    live_x: jnp.ndarray = None    # (nlive, ndim) final live points (unit cube)
    live_logL: jnp.ndarray = None # (nlive,) final live log-likelihoods

MultiEllipsoidState (multi_ellipsoid.py)

Fixed-size array container for multi-ellipsoid decomposition:

class MultiEllipsoidState(NamedTuple):
    centers: jnp.ndarray      # (max_ellipsoids, ndim)
    covs: jnp.ndarray         # (max_ellipsoids, ndim, ndim)
    axes: jnp.ndarray         # (max_ellipsoids, ndim, ndim)
    precision: jnp.ndarray    # (max_ellipsoids, ndim, ndim)
    logvol_ells: jnp.ndarray  # (max_ellipsoids,)
    n_active: int             # number of active ellipsoids

Results (results.py)

Dict wrapper providing both results['logz'] and results.logz access. See /usage skill for full field listing.

Internal Loop State Tuple (Phase 2)

The core loop packs all mutable state into a flat tuple for lax.while_loop. Base state is 18 elements; queue mode extends to 23:

Index	Variable	Shape	Description
0	live_x	(nlive, ndim)	Current live points
1	live_logL	(nlive,)	Live point log-likelihoods
2	worst_x_buffer	(max_iterations, ndim)	Dead point storage
3	worst_logL_buffer	(max_iterations,)	Dead logL storage
4	delta_logZ_buffer	(max_iterations,)	Convergence trajectory
5	scale_buffer	(max_iterations,)	Scale trajectory
6	logZ	scalar	Running evidence
7	delta_logZ	scalar	Current convergence metric
8	iteration	scalar	Loop counter
9	key	PRNGKey	Random state
10	scale	scalar	Current proposal scale
11	hist_accept	scalar	Accumulated acceptances (reset at bound update)
12	hist_total	scalar	Accumulated proposals (reset at bound update)
13	bound_axes	(ndim, ndim)	Axes from current bound
14	me_axes	(max_ell, ndim, ndim)	Multi-ellipsoid axes (all slots)
15	me_logvol_ells	(max_ell,)	Multi-ellipsoid log-volumes
16	calls_at_update	scalar	total_calls at last bound update
17	total_calls	scalar	Total likelihood calls (non-resetting)
18	queue_x	(queue_size, ndim)	Queue: candidate positions
19	queue_logL	(queue_size,)	Queue: candidate logL
20	queue_nacc	(queue_size,)	Queue: per-candidate acceptances
21	queue_ntot	(queue_size,)	Queue: per-candidate totals
22	queue_head	scalar	Queue: read head index

Indices 18-22 only present in queue mode (queue_size > 1).

JAX Patterns Used

lax.while_loop for convergence stopping

final_state = lax.while_loop(cond_fn, body_fn, init_state)

cond_fn checks both convergence (delta_logZ >= threshold) and iteration limit (iter < max_iterations). Used in Phase 1, Phase 2 (both modes), and the retry loop within each iteration.

Chunked loop for periodic bound updates

When using multi-ellipsoid with bound_update_interval > 0, the loop is broken into chunks measured in likelihood calls:

compiled_chunk = jax.jit(lambda s: lax.while_loop(chunk_cond, body_fn, s))
while total_done < max_iterations:
    current_state = compiled_chunk(state_with_chunk)
    # Refit bound
    me_state = fit_multi_ellipsoid(live_x_cur, ...)
    # Reset scale history, repack state

chunk_cond checks (total_calls - calls_at_update) >= bound_update_interval.

io_callback for progress bar

jax.experimental.io_callback(progress_cb, None, iteration, delta_logZ, logZ, loglstar, eff)

Throttled to every 100 iterations to avoid overhead. Uses pbar.write() for bound update messages (not print(), which breaks tqdm).

lax.scan for walk steps

final_state, _ = lax.scan(walk_step, init_state, jnp.arange(n_steps))

Used in _single_walk() (internal_samplers.py) for each individual random walk.

jax.vmap for parallel operations

Batch parallel walks (legacy mode, batch_size > 1):

vmapped_walk = jax.vmap(lambda wk, x0, ax: _single_walk(wk, x0, ..., ax, ...))

Each walk starts from a different live point with a different ellipsoid. First valid candidate is selected.

Queue refill (queue mode):

jax.vmap(_generate_one)(keys)  # queue_size candidates in parallel

Each candidate gets full rwalk_K steps from a random starting point with a random ellipsoid.

Batch likelihood evaluation (Phase 1):

vmapped_loglike = jax.vmap(loglikelihood_fn)
logL_batch = vmapped_loglike(u_batch)  # unit_cube_batch_size evaluations

Compile-time memory estimation for batch capping

# In sampler.py: estimate_batch_size_from_memory()
trial_fn = jax.vmap(lambda wk: _single_walk(...))
compiled = jax.jit(trial_fn).lower(trial_keys).compile()
peak = compiled.memory_analysis().peak_memory_in_bytes
per_walk = peak // trial_batch
max_batch = available_budget // per_walk

Uses XLA's memory_analysis() to get compile-time peak memory estimate. Caps batch_size to fit within memory_frac of GPU memory.

Retry loop for valid point guarantee

_, _, x_new, logL_new, iter_accepted, iter_total = lax.while_loop(
    _retry_cond, _retry_body, _init_retry)

Wraps the walk section to guarantee every NS iteration produces a valid replacement (logL > loglstar). Matches Dynesty's _new_point() while-True behavior. Re-selects starting point, ellipsoid, and randomness on each retry.

Registry / Factory Pattern

Samplers and bounds use string-based lookup:

# internal_samplers.py
SAMPLER_REGISTRY = {'rwalk': RWalkSampler}
sampler = get_sampler('rwalk', ndim, target_acceptance=0.5, batch_size=..., ncdim=...)

# bounding.py
BOUND_REGISTRY = {'none': UnitCube, 'single': SingleEllipsoid, 'multi': MultiEllipsoidBound}
bound = get_bound('multi', ndim, max_ellipsoids=20)

To add new types: implement the base class, add to registry, wire config through.

Results Pipeline

WhileLoopNSResult (raw, JAX arrays)
  │
  ▼  format_results() in results.py
  │  - JAX → numpy conversion
  │  - Trapezoidal log-weight computation (logwt = logaddexp(logL_i, logL_{i-1}) + logdvol)
  │  - Live point addition: sorted by logL, volumes via Dynesty's formula
  │  - Cumulative evidence trajectory via logaddexp.accumulate(logwt)
  │
  ▼
Results(dict) — dict wrapper with attribute access
  │
  ▼  save_results() / load_results()
FITS file (astropy.io.fits)

Demo Scripts

Located in dev/demo/. Each problem has a JNesty and Dynesty variant:

Demo	Problem	Dimension	Key Test
01	Multi-modal Gaussian mixture	5D	Multi-modality handling
02	Rosenbrock banana	2D	Non-Gaussian elongated posterior
03	High-D Gaussian	20D (configurable)	GPU scaling advantage
04	Gaussian shells	2D	Thin degenerate ring structures

Run from dev/demo/:

python 01_multimodal_gaussian_mixture_jnesty.py

Output goes to output_0X_jnesty/ or output_0X_dynesty/ with FITS results and plots.

Test Suite

tests/
├── unit/
│   ├── test_bounding.py            # UnitCube, SingleEllipsoid, MultiEllipsoid
│   ├── test_internal_samplers.py   # RWalkSampler, _single_walk, apply_reflect
│   ├── test_multi_ellipsoid.py     # Multi-ellipsoid fitting
│   ├── test_plotting.py            # Plotting functions
│   ├── test_results.py             # Results formatting, FITS I/O
│   ├── test_sampler_unit.py        # Sampler unit tests
│   ├── test_utils.py               # Utility functions
│   └── test_queue_mode.py          # Queue mode behavior
├── integration/
│   ├── test_sampler.py             # Full NS loop integration
│   ├── test_queue_and_defaults.py  # Queue mode + auto-defaults
│   └── test_jnesty_api.py          # API compatibility

Run with:

pytest tests/ -v

Legacy Code

dev/legacy/ contains retired implementations (old api.py, while_loop_sampler.py, etc.) kept for reference. Do not modify or import from these.