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"sampler-parameters"], [61, "sampler-parameters"]], "Set the Initial State of Each Algorithm": [[53, "set-the-initial-state-of-each-algorithm"]], "Build the Sampling Loop": [[53, "build-the-sampling-loop"], [53, "id1"]], "Sampling": [[53, "sampling"], [53, "id2"]], "General MWG Kernel": [[53, "general-mwg-kernel"]], "Check Result": [[53, "check-result"]], "Developer Notes": [[53, "developer-notes"]], "Use a logdensity function that is not compatible with JAX\u2019s primitives": [[54, "use-a-logdensity-function-that-is-not-compatible-with-jax-s-primitives"]], "Aesara model compiled to Numba": [[54, "aesara-model-compiled-to-numba"]], "Use jax.experimental.host_callback to call Numba functions": [[54, "use-jax-experimental-host-callback-to-call-numba-functions"]], "Use custom XLA calls to call Numba functions faster": [[54, "use-custom-xla-calls-to-call-numba-functions-faster"]], "Sample with multiple chains in parallel": [[55, "sample-with-multiple-chains-in-parallel"]], "Vectorization vs parallelization": [[55, "vectorization-vs-parallelization"]], "NUTS in parallel": [[55, "nuts-in-parallel"]], "Using jax.vmap": [[55, "using-jax-vmap"]], "Using jax.pmap": [[55, "using-jax-pmap"]], "A note on using jax.pmap on CPU": [[55, "a-note-on-using-jax-pmap-on-cpu"]], "Choosing the number of devices": [[55, "choosing-the-number-of-devices"]], "Back to our example": [[55, "back-to-our-example"]], "Conclusions": [[55, "conclusions"]], "Use with Aesara models": [[56, "use-with-aesara-models"]], "Before you start": [[56, null], [57, null], [59, null], [60, null]], "Use with Numpyro models": [[57, "use-with-numpyro-models"]], "Use with Oryx models": [[58, "use-with-oryx-models"]], "Use with PyMC models": [[59, "use-with-pymc-models"]], "Use with TFP models": [[60, "use-with-tfp-models"]], "A Quick Introduction to Blackjax": [[61, "a-quick-introduction-to-blackjax"]], "The Problem": [[61, "the-problem"]], "HMC": [[61, "hmc"]], "Set the Initial State": [[61, "set-the-initial-state"]], "Build the Kernel and Inference Loop": [[61, "build-the-kernel-and-inference-loop"]], "Inference": [[61, "inference"]], "NUTS": [[61, "nuts"]], "Use Stan\u2019s Window Adaptation": [[61, "use-stan-s-window-adaptation"]], "Welcome to Blackjax!": [[62, "welcome-to-blackjax"]], "Hello World": [[62, "hello-world"]], "Installation": [[62, "installation"]], "GPU instructions": [[62, null]]}, "indexentries": {"type_checking (in module blackjax._version)": [[0, "blackjax._version.TYPE_CHECKING"]], "version_tuple (in module blackjax._version)": [[0, "blackjax._version.VERSION_TUPLE"], [0, "blackjax._version.version_tuple"]], "blackjax._version": [[0, "module-blackjax._version"]], "module": [[0, "module-blackjax._version"], [1, "module-blackjax.adaptation.base"], [2, "module-blackjax.adaptation.chees_adaptation"], [3, "module-blackjax.adaptation"], [4, "module-blackjax.adaptation.mass_matrix"], [5, "module-blackjax.adaptation.meads_adaptation"], [6, 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22, 27, 29, 35, 36, 37, 43, 44, 49, 51, 54, 62], "float": [2, 5, 6, 7, 8, 13, 14, 15, 18, 19, 21, 23, 24, 26, 27, 29, 32, 35, 37, 38, 39, 40, 43, 44, 46, 48], "da_stat": 2, "dual_averag": [2, 28], "dualaveragingst": [2, 27], "optstat": [2, 48], "int": [2, 4, 5, 7, 8, 10, 13, 15, 21, 22, 23, 25, 26, 27, 29, 31, 33, 39, 42, 43, 46, 48, 49, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61], "base": [2, 3, 4, 5, 6, 8, 11, 15, 18, 19, 21, 23, 29, 38, 41, 44, 51, 52, 56, 59, 61], "jitter_gener": 2, "callabl": [2, 4, 5, 6, 7, 8, 9, 13, 14, 15, 18, 20, 21, 22, 23, 24, 26, 27, 29, 31, 33, 35, 36, 37, 38, 39, 40, 43, 44, 48, 49], "next_random_arg_fn": [2, 15], "gradienttransform": [2, 48, 50], "target_acceptance_r": [2, 6, 8, 57], "decay_r": 2, "tupl": [2, 4, 7, 8, 20, 22, 23, 26, 27, 29, 33, 39, 48, 49, 56], "chang": [2, 8], "estim": [2, 4, 5, 6, 7, 8, 10, 31, 33, 35, 36, 37, 48, 49, 50, 51, 58], "expect": [2, 55], "squar": [2, 4, 5, 46, 50], "trajectori": [2, 8, 11, 14, 15, 16, 17, 20, 21, 23, 51, 61], "length": [2, 14, 17, 21, 51], "dual": [2, 7, 8, 27, 51], "procedur": [2, 6, 7, 8, 9, 14, 26, 27], "size": [2, 5, 6, 7, 8, 10, 14, 15, 18, 19, 21, 22, 26, 27, 29, 35, 36, 37, 38, 39, 40, 49, 51, 55, 56, 58, 60, 61, 62], "jitter": 2, "hamiltonian": [2, 4, 5, 15, 17, 20, 22, 26, 35, 51, 61], "mont": [2, 4, 5, 35, 51, 61], "carlo": [2, 4, 5, 35, 51, 61], "kernel": [2, 5, 6, 7, 8, 9, 13, 14, 15, 18, 19, 21, 22, 24, 31, 35, 36, 37, 38, 39, 44, 49, 50, 55, 56, 57, 58, 59, 60, 62], "hrs21": [2, 51], "thi": [2, 4, 5, 6, 7, 8, 9, 10, 13, 14, 15, 18, 19, 21, 23, 24, 26, 27, 31, 32, 33, 35, 36, 37, 38, 39, 46, 50, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61], "tune": [2, 4, 5, 6, 7, 8, 51, 57, 59, 60], "i": [2, 4, 5, 6, 7, 8, 9, 10, 13, 14, 15, 17, 19, 20, 21, 22, 23, 24, 26, 27, 29, 31, 38, 39, 40, 43, 44, 46, 48, 49, 50, 51, 53, 55, 56, 57, 58, 59, 60, 61, 62], "e": [2, 6, 7, 8, 23, 31, 52, 53, 55, 56], "integr": [2, 5, 6, 8, 11, 14, 15, 16, 18, 21, 22, 26, 35, 51, 53, 55, 60, 61, 62], "statist": 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38, 40, 44, 53, 54, 56, 57, 58, 59, 60, 62], "option": [2, 19, 23, 38, 40, 55], "1": [2, 4, 6, 7, 8, 10, 20, 22, 23, 24, 26, 27, 29, 31, 39, 46, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62], "given": [2, 5, 6, 7, 8, 14, 15, 19, 20, 22, 23, 24, 27, 31, 38, 44, 46, 50, 53, 54, 61], "prngkei": [2, 7, 14, 23, 37, 39, 42, 45, 46, 48, 49, 58], "propos": [2, 5, 7, 11, 13, 15, 16, 18, 19, 21, 24, 26, 39], "If": [2, 7, 23, 24, 26, 31, 43, 54, 62], "none": [2, 19, 24, 30, 39, 53, 55, 56, 57, 58, 59, 60], "halton": 2, "next": [2, 4, 9, 14, 15, 23, 35, 36, 37, 40, 55], "its": [2, 5, 14, 15, 22, 24, 27, 46, 54, 56, 58], "previou": [2, 4, 8, 13, 14, 15, 22, 23, 24, 53], "compat": [2, 50, 56, 57, 58, 59, 60, 62], "which": [2, 5, 6, 7, 8, 9, 10, 14, 15, 17, 19, 20, 21, 23, 24, 26, 31, 35, 36, 37, 39, 44, 46, 50, 52, 53, 54, 56, 57], "conform": [2, 50], "protocol": [2, 23, 50], "repres": [2, 9, 10, 22, 39, 48, 49], "how": [2, 46, 51, 52, 54, 55, 56, 57, 58, 59, 60], "much": [2, 55], "favor": [2, 23], "recent": [2, 55], "over": [2, 9, 53, 58], "earlier": [2, 7, 27, 55], "ones": [2, 17, 39, 52, 54, 55, 58, 60], "return": [2, 4, 5, 6, 7, 8, 9, 10, 13, 14, 15, 18, 19, 20, 21, 22, 23, 24, 26, 27, 29, 31, 35, 36, 37, 38, 39, 40, 43, 44, 46, 48, 49, 50, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62], "init": [2, 4, 5, 6, 7, 8, 9, 13, 14, 15, 18, 19, 21, 22, 24, 27, 31, 35, 36, 37, 38, 39, 44, 48, 49, 50, 52, 53, 54, 55, 61, 62], "initi": [2, 4, 5, 6, 7, 8, 9, 10, 13, 14, 15, 18, 19, 21, 22, 23, 24, 26, 27, 29, 35, 36, 37, 48, 55, 56, 57, 58, 59, 62], "warmup": [2, 5, 6, 7, 8, 61], "updat": [2, 4, 5, 6, 7, 8, 9, 14, 23, 26, 27, 29, 38, 39, 50, 51, 53, 59], "one": [2, 5, 6, 8, 10, 14, 15, 18, 22, 23, 24, 26, 35, 36, 37, 39, 52, 54, 55], "logdensity_fn": [2, 5, 6, 8, 13, 14, 15, 18, 19, 21, 22, 24, 40, 48, 49, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62], "num_chain": [2, 5, 55], "jitter_amount": 2, "5": [2, 7, 26, 27, 39, 48, 52, 54, 55, 56, 57, 59, 60, 61], 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[2, 15, 18, 22, 23, 55], "varianc": [2, 4, 5, 10, 48, 51, 56], "sampl": [2, 4, 5, 6, 7, 8, 9, 10, 13, 14, 15, 18, 19, 21, 22, 23, 24, 26, 29, 31, 35, 36, 37, 38, 39, 40, 44, 46, 48, 49, 50, 51, 54, 56, 57, 58, 59, 60, 61], "mai": [2, 7, 27, 52, 54, 55, 62], "slow": [2, 7, 8, 26, 27, 55], "lead": [2, 56], "suboptim": 2, "mix": [2, 5, 61], "To": [2, 9, 14, 26, 35, 36, 37, 53, 54, 55, 56, 57, 58], "allevi": 2, "rather": [2, 52], "than": [2, 5, 8, 10, 23, 31, 52, 55], "nois": [2, 14, 46], "we": [2, 5, 6, 7, 8, 13, 14, 15, 18, 19, 20, 21, 22, 24, 26, 31, 35, 36, 37, 38, 39, 40, 43, 46, 48, 49, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62], "ensur": [2, 5, 8, 22, 26, 52], "more": [2, 8, 10, 13, 14, 15, 17, 18, 20, 21, 38, 46, 55], "even": 2, "distribut": [2, 13, 20, 22, 24, 29, 33, 44, 46, 48, 49, 51, 53, 54, 55, 56, 57, 58, 60, 61], "exampl": [2, 13, 14, 15, 18, 19, 21, 22, 23, 24, 35, 36, 37, 39, 46, 52, 53, 54, 56, 57, 58, 59, 60, 61], "can": [2, 7, 8, 9, 13, 14, 15, 18, 19, 20, 21, 22, 23, 24, 31, 35, 36, 37, 39, 43, 46, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62], "learn": [2, 33, 51], "follow": [2, 4, 7, 8, 13, 14, 15, 18, 19, 20, 21, 22, 24, 26, 39, 46, 52, 53, 54, 55, 56, 57, 59, 60, 62], "code": [2, 13, 14, 15, 18, 19, 21, 22, 24, 53, 55, 62], "key_warmup": 2, "key_sampl": 2, "jax": [2, 7, 13, 14, 15, 18, 19, 20, 21, 22, 24, 30, 35, 36, 37, 39, 46, 48, 51, 53, 56, 57, 58, 59, 60, 61, 62], "split": [2, 8, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62], "rng_kei": [2, 7, 9, 13, 14, 15, 18, 19, 21, 22, 23, 24, 29, 35, 36, 37, 38, 39, 42, 44, 46, 48, 49, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62], "adam": [2, 51], "learning_r": 2, "last_stat": [2, 57, 58, 59, 60], "_": [2, 7, 10, 14, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62], "posit": [2, 5, 9, 10, 13, 14, 15, 18, 19, 20, 21, 22, 24, 29, 31, 33, 35, 36, 37, 38, 44, 46, 49, 50, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61], "pytre": [2, 5, 13, 14, 15, 18, 19, 20, 22, 24, 29, 39, 44, 46], "where": [2, 4, 7, 8, 10, 15, 22, 27, 29, 31, 44, 52, 53, 54, 55], "each": [2, 5, 8, 10, 14, 15, 20, 22, 23, 35, 36, 37, 38, 39, 46, 48, 55, 60], "leaf": [2, 5], "ha": [2, 7, 8, 21, 23, 26, 27, 33, 48, 53, 54, 55], "shape": [2, 5, 43, 46, 53, 55, 58, 59], "initial_step_s": [2, 6, 7, 8], "num_warmup_step": 2, "dynamic_hmc": [2, 15], "new_stat": [2, 13, 14, 15, 18, 19, 21, 22, 24, 37, 52, 61], "vmap": [2, 39, 56, 58], "densiti": [2, 5, 6, 8, 9, 14, 15, 18, 19, 20, 21, 22, 23, 24, 31, 33, 35, 36, 37, 38, 44, 48, 49, 50, 52, 53, 56, 58, 60, 62], "wish": [2, 5, 6, 8, 13, 14, 15, 18, 21, 22, 24, 38, 40], "cross": [2, 5, 7], "warm": [2, 5], "up": [2, 5, 7], "train": [2, 5, 58], "jitter_valu": 2, "A": [2, 4, 5, 6, 7, 8, 9, 13, 14, 15, 18, 19, 20, 21, 22, 23, 24, 26, 27, 31, 33, 35, 36, 37, 38, 40, 44, 46, 48, 49, 50, 51, 53, 54, 56], "calcul": [2, 5, 22, 29, 53], "should": [2, 8, 15, 18, 20, 21, 26, 29, 31, 46, 52, 53, 54, 55], "jit": [2, 13, 14, 15, 18, 19, 21, 22, 24, 26, 35, 36, 37, 53, 54, 55, 56, 57, 61, 62], "default": [2, 4, 7, 10, 14, 15, 18, 19, 21, 27, 35, 36, 37, 38, 40, 46, 53, 55, 61, 62], "give": [2, 5, 8, 52, 53], "equal": [2, 5, 17, 22, 23, 24, 31, 55], "weight": [2, 7, 22, 23, 27, 38, 39, 40, 42, 44, 51, 54, 58], "all": [2, 5, 9, 22, 24, 40, 42, 43, 46, 49, 53, 55, 56, 57], "histori": [2, 29, 49], "most": [2, 15, 18, 20, 35, 36, 37, 52, 53, 54], "last": [2, 5, 6, 8, 10, 26], "diagnost": [2, 5, 11, 13, 15, 18, 19, 21, 24, 55], "chees_adapt": [3, 11], "mass_matrix": [3, 8, 11], "meads_adapt": [3, 11], "pathfinder_adapt": [3, 11], "window_adapt": [3, 11, 56, 57, 58, 59, 60, 61], "mass": [4, 6, 7, 8, 15, 20, 21, 22, 46, 60, 61], "matrix": [4, 5, 6, 7, 8, 13, 15, 20, 21, 22, 24, 46, 60, 61], "famili": [4, 6, 8, 26], "geometri": 4, "stan": [4, 8, 10, 51], "manual": [4, 15, 18, 35, 36, 37, 51, 53, 54], "stab": [4, 8, 51], "veri": [4, 8, 19, 52, 55], "good": [4, 5, 7, 8, 14, 19, 52, 54, 55, 58, 60], "refer": [4, 7, 24, 26, 51, 53, 60], "automat": [4, 5, 52, 53, 55, 56], "welfordalgorithmst": 4, "carri": [4, 7, 9, 27], "through": [4, 7, 14, 27, 52], "welford": 4, "m2": 4, "sum": [4, 5, 23, 31, 52, 55, 56, 58, 61, 62], "differ": [4, 7, 14, 15, 17, 19, 21, 23, 24, 26, 27, 31, 55, 61, 62], "see": [4, 7, 8, 23, 24, 27, 46, 54, 55, 59, 61], "document": [4, 57, 58, 59, 60, 62], "welford_algorithm": 4, "explan": [4, 8, 27], "sample_s": 4, "success": [4, 8, 31], "have": [4, 7, 9, 10, 14, 19, 21, 35, 36, 37, 43, 52, 54, 55, 57, 61], "been": [4, 21, 23, 26], "comput": [4, 5, 6, 8, 9, 10, 13, 14, 15, 18, 19, 21, 22, 23, 24, 26, 38, 40, 44, 46, 48, 51, 52, 54, 55, 56, 57, 60], "also": [4, 8, 9, 14, 15, 17, 18, 20, 21, 26, 52, 54, 55, 57, 61], "massmatrixadaptationst": [4, 8], "inverse_mass_matrix": [4, 6, 7, 8, 15, 20, 21, 22, 53, 54, 62], "curent": 4, "invers": [4, 6, 7, 8, 15, 20, 21, 22, 29, 46, 49, 60, 61], "wc_state": 4, "mass_matrix_adapt": 4, "is_diagonal_matrix": 4, "bool": [4, 8, 15, 18, 19, 21, 24, 26, 38, 48], "true": [4, 8, 38, 48, 49, 52, 53, 54, 55, 57, 61], "covari": [4, 5, 8, 13, 19, 24, 49], "when": [4, 5, 9, 10, 15, 20, 21, 22, 23, 24, 29, 38, 46, 49, 53, 55], "diagon": [4, 8, 20, 29, 46], "otherwis": [4, 8, 55], "adap": [4, 8], "dens": [4, 8, 20, 46, 58], "final": [4, 6, 8, 27, 55, 56, 57, 58], "onlin": 4, "possibl": [4, 5, 8, 55], "line": [4, 29, 49, 61], "fashion": 4, "avoid": [4, 9, 52, 53, 54], "store": [4, 14, 15, 18, 20, 49], "intermedi": 4, "result": [4, 10, 29, 46, 48, 49, 55, 57], "naiv": 4, "recurr": 4, "relat": [4, 8, 40, 62], "ar": [4, 5, 6, 7, 8, 9, 14, 15, 17, 18, 22, 23, 24, 26, 27, 29, 33, 35, 36, 37, 48, 52, 53, 54, 55, 56, 60, 61, 62], "numer": [4, 46, 51, 52], "stabl": [4, 8, 38, 59], "m_": [4, 39], "2": [4, 6, 7, 8, 10, 20, 24, 26, 29, 39, 40, 46, 52, 53, 54, 56, 57, 58, 61, 62], "n": [4, 10, 19, 39, 46, 54, 56], "sum_": [4, 10], "left": [4, 7, 62], "x_i": 4, "overlin": [4, 7], "x_n": 4, "right": [4, 7, 26, 53], "relationship": 4, "might": [4, 24, 55], "seem": [4, 21], "pedant": 4, "separ": [4, 8, 53], "other": [4, 8, 9, 14, 15, 21, 29, 49, 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\ No newline at end of file