graph LR idea_076e610a_ca18_4355_a8b0_a7f8f496bd23["Sampling from Unnormalized Densities"] idea_0c9dc87c_51bc_411c_8c9e_0914e502c262["Marginal Likelihood (Evidence)"] idea_1655d8e9_b57f_42ed_b27d_56e95ab6e3b3["Hamiltonian Monte Carlo"] idea_1756f4b4_f422_444f_8aef_38dbdd064c6e["Stationary Distribution"] idea_1f450679_900e_419a_bc29_8e25bbad5ec5["Divergent Transitions"] idea_235dbb27_405c_43a5_8c11_2b9d29b9fe72["R-hat Convergence Diagnostic"] idea_23b4ed1d_8713_4380_923a_259d7faf6eec["Proposal Distribution Tuning"] idea_26f36b8e_2437_4945_9884_4fb3db6f2256["Intractable Normalizing Constant"] idea_2e8edc82_1116_413d_a0a6_35e55543f553["Variance"] idea_3db1fc7d_62a2_4b89_9de2_89652c2dc7c9["Gradient"] idea_413d4322_583f_40a2_90a7_0ebd3b74adbe["Full Conditional Distribution"] idea_444bbbab_2ca2_4d01_aa66_294e24b54ff0["Joint Probability Distribution"] idea_454f8c46_53ab_4927_9ad7_745bc4a59363["Curse of Dimensionality"] idea_52c33945_1329_4f85_abd5_970baccbdccc["Aperiodicity of a Markov Chain"] idea_547067e8_1f29_4714_9e63_68aa271fe5ac["Monte Carlo Method"] idea_549632ab_7dec_447c_94b5_c3e8aa264769["Hamiltonian Mechanics"] idea_57a14c3e_9f38_43ee_bca0_19968ea58836["Markov Chain Monte Carlo"] idea_589be38f_2a96_46f3_98e1_5f5188e10e92["Expectation Value"] idea_5adc3aee_cfe6_4565_a30e_5f9d21600231["Irreducibility of a Markov Chain"] idea_5f3baacf_c132_4792_9daa_bde4d0dee597["Detailed Balance"] idea_653d49fd_1aad_4577_b7e2_bb3c5fc7377b["Autocorrelation"] idea_698362fb_438c_4c81_8ff9_7e1cf1de569e["Gibbs Sampling"] idea_6dec7adc_a294_4dde_9dc5_2106590cfed0["Monte Carlo Estimation"] idea_70afbc4a_a04a_4123_b6bf_ee12b39c0c12["Metropolis-Hastings Acceptance Ratio"] idea_7b7d4ce2_4673_4b1d_8042_a0e5ed6b0da7["Pseudorandom Number Generation"] idea_7ccd46f8_4191_4b6e_a20d_7eba00148206["Uniform Distribution"] idea_7cdbfe9d_d6e4_4d91_bdb2_20c97b35863f["Markov Transition Kernel"] idea_7f8235b3_3c84_4c34_9289_ca52cfef9b91["Bayes' Theorem"] idea_8d21c443_6437_457a_b50a_68e2cae9027c["Proposal Distribution"] idea_8e876691_cebf_42e4_8794_305c0a3c3d46["Metropolis-Hastings Algorithm"] idea_91ca3b27_38dd_4f69_8ac0_120425471aa6["Mixing in MCMC"] idea_9fdd368a_aba2_4add_87d4_7633dd1a8490["Markov Chains"] idea_a8299b68_423a_4ae2_8b8d_f14ccc4a866f["Random Walk"] idea_b6ab3f71_b665_47ac_ad67_f9c511a8e549["Rejection Sampling"] idea_b75faf6e_5848_4c74_a63c_cac9a8841ffd["Gaussian (Normal) Distribution"] idea_bb5c8ae5_dcc6_402f_9136_c489a920ed12["Effective Sample Size"] idea_be991159_7a9f_4395_ada2_2cf69af3c7f8["Ergodicity"] idea_c334c7f8_4749_4f73_b05b_935b00ef1f58["Law of Large Numbers"] idea_c4beb02b_7eed_40d6_8dc6_5502bbdd5faa["Logarithm"] idea_cc8e402f_cf63_4856_9fc8_73bde4e5327a["Posterior Distribution"] idea_d5862663_6040_4ba6_b147_d4670b2d6075["Leapfrog Integration"] idea_dc400ff1_9856_4563_963f_8015015c8295["No-U-Turn Sampler (NUTS)"] idea_e99e0b04_5a37_473d_9814_d81da3b8b9c7["Normalizing Constant"] idea_ef2b73ac_94e4_4fed_b475_53d94ed95b28["Burn-in and Warmup"] idea_f4c64527_f83e_47e4_98d5_3ffc1def9fc8["Likelihood Function"] idea_f7d44604_0dca_49d9_8b67_c6629bfb4867["Trace Plots"] idea_fd9614ee_75b6_40ee_968d_c1cb2f27e6e9["Markov Chain"] idea_2e8edc82_1116_413d_a0a6_35e55543f553 --> idea_bb5c8ae5_dcc6_402f_9136_c489a920ed12 idea_e99e0b04_5a37_473d_9814_d81da3b8b9c7 --> idea_076e610a_ca18_4355_a8b0_a7f8f496bd23 idea_444bbbab_2ca2_4d01_aa66_294e24b54ff0 --> idea_698362fb_438c_4c81_8ff9_7e1cf1de569e idea_8d21c443_6437_457a_b50a_68e2cae9027c --> idea_8e876691_cebf_42e4_8794_305c0a3c3d46 idea_549632ab_7dec_447c_94b5_c3e8aa264769 --> idea_1655d8e9_b57f_42ed_b27d_56e95ab6e3b3 idea_cc8e402f_cf63_4856_9fc8_73bde4e5327a --> idea_076e610a_ca18_4355_a8b0_a7f8f496bd23 idea_d5862663_6040_4ba6_b147_d4670b2d6075 --> idea_1655d8e9_b57f_42ed_b27d_56e95ab6e3b3 idea_70afbc4a_a04a_4123_b6bf_ee12b39c0c12 --> idea_23b4ed1d_8713_4380_923a_259d7faf6eec idea_1655d8e9_b57f_42ed_b27d_56e95ab6e3b3 --> idea_dc400ff1_9856_4563_963f_8015015c8295 idea_2e8edc82_1116_413d_a0a6_35e55543f553 --> idea_235dbb27_405c_43a5_8c11_2b9d29b9fe72 idea_547067e8_1f29_4714_9e63_68aa271fe5ac --> idea_57a14c3e_9f38_43ee_bca0_19968ea58836 idea_b6ab3f71_b665_47ac_ad67_f9c511a8e549 --> idea_57a14c3e_9f38_43ee_bca0_19968ea58836 idea_ef2b73ac_94e4_4fed_b475_53d94ed95b28 --> idea_235dbb27_405c_43a5_8c11_2b9d29b9fe72 idea_653d49fd_1aad_4577_b7e2_bb3c5fc7377b --> idea_bb5c8ae5_dcc6_402f_9136_c489a920ed12 idea_6dec7adc_a294_4dde_9dc5_2106590cfed0 --> idea_57a14c3e_9f38_43ee_bca0_19968ea58836 idea_91ca3b27_38dd_4f69_8ac0_120425471aa6 --> idea_ef2b73ac_94e4_4fed_b475_53d94ed95b28 idea_fd9614ee_75b6_40ee_968d_c1cb2f27e6e9 --> idea_57a14c3e_9f38_43ee_bca0_19968ea58836 idea_454f8c46_53ab_4927_9ad7_745bc4a59363 --> idea_91ca3b27_38dd_4f69_8ac0_120425471aa6 idea_7ccd46f8_4191_4b6e_a20d_7eba00148206 --> idea_8e876691_cebf_42e4_8794_305c0a3c3d46 idea_1756f4b4_f422_444f_8aef_38dbdd064c6e --> idea_5f3baacf_c132_4792_9daa_bde4d0dee597 idea_57a14c3e_9f38_43ee_bca0_19968ea58836 --> idea_8e876691_cebf_42e4_8794_305c0a3c3d46 idea_5adc3aee_cfe6_4565_a30e_5f9d21600231 --> idea_be991159_7a9f_4395_ada2_2cf69af3c7f8 idea_26f36b8e_2437_4945_9884_4fb3db6f2256 --> idea_57a14c3e_9f38_43ee_bca0_19968ea58836 idea_7cdbfe9d_d6e4_4d91_bdb2_20c97b35863f --> idea_5f3baacf_c132_4792_9daa_bde4d0dee597 idea_1756f4b4_f422_444f_8aef_38dbdd064c6e --> idea_ef2b73ac_94e4_4fed_b475_53d94ed95b28 idea_b75faf6e_5848_4c74_a63c_cac9a8841ffd --> idea_23b4ed1d_8713_4380_923a_259d7faf6eec idea_8e876691_cebf_42e4_8794_305c0a3c3d46 --> idea_698362fb_438c_4c81_8ff9_7e1cf1de569e idea_a8299b68_423a_4ae2_8b8d_f14ccc4a866f --> idea_91ca3b27_38dd_4f69_8ac0_120425471aa6 idea_23b4ed1d_8713_4380_923a_259d7faf6eec --> idea_91ca3b27_38dd_4f69_8ac0_120425471aa6 idea_cc8e402f_cf63_4856_9fc8_73bde4e5327a --> idea_1f450679_900e_419a_bc29_8e25bbad5ec5 idea_f4c64527_f83e_47e4_98d5_3ffc1def9fc8 --> idea_70afbc4a_a04a_4123_b6bf_ee12b39c0c12 idea_23b4ed1d_8713_4380_923a_259d7faf6eec --> idea_dc400ff1_9856_4563_963f_8015015c8295 idea_0c9dc87c_51bc_411c_8c9e_0914e502c262 --> idea_076e610a_ca18_4355_a8b0_a7f8f496bd23 idea_c4beb02b_7eed_40d6_8dc6_5502bbdd5faa --> idea_70afbc4a_a04a_4123_b6bf_ee12b39c0c12 idea_1756f4b4_f422_444f_8aef_38dbdd064c6e --> idea_57a14c3e_9f38_43ee_bca0_19968ea58836 idea_f7d44604_0dca_49d9_8b67_c6629bfb4867 --> idea_235dbb27_405c_43a5_8c11_2b9d29b9fe72 idea_5f3baacf_c132_4792_9daa_bde4d0dee597 --> idea_8e876691_cebf_42e4_8794_305c0a3c3d46 idea_653d49fd_1aad_4577_b7e2_bb3c5fc7377b --> idea_91ca3b27_38dd_4f69_8ac0_120425471aa6 idea_7f8235b3_3c84_4c34_9289_ca52cfef9b91 --> idea_076e610a_ca18_4355_a8b0_a7f8f496bd23 idea_589be38f_2a96_46f3_98e1_5f5188e10e92 --> idea_6dec7adc_a294_4dde_9dc5_2106590cfed0 idea_9fdd368a_aba2_4add_87d4_7633dd1a8490 --> idea_be991159_7a9f_4395_ada2_2cf69af3c7f8 idea_9fdd368a_aba2_4add_87d4_7633dd1a8490 --> idea_57a14c3e_9f38_43ee_bca0_19968ea58836 idea_8d21c443_6437_457a_b50a_68e2cae9027c --> idea_23b4ed1d_8713_4380_923a_259d7faf6eec idea_d5862663_6040_4ba6_b147_d4670b2d6075 --> idea_1f450679_900e_419a_bc29_8e25bbad5ec5 idea_91ca3b27_38dd_4f69_8ac0_120425471aa6 --> idea_1655d8e9_b57f_42ed_b27d_56e95ab6e3b3 idea_6dec7adc_a294_4dde_9dc5_2106590cfed0 --> idea_bb5c8ae5_dcc6_402f_9136_c489a920ed12 idea_3db1fc7d_62a2_4b89_9de2_89652c2dc7c9 --> idea_1655d8e9_b57f_42ed_b27d_56e95ab6e3b3 idea_8e876691_cebf_42e4_8794_305c0a3c3d46 --> idea_70afbc4a_a04a_4123_b6bf_ee12b39c0c12 idea_1655d8e9_b57f_42ed_b27d_56e95ab6e3b3 --> idea_1f450679_900e_419a_bc29_8e25bbad5ec5 idea_c334c7f8_4749_4f73_b05b_935b00ef1f58 --> idea_6dec7adc_a294_4dde_9dc5_2106590cfed0 idea_52c33945_1329_4f85_abd5_970baccbdccc --> idea_be991159_7a9f_4395_ada2_2cf69af3c7f8 idea_7b7d4ce2_4673_4b1d_8042_a0e5ed6b0da7 --> idea_6dec7adc_a294_4dde_9dc5_2106590cfed0 idea_413d4322_583f_40a2_90a7_0ebd3b74adbe --> 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