快速开始 ======== 本指南将带你快速上手 HIcosmo，实现宇宙学参数估计。 3 行代码完成推断 ---------------- HIcosmo 的设计哲学是 **3 行代码完成核心功能**： .. code-block:: python from hicosmo import hicosmo inf = hicosmo(cosmology="LCDM", likelihood="sn", free_params=["H0", "Omega_m"]) samples = inf.run() 运行完毕后，你将获得 :math:`H_0` 和 :math:`\Omega_m` 的后验分布样本。 .. tip:: **并行加速**：在脚本最开头添加以下代码启用多设备并行： .. code-block:: python import hicosmo as hc hc.init(8) # 8 个并行设备 = 8 条并行链 = ~800% CPU 必须在导入其他模块之前调用！ 基本示例 -------- 单探针分析（超新星） ~~~~~~~~~~~~~~~~~~~~ .. code-block:: python from hicosmo import hicosmo # 使用 Pantheon+ 超新星数据约束 ΛCDM 模型 inf = hicosmo( cosmology="LCDM", likelihood="sn", # Pantheon+ 数据 free_params=["H0", "Omega_m"], num_samples=4000, # 总样本数 num_chains=4 # 并行链数 ) # 运行 MCMC 采样 samples = inf.run() # 查看结果摘要 inf.summary() # 生成 corner plot inf.corner_plot('corner_sn.pdf') 多探针联合分析 ~~~~~~~~~~~~~~ .. code-block:: python from hicosmo import hicosmo # 联合 SN + BAO + CMB 约束 inf = hicosmo( cosmology="LCDM", likelihood=["sn", "bao", "cmb"], # 多探针联合 free_params=["H0", "Omega_m"], num_samples=8000, num_chains=4 ) samples = inf.run() inf.summary() inf.corner_plot('corner_joint.pdf') 支持的 Likelihood 字符串 ------------------------ HIcosmo 支持以下便捷的 likelihood 字符串： .. list-table:: :header-rows: 1 :widths: 15 35 50 * - 字符串 - 对应类 - 说明 * - ``sn`` - ``SN_likelihood("pantheon+")`` - Pantheon+ 1701个 SNe Ia * - ``sn_shoes`` - ``SN_likelihood("pantheon+shoes")`` - 含 Cepheid 标校 * - ``bao`` - ``BAO_likelihood("desi2024")`` - DESI 2024 BAO * - ``bao_sdss_dr12`` - ``BAO_likelihood("sdss_dr12")`` - SDSS DR12 BAO * - ``cmb`` - ``Planck2018DistancePriorsLikelihood`` - Planck 2018 压缩似然 * - ``h0licow`` - ``H0LiCOWLikelihood`` - 强透镜时延 * - ``tdcosmo`` - ``TDCOSMOLikelihood`` - TDCOSMO 层次贝叶斯 * - ``sh0es`` - ``SH0ESLikelihood`` - SH0ES 局部 :math:`H_0` 扩展暗能量模型 -------------- **wCDM 模型**（常数暗能量状态方程）： .. code-block:: python inf = hicosmo( cosmology="wCDM", likelihood=["sn", "bao", "cmb"], free_params=["H0", "Omega_m", "w0"], num_samples=10000 ) samples = inf.run() **CPL 参数化**（时变暗能量）： .. math:: w(a) = w_0 + w_a (1 - a) .. code-block:: python inf = hicosmo( cosmology="CPL", likelihood=["sn", "bao", "cmb"], free_params=["H0", "Omega_m", "w0", "wa"], num_samples=16000 ) samples = inf.run() 自定义似然函数 -------------- HIcosmo 不仅可以用于宇宙学分析，还可以用于任意参数拟合问题。以下示例展示如何拟合二次多项式 :math:`y = ax^2 + bx + c`： .. code-block:: python #!/usr/bin/env python """ Simple MCMC Example: Polynomial Fitting (y = a*x² + b*x + c) """ import hicosmo as hc hc.init() import numpy as np import jax.numpy as jnp from pathlib import Path from hicosmo.samplers import MCMC from hicosmo.visualization import Plotter # Load data data_path = Path(__file__).parent / 'data' / 'sim_data.txt' x, y_obs, y_err = np.loadtxt(data_path, unpack=True) x, y_obs, y_err = jnp.asarray(x), jnp.asarray(y_obs), jnp.asarray(y_err) def log_likelihood(a, b, c): """Log-likelihood: -0.5 * chi²""" y_th = a * x**2 + b * x + c return -0.5 * jnp.sum((y_obs - y_th)**2 / y_err**2) # Parameters: {name: (initial, min, max, latex)} params = { 'a': (3.5, 0.0, 10.0, r'$a$'), 'b': (1.0, 0.0, 4.0, r'$b$'), 'c': (1.0, 0.0, 3.0, r'$c$'), } if __name__ == '__main__': # Run MCMC mcmc = MCMC(params, log_likelihood, chain_name='polynomial_fit') mcmc.run(num_samples=20000) # Plot results plotter = Plotter('polynomial_fit') plotter.corner() plotter.report() **参数格式说明**： .. code-block:: python # 字典格式: {name: (initial, min, max, latex)} params = { 'a': (3.5, 0.0, 10.0, r'$a$'), # 参数 a: 初值 3.5，范围 [0, 10] 'b': (1.0, 0.0, 4.0, r'$b$'), # 参数 b: 初值 1.0，范围 [0, 4] 'c': (1.0, 0.0, 3.0, r'$c$'), # 参数 c: 初值 1.0，范围 [0, 3] } **运行结果**： .. code-block:: text INFO:hicosmo.samplers.init:✅ HIcosmo: 8 devices ready for parallel MCMC INFO:hicosmo.samplers.inference:MCMC completed: INFO:hicosmo.samplers.inference: Start time: 2026-01-08 16:54:43 INFO:hicosmo.samplers.inference: End time: 2026-01-08 16:54:45 INFO:hicosmo.samplers.inference: Duration: 1.94s INFO:hicosmo.samplers.inference: Saved to: mcmc_chains/polynomial_fit.h5 .. tip:: 生成的报告 (``plotter.report()``) 包含： - 参数约束（均值、中位数、68%/95% 置信区间） - LaTeX 格式输出（可直接用于论文） - MCMC 诊断（ESS、R̂） - 模型选择准则（AIC、贝叶斯证据） 使用类接口（高级） ------------------ 对于需要更多控制的场景，可以直接使用类接口： .. code-block:: python # 1. 首先初始化（必须在最前面！） import hicosmo as hc hc.init(8) # 8 个并行设备 # 2. 导入其他模块 from hicosmo.models import LCDM from hicosmo.likelihoods import SN_likelihood, BAO_likelihood from hicosmo.samplers import MCMC # 3. 创建 likelihood 对象 sne = SN_likelihood(LCDM, "pantheon+", M_B="marginalize") bao = BAO_likelihood(LCDM, "desi2024") # 联合 likelihood joint_likelihood = sne + bao # 4. 配置参数 params = { "H0": (70.0, 60.0, 80.0), # (参考值, 最小值, 最大值) "Omega_m": (0.3, 0.1, 0.5), } # 5. 创建 MCMC 并运行（num_chains 默认 = 设备数 = 8） mcmc = MCMC(params, joint_likelihood, chain_name="lcdm_sn_bao") samples = mcmc.run(num_samples=4000) # 6. 输出结果 mcmc.print_summary() 可视化结果 ---------- **Corner Plot**： .. code-block:: python from hicosmo.visualization import Plotter # 从保存的链加载 plotter = Plotter("lcdm_sn_bao") plotter.corner(["H0", "Omega_m"], filename="corner.pdf") **多链对比**： .. code-block:: python plotter = Plotter( ["chain_planck", "chain_shoes", "chain_bao"], chain_labels=["Planck", "SH0ES", "DESI BAO"] ) plotter.corner(["H0", "Omega_m"], filename="h0_tension.pdf") 保存和加载结果 -------------- .. code-block:: python # 保存结果 inf.save_results("results/my_analysis.pkl") # 加载并继续分析 from hicosmo.visualization import Plotter plotter = Plotter("results/my_analysis.pkl") plotter.corner(["H0", "Omega_m"]) YAML 配置驱动 ------------- 对于可复现的分析，推荐使用 YAML 配置文件： **config.yaml**： .. code-block:: yaml name: joint_analysis theory: LCDM likelihood: - name: sn dataset: pantheon+ - name: bao dataset: desi2024 - name: cmb dataset: planck2018 params: H0: prior: {dist: uniform, min: 50, max: 100} ref: 70.0 Omega_m: prior: {dist: uniform, min: 0.1, max: 0.5} ref: 0.3 sampler: name: numpyro num_samples: 8000 num_chains: 4 num_warmup: 1000 output: root: results chain_name: joint_lcdm **运行配置**： .. code-block:: python from hicosmo import run_from_config run_from_config("config.yaml") 下一步 ------ - 阅读 `核心概念 `_ 了解 HIcosmo 架构 - 查看 `似然函数 `_ 了解更多数据集 - 学习 `可视化 `_ 生成出版级图表 - 探索 `Fisher 预测 `_ 进行巡天预测