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：

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 \(H_0\) 和 \(\Omega_m\) 的后验分布样本。

小技巧

并行加速：在脚本最开头添加以下代码启用多设备并行：

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）

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

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：

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 \(H_0\)

扩展暗能量模型

**wCDM 模型**（常数暗能量状态方程）：

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）：

\[w(a) = w_0 + w_a (1 - a)\]
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 \(y = ax^2 + bx + c\)：

#!/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：

# 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：

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

小技巧

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：

# 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：

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：

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

# 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：

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：

from hicosmo import run_from_config

run_from_config("config.yaml")

下一步