MCMC Analysis

Complete MCMC workflow with diagnostics and visualization.

Code

import pandas as pd
import matplotlib.pyplot as plt
import ezfit
from ezfit.examples import generate_multi_peak_data

# Generate data
df = generate_multi_peak_data(n_points=200, seed=42)

from ezfit import gaussian

def two_peaks(x, A1, c1, w1, A2, c2, w2, B):
    return gaussian(x, A1, c1, w1) + gaussian(x, A2, c2, w2) + B

# Step 1: Get initial guess
model_init, _, _ = df.fit(
    two_peaks, "x", "y", "yerr",
    method="curve_fit",
    A1={"value": 7.0, "min": 0, "max": 15},
    c1={"value": 7.0, "min": 5, "max": 9},
    w1={"value": 2.0, "min": 0.5, "max": 5},
    A2={"value": 5.0, "min": 0, "max": 15},
    c2={"value": 12.0, "min": 10, "max": 14},
    w2={"value": 3.0, "min": 0.5, "max": 5},
    B={"value": 0.5, "min": 0, "max": 2}
)

# Step 2: Run MCMC
model_mcmc, ax, ax_res = df.fit(
    two_peaks, "x", "y", "yerr",
    method="emcee",
    fit_kwargs={"nwalkers": 50, "nsteps": 2000, "progress": True},
    A1={"value": model_init["A1"].value, "min": 0, "max": 15},
    c1={"value": model_init["c1"].value, "min": 5, "max": 9},
    w1={"value": model_init["w1"].value, "min": 0.5, "max": 5},
    A2={"value": model_init["A2"].value, "min": 0, "max": 15},
    c2={"value": model_init["c2"].value, "min": 10, "max": 14},
    w2={"value": model_init["w2"].value, "min": 0.5, "max": 5},
    B={"value": model_init["B"].value, "min": 0, "max": 2}
)

plt.show()

# Step 3: Check diagnostics
print(model_mcmc.summary())

# Step 4: Visualize
model_mcmc.plot_trace()
plt.show()

model_mcmc.plot_corner()
plt.show()