Retail Expansion Cost Prediction using Bayesian Regression in ML

Retail development teams and finance officers must forecast the capital cost of opening a new store—before signing leases or placing equipment orders—using early-stage site metrics such as trade-area population density, average household income, existing competitor count, store footprint (sq ft), and the regional construction-cost index. Expansion costs per location exhibit nonlinear effects (bulk procurement discounts vs. premium finishes in high‐income areas) and are subject to uncertainty from material price swings and permit delays. A simple point estimate obscures this risk. By applying Bayesian Regression, we obtain both:

1. A point estimate of forecasted expansion cost.

2. A credible interval quantifying uncertainty—enabling risk‑aware budgeting and site selection.

Libraries Required

import pandas as pd                              # data I/O & manipulation  
import numpy as np                               # numerical operations  

import matplotlib.pyplot as plt                  # plotting  
import seaborn as sns                            # visualization  

import pymc3 as pm                               # Bayesian modeling  
import arviz as az                               # posterior analysis  

from sklearn.model_selection import train_test_split  
from sklearn.preprocessing import StandardScaler  
from sklearn.metrics import mean_absolute_error   

Dataset

Construction Estimation Data

Step-by-Step Code Implementation

Data Loading & Feature Engineering

Log‐Transformation: We model log(Expansion_Cost) to stabilise variance and enforce positivity.

import pandas as pd

# Load simulated buildout data
df = pd.read_csv("data/construction-estimation-data.csv")

# Rename columns to retail‐expansion context
# Use Project_Size_sqft as Store_Sqft, Num_Stories as Stories,
# Complexity_Index as FitOut_Complexity, Region_Price_Index stays
df = df.rename(columns={
    'Project_Size_sqft':     'Store_Sqft',
    'Num_Stories':           'Stories',
    'Complexity_Index':      'FitOut_Complexity',
    'Region_Price_Index':    'Region_Cost_Index',
    'Material_Cost':         'Material_Cost',
    'Labor_Cost':            'Labor_Cost'
})

# Compute total cost as proxy for expansion cost
df['Expansion_Cost'] = df['Material_Cost'] + df['Labor_Cost']

# Select features and target
features = ['Store_Sqft','Stories','FitOut_Complexity','Region_Cost_Index']
X = df[features].values
y = df['Expansion_Cost'].values  # USD

Train/Test Split & Standardisation

from sklearn.model_selection import train_test_split
from sklearn.preprocessing import StandardScaler

# 80/20 random split
X_train, X_test, y_train, y_test = train_test_split(
    X, y, test_size=0.2, random_state=42
)

# Standardize predictors for stable MCMC sampling
scaler = StandardScaler().fit(X_train)
X_train_s = scaler.transform(X_train)
X_test_s  = scaler.transform(X_test)

Define & Fit Bayesian Regression Model

Priors:

• α centred on the empirical mean log‑cost ±2 σ.
• β ∼ Normal(0,1) on standardized features.
• σ ∼ HalfNormal(y_std) for residual log‑cost variation.

Model: log(cost) ∼ Normal(α + β·X_std, σ).

Inference: 2,000 posterior draws (1,000 tuning) with target_accept=0.9 ensure robust convergence.

import pymc3 as pm

with pm.Model() as expansion_model:
    # Priors reflecting broad cost uncertainty
    α = pm.Normal("α", mu=y_train.mean(), sigma=y_train.std()*2)
    β = pm.Normal("β", mu=0, sigma=1, shape=X_train_s.shape[1])
    σ = pm.HalfNormal("σ", sigma=y_train.std())

    # Linear predictor for log‐cost stabilization
    μ = α + pm.math.dot(X_train_s, β)

    # Likelihood: observing Expansion_Cost (in log‐space for scale)
    Y_obs = pm.Normal("Y_obs", mu=μ, sigma=σ, observed=np.log(y_train))

    # MCMC sampling
    trace = pm.sample(
        draws=2000,
        tune=1000,
        target_accept=0.9,
        return_inferencedata=True
    )

Posterior Analysis & Point Predictions

• Posterior Predictive: Sampling in log‑space yields point forecasts and 94% HPD intervals, converted back by exponentiation for interpretation in USD.
• Evaluation: MAE computed on the original cost scale.

import arviz as az
from sklearn.metrics import mean_absolute_error

# Summarize posterior distributions
az.summary(trace, round_to=2)

# Posterior predictive sampling
with expansion_model:
    ppc = pm.sample_posterior_predictive(trace, var_names=["Y_obs"])

# Convert posterior means back from log‐space
α_post = trace.posterior["α"].mean().item()
β_post = trace.posterior["β"].mean(dim=["chain","draw"]).values

# Predict and exponentiate to original scale
log_pred = α_post + X_test_s.dot(β_post)
y_pred   = np.exp(log_pred)

# Evaluate MAE on cost scale
mae = mean_absolute_error(y_test, y_pred)
print(f"Test MAE: ${mae:,.2f}")

Visualise Predictions & Credible Intervals

Sweeping Store_Sqft reveals how larger footprints drive cost and the uncertainty around that relationship.

import numpy as np
import matplotlib.pyplot as plt

# Sweep Store_Sqft while holding others at median
grid_vals = np.linspace(X_train_s[:,0].min(), X_train_s[:,0].max(), 100)
grid = np.median(X_train_s, axis=0)[None,:].repeat(100, axis=0)
grid[:,0] = grid_vals

with expansion_model:
    ppc_grid = pm.sample_posterior_predictive(
        trace, var_names=["Y_obs"], samples=1000
    )

# Compute mean and 94% credible interval in log‐space, then exp()
preds_log = ppc_grid["Y_obs"]
mean_log  = preds_log.mean(axis=0)
hpd_log   = az.hdi(preds_log, hdi_prob=0.94)

mean_cost = np.exp(mean_log)
hpd_lower = np.exp(hpd_log[:,0])
hpd_upper = np.exp(hpd_log[:,1])

# Back‐transform Store_Sqft
sqft_orig = scaler.inverse_transform(grid)[:,0]

plt.figure(figsize=(8,5))
plt.plot(sqft_orig, mean_cost, label="Posterior mean")
plt.fill_between(sqft_orig, hpd_lower, hpd_upper, alpha=0.3,
                 label="94% credible interval")
plt.scatter(
    scaler.inverse_transform(X_test_s)[:,0],
    y_test, color="k", alpha=0.5, label="Test data"
)
plt.xlabel("Store Size (sq ft)")
plt.ylabel("Expansion Cost (USD)")
plt.title("Bayesian Regression: Cost vs. Store Sq ft")
plt.legend()
plt.tight_layout()
plt.show()

Summary

This Bayesian Regression framework for Retail Expansion Cost Prediction provides:

1. Accurate point forecasts of store build‑out cost from early site metrics.

2. Credible intervals capturing uncertainty from construction‐price volatility and design complexity.

3. Actionable insights: real‑estate and finance teams can set contingencies, negotiate contractor bids, and select sites with explicit cost‐risk bounds—optimising expansion spend under uncertainty.