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Gibbs Sampling for Bayesian Linear Regression

MCMC methods can be used to estimate linear regression models. In what follows, we derive the distributional forms and algorithms associated with two Gibbs sampling approaches: the full conditionals approach and the composition method.

The dataset is available here and represents refrigerator price as a function of available features. Our objective is to estimate PRICE as a function of ECOST, FSIZE, SHELVES and FEATURES, where:

• PRICE: Response, cost of refrigerator.

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• $ (e.g., $4) represents columns, @ (e.g., @2) represents rows.
• $> means the last column.

Last row sum of all above:

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/*
- 2021-09-24 Received this from He
*/

with elasticity_xp as 
(select
        msg.load_uuid
        , max_by(msg.elasticity_experiment.pre_xp_price, ts) as pre_xp_price
        , max_by(msg.elasticity_experiment.post_xp_price, ts) as post_xp_price
        , max_by(msg.elasticity_experiment.perturbation_factor, ts) as perturbation_factor

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# test partial

from functools import partial


def frozen_func():
    return 2


def target_func(x, frozen_func):

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numpy.seterr(all='raise')

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from IPython.display import display

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import datetime

# get UTC timestamp in seconds
datetime_utc_origin = datetime.datetime(1970, 1, 1)

# now 
utc_timestamp_now = (datetime.datetime.utcnow() - datetime_utc_origin).total_seconds()

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import math

n = 33  # number of questions
r = 6  # number of correct answers

probs = []



for r in range(n):

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# specify time frequency of groupby
groupby_freq = 'W'

gr = df.groupby(
    pd.Grouper(key='date', freq=groupby_freq)
)

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# 2021-06-09 This is older way

import matplotlib.pyplot as plt

def plot_bar_chart_interaction(
    means_var1_low,
    means_var1_high,
    var1_name="",
    var2_name="",
    title="",