phys_230 | Deepnote

Communication

!pip install pymc3 !pip install arviz !pip install empiricaldist import pymc3 as pm import arviz as az import seaborn as sns import numpy as np import matplotlib import matplotlib.pyplot as plt import empiricaldist as emp import pandas as pd

Abstract

The purpose of this lab is to use an Arduino over the serial port and collect some sort of data with a sensor. Our lab group chose to use a temperature sensor, with the output collected on the serial monitor and displayed on an OLED display. The sensor was proving unable to read anything above room temperature, so we had it read lower temperatures by moving it towards a cold source and collecting those changes in temperatures.

code_1 code_2

Shown in the code above, a data point is collected, the period is printed, then the data value onto the serial monitor. The data value is also displayed on the OLED.

df = pd.read_csv('proj4_data.csv') df.head()

Looking at the data above, the important columns to note are Room Temperature and Collected Temperature. You can see while there are very small changes in Room Temperature, there is a greater difference between data points in the Collected Temperature column (when a cold source approaches).

Exericise 1

x = np.array([1.73463558, 1.66331533, 1.87292601, 1.1716075 , 0.75154392, 1.56373077, 2.66792105, 2.99850011, 2.06616619, 2.35189101]) with pm.Model() as Difference: mu1 = pm.Uniform("mu", lower=1, upper=3) sigma1 = pm.Uniform("sigma1", lower=0, upper=1) Obs = pm.Normal("x_obs", mu=mu1, sigma=sigma1, observed=x) trace = pm.sample(1000, return_inferencedata=True) print(az.summary(trace,kind="stats")) print(az.plot_trace(trace))

Exercise 2

x1 = np.array([67.1,67,67.1,67.1,67.1,67.1,67.1,67.2,67.2,67.2,67.2,67.1,67.1,67.2,67.1,67.1,67.3,67.1,67.2,67.2,67.1,67.1,67.1,67.1,67.1,67.2,67.3,67.2,67.2,67.1,67.2,67.1,67,67.3,67.2,67.1,67.1,67.1,67.1,67.1,67.1,67.2,67.1,67.2,67.1,67,67,67,67.1,67.2]) x1

x2 = np.array([66.5,66.6,66.5,66.4,66.4,66.3,66.3,66.4,66.3,66.2,66.3,66.1,66.2,65.9,66,66,65.9,65.9,66,65.8,65.8,65.8,65.8,65.6,65.8,65.6,65.5,65.6,65.8,65.5,65.5,65.5,65.4,65.5,65.3,65.5,65.4,65.2,65.2,65.2,65.2,65.1,65.1,65,65.1,65.1,64.9,65,64.9,64.9]) x2

with pm.Model() as Difference: mu1 = pm.Uniform("mu1", lower=67, upper=67.2) mu2 = pm.Uniform("mu2", lower=64, upper=67) diff = pm.Deterministic("Diff", mu2 - mu1) sigma1 = pm.Uniform("sigma1", lower=0, upper=1) sigma2 = pm.Uniform("sigma2", lower=0, upper=1) Obs1 = pm.Normal("Obs1", mu=mu1, sigma=sigma1, observed=x1) Obs2 = pm.Normal("Obs2", mu=mu2, sigma=sigma2, observed=x2) trace = pm.sample(1000, return_inferencedata=True) print(az.summary(trace, kind="stats")) print(az.plot_trace(trace))

You can tell that the generative model produced data very similar to the data we collected because the means of mu1 and mu2 are quite close to the means of x1 and x2.

Communication

Abstract

Exericise 1

Exercise 2

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