"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"plt.plot(np.array(t_days) / 365., weights)\n",
"plt.xlabel(u'time (years)')\n",
"plt.ylabel('weight (kg)')"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We can do an interactive simulation for any person based on the same type of computation:"
]
},
{
"cell_type": "code",
"execution_count": 67,
"metadata": {},
"outputs": [],
"source": [
"def plot_simulation(sex, physical_activity, weight_kg, height_cm, age, caloric_delta_from_starting_weight):\n",
" p = Person(sex, physical_activity, weight_kg, height_cm, age)\n",
" \n",
" initial_energy_need = p.energy_need()\n",
" daily_consumption = initial_energy_need - caloric_delta_from_starting_weight\n",
"\n",
" t_days = range(365 * 10)\n",
" weights = []\n",
" for i in t_days:\n",
" weights.append(p.current_weight)\n",
" p.increment_day(daily_consumption)\n",
" \n",
" \n",
" plt.plot(np.array(t_days) / 365., weights)\n",
" plt.xlabel(u'time (years)')\n",
" plt.ylabel('weight (kg)')\n",
" plt.show()"
]
},
{
"cell_type": "code",
"execution_count": 68,
"metadata": {},
"outputs": [
{
"data": {
"application/vnd.jupyter.widget-view+json": {
"model_id": "9d21dd45666942a8bb6430be2c080e83",
"version_major": 2,
"version_minor": 0
},
"text/html": [
"Failed to display Jupyter Widget of type interactive.
\n",
"\n",
" If you're reading this message in the Jupyter Notebook or JupyterLab Notebook, it may mean\n",
" that the widgets JavaScript is still loading. If this message persists, it\n",
" likely means that the widgets JavaScript library is either not installed or\n",
" not enabled. See the Jupyter\n",
" Widgets Documentation for setup instructions.\n",
"
\n",
"\n",
" If you're reading this message in another frontend (for example, a static\n",
" rendering on GitHub or NBViewer),\n",
" it may mean that your frontend doesn't currently support widgets.\n",
"
\n"
],
"text/plain": [
"interactive(children=(Dropdown(description='sex', options=('male', 'female'), value='male'), FloatSlider(value=1.5999999999999999, description='physical_activity', max=1.8, min=1.4, step=0.01), FloatSlider(value=85.0, description='weight_kg', max=150.0, min=20.0, step=0.5), FloatSlider(value=185.0, description='height_cm', max=220.0, min=150.0, step=0.5), IntSlider(value=58, description='age', max=99, min=18), IntSlider(value=0, description='caloric_delta_from_starting_weight', max=2000, min=-2000, step=10), Output()), _dom_classes=('widget-interact',))"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
"text/plain": [
""
]
},
"execution_count": 68,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"interact(plot_simulation,\n",
" sex=['male', 'female'],\n",
" physical_activity=(1.4, 1.8, 0.01),\n",
" weight_kg=(20, 150, 0.5),\n",
" height_cm=(150, 220, 0.5),\n",
" age=(18, 99),\n",
" caloric_delta_from_starting_weight=(-2000, 2000, 10))"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Taking into account the age in the weight change over time"
]
},
{
"cell_type": "code",
"execution_count": 69,
"metadata": {},
"outputs": [],
"source": [
"class AgingPerson(Person):\n",
" def increment_day(self, daily_energy_intake):\n",
" energy_balance = daily_energy_intake - self.energy_need()\n",
" self.current_weight += energy_balance / 7700\n",
" self.current_age += 1 / 365."
]
},
{
"cell_type": "code",
"execution_count": 70,
"metadata": {},
"outputs": [],
"source": [
"def plot_simulation_with_aging(sex, physical_activity, weight_kg, height_cm, age, caloric_delta_from_starting_weight):\n",
" p = AgingPerson(sex, physical_activity, weight_kg, height_cm, age)\n",
" \n",
" initial_energy_need = p.energy_need()\n",
" daily_consumption = initial_energy_need - caloric_delta_from_starting_weight\n",
"\n",
" t_days = range(365 * 10)\n",
" weights = []\n",
" for i in t_days:\n",
" weights.append(p.current_weight)\n",
" p.increment_day(daily_consumption)\n",
" \n",
" \n",
" plt.plot(np.array(t_days) / 365., weights)\n",
" plt.xlabel(u'time (years)')\n",
" plt.ylabel('weight (kg)')\n",
" plt.show()"
]
},
{
"cell_type": "code",
"execution_count": 71,
"metadata": {},
"outputs": [
{
"data": {
"application/vnd.jupyter.widget-view+json": {
"model_id": "bd158f1a3a4a4aeb9261d6d9fbfd54fe",
"version_major": 2,
"version_minor": 0
},
"text/html": [
"Failed to display Jupyter Widget of type interactive.
\n",
"\n",
" If you're reading this message in the Jupyter Notebook or JupyterLab Notebook, it may mean\n",
" that the widgets JavaScript is still loading. If this message persists, it\n",
" likely means that the widgets JavaScript library is either not installed or\n",
" not enabled. See the Jupyter\n",
" Widgets Documentation for setup instructions.\n",
"
\n",
"\n",
" If you're reading this message in another frontend (for example, a static\n",
" rendering on GitHub or NBViewer),\n",
" it may mean that your frontend doesn't currently support widgets.\n",
"
\n"
],
"text/plain": [
"interactive(children=(Dropdown(description='sex', options=('male', 'female'), value='male'), FloatSlider(value=1.5999999999999999, description='physical_activity', max=1.8, min=1.4, step=0.01), FloatSlider(value=85.0, description='weight_kg', max=150.0, min=20.0, step=0.5), FloatSlider(value=185.0, description='height_cm', max=220.0, min=150.0, step=0.5), IntSlider(value=58, description='age', max=99, min=18), IntSlider(value=0, description='caloric_delta_from_starting_weight', max=2000, min=-2000, step=10), Output()), _dom_classes=('widget-interact',))"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
"text/plain": [
""
]
},
"execution_count": 71,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"interact(plot_simulation_with_aging,\n",
" sex=['male', 'female'],\n",
" physical_activity=(1.4, 1.8, 0.01),\n",
" weight_kg=(20, 150, 0.5),\n",
" height_cm=(150, 220, 0.5),\n",
" age=(18, 99),\n",
" caloric_delta_from_starting_weight=(-2000, 2000, 10))"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"What we see now is the effect of aging: the older you are, the less energy you need. So eating the same amount of food will, at some point, will make you gain weight."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# The problem with weighing yourself"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"It is known from the litterature that your weight fluctuates daily with important variations. Suppose you weight 70 kilos, your weight might be between 68 and 72 kilos. We can simulate the real weight measured over 15 days with very little code:"
]
},
{
"cell_type": "code",
"execution_count": 72,
"metadata": {},
"outputs": [],
"source": [
"np.random.seed(42)\n",
"weights = np.random.random(size=15) * 4 - 2 + 70"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Let's plot this:"
]
},
{
"cell_type": "code",
"execution_count": 73,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"Text(0,0.5,'weight')"
]
},
"execution_count": 73,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
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53FFQ50EskUK3N4IahwGMxHsr56K22ox/Wj8DgXAc2187jlS6MI8hSfaSqTR6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\nsbERs2bNwpUrV8Quxam2b9+O2NhYLFy4ELt27RK7HIczm81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"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"plt.plot(weights)\n",
"plt.xlabel('day')\n",
"plt.ylabel('weight')"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Now suppose you measure your weight every week once. This corresponds to measures on day 0 and 7. Your measured average will be:"
]
},
{
"cell_type": "code",
"execution_count": 74,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"70.4814325292446"
]
},
"execution_count": 74,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"(weights[0] + weights[7])/2."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"If you do that, you might think you gained weight since you last weighed yourself. What if you measured yourself on the fourth day of every week?"
]
},
{
"cell_type": "code",
"execution_count": 75,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"69.23848595698568"
]
},
"execution_count": 75,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"(weights[3] + weights[10])/2."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"In that case you migth think you have lost some weight, even if you haven't. \n",
"\n",
"The point is: due to the randome fluctuations of your weight, you should measure it more often than not! Practically, this means that if you average your weight over every day in the last two weeks, you fill get an accurate measurement of your weight:"
]
},
{
"cell_type": "code",
"execution_count": 76,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"69.97825824657875"
]
},
"execution_count": 76,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"weights.mean()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"See? Very close to 70 kilograms!\n",
"\n",
"To demonstrate the effect of this \"how often do your weigh yourself\", we can write a little program that takes as input the period of measurement (14 days in our previous example) and the interval between each time you weigh yourself during that period. Based on this data, we can compute the mean error based on the fact that the true weight is known as a simulation input:"
]
},
{
"cell_type": "code",
"execution_count": 77,
"metadata": {},
"outputs": [],
"source": [
"def simulate_weight_measurement(true_weight, observation_period, measure_every_x_days):\n",
" weights = true_weight + np.random.random(size=observation_period * 1000) * 4 - 2\n",
" measured_error = (true_weight - np.mean(weights[::measure_every_x_days])) / true_weight\n",
" return np.abs(measured_error.mean())"
]
},
{
"cell_type": "code",
"execution_count": 82,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"0.03607601444431095"
]
},
"execution_count": 82,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"simulate_weight_measurement(70, 7, 7) * 100"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": []
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": []
}
],
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"language": "python",
"name": "python3"
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"language_info": {
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"file_extension": ".py",
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"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
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"toc": {
"colors": {
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"selected_highlight": "#FFD700",
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