analysis of initial risk attitude distributions & population outcomes¶
Analyzing data generated from a batch run with 1000 iterations each per risk distribution
- maximum run length of 3000 steps
- convergence threshold at <=7% agents changing for two adjustment rounds in a row
In [1]:
import polars as pl
df = pl.read_csv("../../data/hawkdovemulti/dist_c7_3k_2024-02-27T162947_580557_model.csv")
In [2]:
total_runs = len(df)
print(f"Analyzing {total_runs} runs")
Analyzing 5000 runs
what % converged?¶
In [3]:
converged_df = df.filter(df["status"] == "converged")
len(converged_df)
Out[3]:
4594
almost all of them!
how long does it take to converge?¶
In [4]:
converged_df["Step"].describe()
Out[4]:
shape: (9, 2)
| statistic | value |
|---|---|
| str | f64 |
| "count" | 4594.0 |
| "null_count" | 0.0 |
| "mean" | 147.572921 |
| "std" | 135.641494 |
| "min" | 50.0 |
| "25%" | 70.0 |
| "50%" | 110.0 |
| "75%" | 170.0 |
| "max" | 2410.0 |
In [5]:
converged_df["Step"].plot.hist()
Out[5]:
compare different initial distributions¶
In [6]:
df["risk_distribution"].unique()
Out[6]:
shape: (5,)
| risk_distribution |
|---|
| str |
| "bimodal" |
| "skewed left" |
| "normal" |
| "skewed right" |
| "uniform" |
How many converged runs in each subset?
In [7]:
converged_df.group_by("risk_distribution").len().rename({"len": "count"})
Out[7]:
shape: (5, 2)
| risk_distribution | count |
|---|---|
| str | u32 |
| "skewed right" | 987 |
| "skewed left" | 963 |
| "uniform" | 938 |
| "bimodal" | 710 |
| "normal" | 996 |
In [8]:
# filter converged run data into subsets by risk distribution
subset = {}
for distribution in converged_df["risk_distribution"].unique():
subset[distribution] = converged_df.filter(pl.col("risk_distribution") == distribution)
How does initial distribution affect convergence?¶
In [9]:
status_by_dist = df.group_by("risk_distribution", "status").len().rename({"len": "count"})
status_by_dist
Out[9]:
shape: (10, 3)
| risk_distribution | status | count |
|---|---|---|
| str | str | u32 |
| "skewed right" | "running" | 13 |
| "bimodal" | "running" | 290 |
| "normal" | "converged" | 996 |
| "bimodal" | "converged" | 710 |
| "normal" | "running" | 4 |
| "uniform" | "converged" | 938 |
| "skewed left" | "running" | 37 |
| "uniform" | "running" | 62 |
| "skewed left" | "converged" | 963 |
| "skewed right" | "converged" | 987 |
In [10]:
import altair as alt
alt.Chart(status_by_dist).mark_bar().encode(
x='risk_distribution:N',
y='count',
color='status:N'
).properties(title="Simulation status (converged/running) by risk distribution", width=250, height=400)
Out[10]:
In [11]:
alt.Chart(converged_df).mark_boxplot(size=20).encode(
x='risk_distribution:N',
y='Step',
).properties(
title=alt.TitleParams(
"Simulation run length by risk distribution",
subtitle="(converged runs only)"),
width=350, height=450)
Out[11]:
population categories by risk distribution¶
In [15]:
import altair as alt
from simulatingrisk.hawkdovemulti import analysis_utils
uniform_chart = analysis_utils.graph_population_risk_category(
analysis_utils.groupby_population_risk_category(subset["uniform"])
).properties(title="Uniform")
normal_chart = analysis_utils.graph_population_risk_category(
analysis_utils.groupby_population_risk_category(subset["normal"])
).properties(title="Normal")
bimodal_chart = analysis_utils.graph_population_risk_category(
analysis_utils.groupby_population_risk_category(subset["bimodal"])
).properties(title="Bimodal")
skewedleft_chart = analysis_utils.graph_population_risk_category(
analysis_utils.groupby_population_risk_category(subset["skewed left"])
).properties(title="Skewed Left")
skewedright_chart = analysis_utils.graph_population_risk_category(
analysis_utils.groupby_population_risk_category(subset["skewed right"])
).properties(title="Skewed Right")
(uniform_chart | normal_chart | bimodal_chart | skewedleft_chart | skewedright_chart) \
.properties(title=alt.TitleParams("Distribution of Convergence States by Initial Risk Attitude Distribution", anchor="middle")).resolve_scale(y='shared')
Out[15]:
In [16]:
# display the same charts but in two rows
((uniform_chart | normal_chart | bimodal_chart ) & (skewedleft_chart | skewedright_chart)) \
.properties(
title=alt.TitleParams("Distribution of Convergence States by Initial Risk Attitude Distribution", anchor="middle")
).resolve_scale(
y='shared'
).configure_legend(orient="none", legendX=750, legendY=400)
Out[16]:
In [20]:
# output just the uniform/random distribution chart by itself, for inclusion in the paper
uniform_chart.properties(title="Distribution of Convergence States across Simulation Runs")
Out[20]:
In [ ]: