What entrepreneurial problem can Bayes solve?

[hyunjimoon]

Goal

I wish to make the case for the need of tools/computation, which is in line with #156. Entrepreneurial decision-making is a great application area becase

1. I have MIT advantage (much accessible to cases and experts (Charlie Fine, Scott Stern, Erin Scott, Fiona Murray, Bill Autlet and delta V)
2. its operation has high uncertainty, which I categorized as atom, bit supply and customer and demand
3. Bayes rule is at the center of the entrepreneurial compass's slogan "test two, choose one" (p.748 of Gans3_EntrepreneurialStrategy.pdf). This brainchild of professor Scott Stern and Erin Scott even has a song, but computation is missing. Meaning implementation of compass which can further record and take into account the behavioral response to its strategic recommendation is room for improvement.

AOM 2023 conference summary

1. hosting Bayes in business lunch yesterday and took photo with six bayes supporters. I was able to meet from the conference session "Why everyone should be Bayesian". One insight was from extracting common traits from the domain where Bayes is trending: Biostatistics and quant marketing. Their data is wide, meaning diverse individuals (millions), but small data for each. Also, where performance matters -- meaning using Bayes contributes to performance, which is in line with my experiment in 2017.

2. Charlie suggested framing our work as Entrepreneur decision-making under uncertainty

3. I met with James Evans who was very supportive of bringing Bayes & probabilistic programming (suggested talking to joshua tenenbaum @ mit) into entrepreneurship. James' talk on designing diversity for sustained innovation is a good example of David Krackhardth's advice: to use a Bayesian hierarchical model to guide exploration i.e. which layer along the hierarchy [department, institution, city, country, world] to focus on. In Jame's example below, institution.

profile of entrepreneurial data

1. lack of data
2. survivor bias
3. contextual/contingency

[hyunjimoon]

Counterfactual simulation experimenting with different data (for compass);

• With or without attaching case studies

[hyunjimoon]

Infinite loop of alignment and capability to maximize agent's growth

As a Stan modeler, I accounted for different rates of growth in the Stan libraries' generators and estimators. As a Stan developer, our team accounted for the bigger community's growth. Different ways exist to improve the quality of modeling, but I feel research on how to sync this hierarchy of growths between different levels of agents (e.g. individual, Stan community, Statistical modeling community), how to bring consensus and governance would be beneficial.

[hyunjimoon]

I wish to put the chapter (annotated) below from this textbook (famous in bayes comp) on your radar as my simulation models will have high resemblance with model 13.2 from the book with code below.
McElreath_stat_rethiking_hierarchical_bayes.pdf

data{
    array[48] int N;
    array[48] int S;
    array[48] int tank;
}
parameters{
     vector[48] a;
     real a_bar;
     real<lower=0> sigma;
}
model{
    vector[48] p;
    sigma ~ exponential( 1 );
    a_bar ~ normal( 0 , 1.5 );
    a ~ normal( a_bar , sigma );
    for ( i in 1:48 ) {
        p[i] = a[tank[i]];
        p[i] = inv_logit(p[i]);
    }
    S ~ binomial( N , p );
}

e.g. by replacing tank as market segment, S as real utility

data{
    int E; // number of experiments in one segment
    array[E] int N;
    array[E] int S; // utility given from the environment
    array[E] int segment; //beachhead market
}
parameters{
     vector[E] a; // 
     real a_bar;
     real<lower=0> sigma;
}
model{
    vector[E] p;
    sigma ~ exponential( 1 );
    a_bar ~ normal( 0 , 1.5 );
    a ~ normal( a_bar , sigma );
    for ( m in 1:E ) {
        p[m] = a[segment[m]];
        p[m] = inv_logit(p[m]);
    }
    S ~ binomial( N , p );
}

when we run the above stan code for

• every experiment (E=1) - total of SM times
• every market segment (segment = [1,1, ...,1]) - total of S times
• once after experimenting over all experiment

[hyunjimoon]

for "every experiment (E=1)"