We build a simple AI to aid decision makers who ask: what are the average waiting times for a set of 20 sites to serve customers? An Artificial Intelligence? The model is definitely artificial in materials, here a computer and supporting software. AI encodes and embodies some aspects of human intelligence in the form of probabilistic expression of decision maker beliefs, an objective-hypothetical framework, transformed data, and consumable outputs. Here we will be generating new data from human inputs and instructions all to answer a human question posed by human decision makers.
We start with pencil and paper to design our approach based on our knowledge and experience. To help answer our posed question, our model uses a single binary feature: {AM = 0, PM=1} with prior beliefs about the mean and standard deviation of average AM and PM waiting times. We also know that customers go from site to site across the AM-PM time boundary and thus we believe that AM and PM times are correlated. We also believe that customers can pick mornings at one eatery and afternoons at another. Our prior beliefs have already computed average and variation of waiting times and correlations. We feed our prior beliefs into a Gaussian observation model for waiting time outcomes. This is a hierarchical probabilistic model of waiting times with two states. In ML (Machine Learning) lingo we build a simple probabilistic quasi-Bayesian classification generative model.
To implement this model in a spreadsheet, we deploy NORM.DIST and NORM.INV to model outcomes; Cholesky transformation of variates to embody our correlation beliefs; INDEX and MATCH to perform table lookups; INDIRECT to use lists of data validated named ranges in functions; MAX, MIN, PERCENTILE, AVERAGE, AVEDEV, among others to produce an Exploratory Data Analysis (EDA) table; FORMULATEXT to document cells; borders to delimit cell areas and separate worksheets to delimit tasks; COUNTIFS to count outcomes in non-overlapping intervals of generated data; & to concatenate text elements for chart title dynamically in overlaid plots of frequency, relative frequency, cumulative relative frequency, and Gaussian cumulative frequency.
With all of this, the human decision maker can pose alternative assumptions, direct further development, and test the infant AI on a known problem.
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