Updating with data, expanding our hypotheses

In this episode we use Google Sheets to build a simple model of observations (binary) of sighting or not sighting one of Elon Musks carbon life-affirming planets with his new panoramic telescope. Here is the Google Sheets model for the video: https://docs.google.com/spreadsheets/... We start with a grid of 5 hypotheses ranging from 0% to 100% probabilities of a single sighting (mutually exclusive and comprehensively exhaustive - MECE, thus the 0 and the 100) and 2 sightings (1= a sighting) and 1 no-sighting (0= no sighting) for a total of 3 tries (trials, total observations). We develop a grid generator for the 4 transitions (edges) across the 5 hypotheses (vertices). A hypothesis setup with index, parameters representing the 5 hypotheses, and the prior probability of a hypothesis. We assume we know as little as possible at first about the relative strength (probability of a hypothesis), the least informative probability distribution called the uniform distribution. With 5 hypotheses, the equal probabilities are 1/5. The prior thus represents our initial experience impounded into our theories, the hypotheses, all five of them. We then throw the hypotheses (our theory) against the reality of the 3 observations (1 1 0 in our coding). We obey the epistemological directive of Lonergan's critical realism (*Insight* (1992)) to conform the theory to the data, not the other way around. The probability associated with each hypothesis is the prior probability of a single occurrence times the probability of multiple (2 here) sightings time the probability of non-sightings (1 here). We then sum these hypothetically generated data probabilities across all of the 5 hypotheses. We can now build the relative probabilities of occurrence of each hypothesis with one another, allowing a reasonable (data and theory together) comparison of each hypothesis. We just need to divide each likelihood (already times it prior probability) by the total likelihood (the fabled probability of the data, unconditional since summed across all hypotheses). We then, if that was not enough, expand the data to update observations and the grid to expand the intensity, the fineness, of the grid. We have further discussions of focusing of certain high posterior probability hypotheses, as well as spreadsheet engineering practices (formatting, absolute/relative addressing of cells in formulae, deriving model generating data from sources, troubleshooting using commonsense!).