The document discusses using Bayesian updating to analyze SAAM data. It describes using a Bayesian inversion approach to calculate the probability of success given observed data. The key points are:
- It formulates the approach using evidence ratios and probable probabilities rather than raw probabilities, which provides a simpler additive function of the prior probability.
- It establishes probabilities of different data observations given success or failure by analyzing frequencies in a database of past observations.
- The evidence implied by a single data indicator provides information on how significant and reliable that indicator is. Binning data works best with around 5 bins partitioned by samples rather than a continuous index. A hybrid model combines continuous modeling with binning.
4. Using database to update probability of success in the light
of observed DHIs using a database of DHI observations
Bayesian inversion, page 4
Prior probability of success
Observed DHI
DHI database
Probability of success GIVEN observed DHI
5. Using database to update probability of success in the light
of observed DHIs using a database of DHI observations
Bayesian inversion,
page 5
Prior probability of success
Observed DHI
DHI database
Probability of success GIVEN observed DHI
Probability of observed DHI GIVEN success
8. What is the probability we see the observed DHI if
there is [not] oil in the ground
Bayesian inversion, page 8
Success
Victory
Triumph
Sensation
Glory
Riches
Fortune
Fortuity
Serendipity
Fluke
Failure
Loser
Write-off
Defeat
Fiasco
Debacle
Blunder
Catastrophe
Turnip
Washout
X
X
X
X
X
X
X
X
X
X
X
9. What is the probability we see the observed DHI if
there is [not] oil in the ground
Bayesian inversion, page 9
Success Flat spot=โ4โ
Victory Flat spot=โ3โ
Triumph Flat spot=โ5โ
Sensation Flat spot=โ2โ
Glory Flat spot=โ4โ
Riches Flat spot=โ1โ
Fortune Flat spot=โ5โ
Fortuity Flat spot=โ3โ
Serendipity Flat spot=โ2โ
Fluke Flat spot=โ1โ
Failure Flat spot=โ4โ
Loser Flat spot=โ2โ
Write-off Flat spot=โ3โ
Defeat Flat spot=โ4โ
Fiasco Flat spot=โ2โ
Debacle Flat spot=โ1โ
Blunder Flat spot=โ3โ
Catastrophe Flat spot=โ2โ
Turnip Flat spot=โ3โ
Washout Flat spot=โ1โ
X
X
X
X
X
X
X
X
X
X
X
Condition on single DHI score, say flat spot
๐(flat spot = "3"|๐) ๐(flat spot = "3"|๐น)
Use the incidence of 3s amongst the success (failure
cases) to establish these probabilities
10. What is the probability we see the observed DHI if
there is [not] oil in the ground
Bayesian inversion, page 10
Success Index=14% bin 3
Victory Index=21% bin 4
Triumph Index=11% bin 3
Sensation Index=16% bin 4
Glory Index=12% bin 3
Riches Index=14% bin 3
Fortune Index=18% bin 4
Fortuity Index=25% bin 5
Serendipity Index=10% bin 3
Fluke Index=7% bin 2
Failure Index=14% bin 3
Loser Index=11% bin 3
Write-off Index=3% bin 2
Defeat Index=6% bin 2
Fiasco Index=30% bin 5
Debacle Index=3% bin 2
Blunder Index=2% bin 2
Catastrophe Index=12% bin 3
Turnip Index=-5% bin 1
Washout Index=1% bin 2
X
X
X
X
X
X
X
X
X
X
X
Condition on DHI index: Bins
๐(bin 3|๐) ๐(bin 3|๐น)
-23% ๏ฃ index < 1% Bin 1
1% ๏ฃ index < 9% Bin 2
9% ๏ฃ index < 16% Bin 3
16% ๏ฃ index < 24% Bin 4
24% ๏ฃ index < 45% Bin 5
Use incidence rate.
Choice on how many bins and where to set transitions
11. What is the probability we see the observed DHI if
there is [not] oil in the ground
Bayesian inversion, page 11
Success Index=14%
Victory Index=21%
Triumph Index=11%
Sensation Index=16%
Glory Index=12%
Riches Index=14%
Fortune Index=18%
Fortuity Index=25%
Serendipity Index=10%
Fluke Index=7%
Failure Index=14%
Loser Index=11%
Write-off Index=3%
Defeat Index=6%
Fiasco Index=30%
Debacle Index=3%
Blunder Index=2%
Catastrophe Index=12%
Turnip Index=-5%
Washout Index=1%
X
X
X
X
X
X
X
X
X
X
X
Condition on DHI index: Model
๐(index = 14%|๐) ๐(index = 14%|๐น)
13. Evidence: A mathematical sleight of hand
โข Probability
โข 0 certain failure
โข 1 certain success
โข Bayesโ theorem
๐ ๐|๐ท =
๐ ๐ท|๐
๐ ๐ท|๐ ๐ท ๐บ + ๐ ๐ท|๐น 1 โ ๐ท ๐บ
๐ท ๐บ
โข Complicated function of prior
โข Requires two numbers from database
โข Evidence
โข ๐ ๐ = 10 log
๐ ๐
1โ๐ ๐
โข โโ certain failure
โข โ certain success
โข Bayesโ theorem
๐ ๐|๐ท = ๐ ๐ + 10log
๐ ๐ท|๐
๐ ๐ท|๐น
โข Simple, additive function of prior
โข Single number captures effect of DHI data
Bayesian inversion, page 13
14. By working with evidence, a single number
captures the significance of your DHI data
Bayesian inversion, page 14
๐(๐)
๐(๐)
ฮ(๐ท)
๐(๐|๐ท)
๐(๐|๐ท)
15. Probable probabilities
Bayesian inversion, page 15
Success Flat spot=โ4โ
Victory Flat spot=โ3โ
Triumph Flat spot=โ5โ
Sensation Flat spot=โ2โ
Glory Flat spot=โ4โ
Riches Flat spot=โ1โ
Fortune Flat spot=โ5โ
Fortuity Flat spot=โ3โ
Serendipity Flat spot=โ2โ
Fluke Flat spot=โ1โ
Failure Flat spot=โ4โ
Loser Flat spot=โ2โ
Write-off Flat spot=โ3โ
Defeat Flat spot=โ4โ
Fiasco Flat spot=โ2โ
Debacle Flat spot=โ1โ
Blunder Flat spot=โ3โ
Catastrophe Flat spot=โ2โ
Turnip Flat spot=โ3โ
Washout Flat spot=โ1โ
X
X
X
X
X
X
X
X
X
X
Counting only really works if you have a very large number of
prospects and a large number in each category
Treat incident rates as evidence for a certain level of probability
๐(flat spot = "3"|๐)
X
๐(flat spot = "3"|๐น)
Score Total Success Failure
1 10 1 9
2 25 7 18
3 50 25 25
4 40 28 12
5 20 18 2
145 79 66 Probability distribution over evidence
implied by each score
17. The evidence implied by a single indicator tells you
about the significance and reliability of that indicator
Bayesian inversion, page 17
ฮ(๐ท)
๐ท
18. Binning the DHI index works best with around 5
bins and by partitioning samples, not the index
Bayesian inversion, page 18
19. Model based inference works well for mid-range
indices, but falls apart at the extremes
Bayesian inversion, page 19
20. Hybrid approach uses continuous model where it
agrees with binning
Bayesian inversion, page 20