Lecture 3 Statistical Workflows

• Predicting BMI from Gut micro biome counts

• p >> n e.g; counts for 2000 species but only 100 subjects

• define statistical regression model

• define a penalized likelihood function

• estimate parameters by solving

• determine tuning param in a data driven way

• How do I normalize my data

• What does the data look like

• How would unsupervised learning look on this kind of data

• How can I detect changes accross conditions

• exploratory data analysis

• How can species-species associations be infered from the data

• e.g: Which species are propably closely related or have a symbiotic relationship based on the sequencing data

1. Sample 2000 samples with 600 features each from a multivariate normal distribution

2. => We know there is no correlation among the features

3. However if we sample just the first 200 there will be pseudo correlation values among some features

4. This pseudo correlation disappears with more data sampled

Without peanlization the resutls are shit

1. Get the data

2. Normalize the data

3. Parametric association estimation

4. Model selection

5. Dependency Graph / Covariance matrix

• λ = expected events in a given time interval

• P(X=k) is the propablity of seeing exactly k occurances

• λ can be computed by the average rate r * t

• Generalization of the binomial distribution

• Applied to data with more than 2 categories e.g ATCG

You can compute the propability that you will get a set value for each category, given their category propabilities and abs number.

• Negative binomial

• Models number of failures before set amount of success is reached

• Intuitively with dice rolls; 6=success 1-5=Failure => How many failures will be there before the third success given as a propability