Übung

• Compositinal data

• If VAR is larger than the empiric VAR of the binomial-modell / poisson-modell theoretical VAR

• The modell needs to be adapted to account for this overdisperson

• quatintive data in a relative description

• bacterial 16s ribosome gene

• super conserved region next unconserved region

• fucking amazing for pirmer creation

• From the negative binomial we can sample absolute counts for a given sample

  • But no relative data

  • For relative abundances we would have to sample all cases and divide by the total counts

• From the dirichlet distribution relative abundances can be sampled

• data driven approach

  • hypothesis derived from complex data analysis

• Hypothesis is defince based in deep biological understanding

• Pro:

  • Only relevant data / covariates collected

  • Researcher spends less time gathering (and analyzing) the data

• Con:

  • solid hypothesis needed

• Exploratory data analysis

• Regressional analysis (BMI prediction from gut bacteria)

  • well defined regression if all p,q are independent

  • => penalized and sparse regression

• Differential abundance testing

  • multiple testing problem

  • A lot of univariate hypothesis tests

• propability of an event is low

• number of trials is large

• No selection

• No mutation

• No mirgration

• Large population

• Random mating

• The average

• We know we get the best params for our model by MLE but we don’t know how good we acctually approximated the data

• Compare different fitting approaches (e.g. different base distributions)

• Oi = observed

• Ei = expected

• NULL hypothesis: Same as with t-test, that 2 distributions are similar

• Yes, we need to nromalize that

• MA plots can help to asses this

• DA / DE

  • compare gene value against mean of all other samples

  • Fold change of gene against mean of all others

• MA plot

  • Log fold change between means of 2 groups

  • x axis total average mean

  • Lower log fold change is significant if the mean is high

• Step 1: creates a pseudo-reference sample (row-wise geometric mean)

  • root( genecounts1 x genecounts2)

• Step 2: calculates ratio of each sample to the reference

  • gene_count / pseudo-reference

• Step 3: calculate the normalization factor for each sample (size factor)

  • median of all sample ratios

• Step 4: calculate the normalized count values using the normalization factor

  • raw count data / size factor

• Median of ratios normailzes for sequencing depth

• I does not do variance stablization

• CLR (centered log ratio)

  • good for compositinoal data

  • log of counts dividided by sample geometric mean

• VST (DESEQ2)

• rLOG

  • computational costly

  • good if we have highly variying size factors => very different sequencing depth

From rank(mean) to sd plots the performance of a normalization can be evaluated. Desired uniform distribution

• Modell selection plot

• MSE for different lambda value for LASSO

• We want highest possible lambda and best performance

• look at lambda at lowest MSE, take Lambda that is farthest to the right

• robustness testing

• Do i get the same results for different subsamples of my data ?

• This is shit

• For an instable model (e.g. different amounts of predictive genes after different cross val runs)

• hdi can identify stable genes (most commonly selected ones )

• H0: All genes are euqally often selected by our model

  
  

• Spurious correlations due to compositionality of the data.

• Spurious correlations due to high dimensionality (p>>n).

• (Correlations can exist between features without a direct relationship -> Depending on the research questions, one may still be interested in correlations).

• Data transformation -> Make counts comparable and account for compositionality

• Sparse inverse covariance estimation -> Associations between taxa

• Model selection -> Get a sparse network

• MB and GLASSO: Stability-based approach (StARS)

• SparCC: Threshold (Correlations with a magnitude below the threshold are set to zero)

• The distribution of node degrees follows a powerlaw

1. Data perparation

   1. taxa filtering ( taxa that are in too littel samples or just bad)

   2. zero treatment

   3. Normalization ( median of ratios / variance stabalizing transformations)

2. Network construction

3. Network analysis

4. Visualization

5. Network comparisson

• Correlation

• nFeatrueRNA

  • number of unique genes detected in a cell

  • Low-quality cells /empty low count

  • Cell duplets of multiplets aberrantly high gene count

• nCountRNA

  • total number of molecules detected in a cell

• percent.mt

  • precentage of reads that map to mitchondiral RNA

    
    

• Trying to distinguish what are sequencing errors and what are mutations

• The propabilites that a sequencing error is misidentified as a mutation, depends on the base and the mutation.

• mixture model

• diract delta

• e.g gamma dist

• multi omics factor analysis

• similar to metric euclidean MDS

• used to identify the ideal number of clusters

• simulation based validation

• monte carlo sampled reference data

• lk is average over log(WSS) of random graphs

• sk+1 is std of next gap (std computed on random models)

• get background distribution of test statistic by computing a ton of test statistics on permutations

1. Set a lambda

2. Create multiple networks with the set lambda on subsamples

3. Get per edge propability of occuring in a network

4. Get variance over all propabilities

   1. if all propabilities are the same => very low variance

   2. if there are very huge differences => high varainces

5. Select a model baseh on threshold ß on the edge prop variance graph