Gibbs in genetics
August 24, 2018
The notes is for Gilks, W. R., Richardson, S., & Spiegelhalter, D. (Eds.). (1995). Markov chain Monte Carlo in practice. CRC press..
Introduction
- essential feature of genetic studies: involve related individuals.
- standard analysis methods of epidemiology is inappropriate which assume independence.
Standard methods in genetics
Genetic terminology
- genes, alleles, diallelic, genotype,
- homozygous, heterozygous
- dominant trait, recessive, codominant
- fully penetrant, locus, partially penetrant
- polygene
- Hardy-Weinberg equilibrium
- Linkage analysis
Genetic models
- $y_i$: phenotype for subject $i=1,\ldots,I$
- $x_i$: measured risk factors
- $z_i$: polygene
- $P$: a probability
比较表型和性状：
性状是指生物体所有特征的总和，由基因决定，必须是可以遗传的。而表型则是这些基因决定的性状在环境作用下的具体表现，与性状的概念有着本质区别，表型是不可遗传的。所以说表型又称性状的观点是不符合遗传学概念的。
a genetic model is specified in terms of two submodels.
- penetrance model $P(y\mid G, x,\Omega)$
- genotype model $P(G,z\mid\Theta)$
penetrance model:
- $y_i$ are conditionally independent given their genotype
- consider late-onset disease traits, characterized by a dichotomous disease status indicator $d$.
- an age variable $t$
- hazard function: $\lambda(t)$
- the penetrance for an unaffected individual is the probability of surviving to age $t$ free of the disease,
- the penetrance for an affected individuals is the density function $\lambda(t)S(t)$
- proportional hazards model:
- genotype model:
segregation analysis.
New words
- nuisance
- frailty
- meiosis
- sperm
- pedigree
- daunting
- spouse
ECOC
August 18, 2018
Abstract
Approaches to multiclass learning problems
- direct application of multiclass algorithms, such as C4.5 and CART
- application of binary concept learning algorithms to learn individual binary functions for each of the $k$ classes
- application of binary concept learning algorithms with distributed output representations.
New techinique
Error-correcting codes are employed as a distributed output representation
It is robust with respect to
- changes in the size of the training sample
- assignment of distributed representations to particular pruning 3, application of overfitting avoidance techniques such as decision-tree pruning.
And it can provide reliable class probability estimates.
Introduction
Two class
- decision-tree methods, such as C4.5 and CART.
- artificial neural network algorithms, such as the perceptron algorithm and the error BP algorithm.
Multiclass
- direct multiclass approach: generalize decision-tree algorithms
- one-per-class approach: learn one binary function for each class with connectionist algorithms. ($f_i,i=1,2,\ldots,k$)
- distributed output code.
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