Major Application Areas of Molecular Evolution. The Role of Models The Assumption of Basic Models The Famous Models: JC69, K80, F81, HKY85, REV,… Finer points: Codons, Heterogeneity, Local Dependency, overlapping constraints, Hidden Structure Dependency, Selection, Testing Models

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Likelihood. probability of observing the data given a model with certain parameters Maximum Likelihood Estimation (MLE) find the parameter combination that maximizes the likelihood requires some basic knowledge of probability. A Poisson Example. Pr(Observation= x ) = e - l l x / x !

Likelihood. Likelihood احتمال. apparent. apparent مبرهن. Literature. Literature. ادبيات. Lump sum. Lump sum. روي هم ، درهم. Attribute. Attribute ويژگي. Manner. Manner روش. Arrears. Arrears. عقب. As co-owner. As co-owner. به طور مشاع. Arbitrarily. Arbitrarily

Topics. DefinitionsDemonstration in EXCELExample of ML in ASREML. Definition. Maximum = ?????????Likelihood = ?????????????ML = ????????? ?????????. x2 = 1225. X = ?????? 2 ??? 1225???????????? ?????? ?????? ??????? 122510?10 = 100 ?????????? ????????????100?100 = 10000 ????????? ????????????

Maximum Likelihood. Likelihood The likelihood is the probability of the data given the model. Likelihood. If we flip a coin and get a head and we think the coin is unbiased, then the probability of observing this head is 0.5.

Empirical Likelihood. Dario Nappa Jon Sanders. What we are going to talk about. Parametric Likelihood Empirical likelihood Empirical Likelihood Statistical properties Pseudo Empirical Likelihood Use of auxiliary information Comparison with other statistical confidence intervals

Maximum Likelihood. There are three major paradigms of estimating linear models Method of Moments Oldest estimation method Population moments are best estimated by sample moments Not too useful for complex estimation Least Squares Minimize the sum of the squared errors

Maximum likelihood. The maximum likelihood criterion. The optimal tree is that which would be most likely to give rise to the observed data (under a given model of evolution). An outline of the ML approach: Consider one character, i. (It is useful to arbitrarily root the tree).

Maximum Likelihood. We have studied the OLS estimator. It only applies under certain assumptions In particular, e ~ N(0, s 2 ) But what if the sampling distribution is not Normal? We can use an alternative estimator: MLE. See “Generalized Linear Models” in S-Plus. OLS vs. MLE.

Maximum Likelihood. Benjamin Neale Boulder Workshop 2012. We will cover. Easy introduction to probability Rules of probability How to calculate likelihood for discrete outcomes Confidence intervals in likelihood Likelihood for continuous data. Starting simple.