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  • Logger: each time a sample is collected, the program prints out the Posterior value, current ESS (Effective Sample Size) based on the posterior values, likelihood value, prior value, current ESS based on the prior values, and the sampled phylogenetic network sampled.
  • Summarization: the program prints out the chain length, burn-in length, sample frequency and the overall acceptance rate of proposals.
  • Operations: the usage and the acceptance rate for each operation.
  • Topologies: the MAP (Maximum A Posterior) topology is given. For The 95% credible set: For each unique topology in the 95% credible set, the network with the maximum posterior value and the averaged (branch lengths and inheritance probabilities) network are printed out. The topologies are ranked on their posterior probabilities.
  • Run time: the elapsed time.

 

Output of the second example

 

----------------------- Logger -----------------------
 Iteration

Iteration;    Posterior;  ESS;    Likelihood;    Prior;  ESS;    #Reticulation

0;    -

2736

32.

29030

31804;    0.00000;    -

2732

26.

29030

31804;   -

4

6.00000;    0.00000;    0;

(

TaB

C:1.0,(F:1.0,(

TaA

G:1.0,

TaD

K:1.0):1.0):1.0);

1;    -

2466

30.

11338

67945;    0.00000;    -

2461

24.

94926

36941;   -

4

6.

16411

31004;    0.00000;    0;

((

TaB:0.3961637257713907,(TaA

(F:1.

9334838641021195

100296825380626,

TaD

G:

1

3.

6038362742286094

091462635493304):0.

23062827100884262);

0672071335563177,C:1.2631834608546109):0.022439620222693815,K:0.7654486703017418);

......

18

9;    -

2441

39.

04154

23243;

2

    5.

93524

00000;    -

2430

24.

03388

51469;   -

11

14.

00767

71774;

2

    5.

73299

00000;

1

    0;

(

((TaD

C:

0

1.

09597337108498416

303229359865713,(

TaB

G:

0.23136218040818857)I2#H1:0.3566653185047678::0.3491095120667689)I3:0.868706329833222,TaA

1.184262389767834,(F:9.355326885355721,K:1.

9312992553517092

9913949707859038)

I1

I0:0.

6058432353787028,I2#H1

8785013943118355)I3:0.

6744658622739422::0.6508904879332311)I0

005027219859507291)I2;

19

10;    -

2438

47.

81459

01271;

3

    6.

12108

00000;    -

2428

23.

96331

75691;   -

9

23.

85129

25580;

3

    6.

06350

00000;    1;

((((

TaD

G:0.

9712042239200506

6775006643112376)

I3#H1

I1#H1:0.

11593455786736508:

10254403746151251::0.6222138281679854,(K:0.

3709418852580564,TaA

40305290671104776,F:11.774054935191478)I3:1.

665769657982743

0127444936379693)

I1

I4:0.

9242235576727479,(TaB

11119651081773953,C:0.6245266587065907)I2:0.

5027340616085754

24534630112752273,

I3#H1

I1#H1:0.

12410067880026514

6332472675472998::0.

6290581147419436)I2:0.32269541431429016)I0;
20; -2442.52537; 3.71247; -2430.97186; -11.55351; 3.29413; 1;
((TaA:0.407024316728807,(TaD:0.08498134125891532)I3#H1:0.1385571192167834::0.3614459570126758)I1:1.8568299946014093,(TaB:0.42061630776567865,I3#H1:1.0672749770829797::0.6385540429873242)I2:0.3889481921313129)

3777861718320146)I0;

----------------------- Summarization: -----------------------

Burn-in =

10000

5000, Chain length =

20000

10000, Sample size =

10

5 Acceptance rate = 0.

52930 

62080 

         --------------- Operations ---------------

Operation:Move-Head; Used:

2503

196; Accepted:

0

35 ACrate:0.

0

17857142857142858

Operation:Change-Length; Used:

9514

5782; Accepted:

8764

5628 ACrate:0.

921168803867984

9733656174334141

Operation:Add-Reticulation; Used:

104

92; Accepted:1 ACrate:0.

009615384615384616

010869565217391304

Operation:Flip-Reticulation; Used:

2572

191; Accepted:

314

44 ACrate:0.

12208398133748057

23036649214659685

Operation:Change-Probability; Used:

2339

172; Accepted:

1482

165 ACrate:0.

6336041043180847

9593023255813954

Operation:Move-Tail; Used:

2864

3564; Accepted:

2

332 ACrate:

6

0.

983240223463687E-4

0931537598204265

Operation:Delete-Reticulation

; Used:104; Accepted:23 ACrate:0.22115384615384615

; Used:3; Accepted:3 ACrate:1.0

 

Overall MAP = -39.13178296704008

(((G:1.8467353971326255,F:3.669429912707025)I4:0.72972613976057,C:0.7672463997220461)I0:0.14233512944191162,K:7.34631035390478)I3;

         --------------

- Topologies -

95% credible set of topologies: --------------

 Overall MAP = -2437.0654296232783

((TaB:0.561805846080817)I2#H1:0.46079502961747665::0.5721872707642428,(TaA:0.8950782820984362,(I2#H1:0.3411560735694928::0.4278127292357572,TaD:0.006727870085083132)I3:0.5352165283781162)I1:0.5975616454139091)I0;

Rank = 0; Size = 5; Percent = 0.5; MAP = -2437.1534368461857:(((TaD:0.3698584300172657)I3#H1:0.5289684026069202::0.4412419361674995,TaA:0.7616303047346242)I1:0.7750966068147521,(I3#H1:0.1429345953478124::0.5587580638325005,TaB:0.4229104875916929)I2:0.3596176393163555)I0; Ave=-2438.818599313804; ((TaB:0.4160163591812,(TaD:0.3919469161549564)I3#H1:0.31796822920332624::0.47841193003273014)I2:0.3651396905586732,(TaA:0.8638161723172626,I3#H1:0.4573559657851387::0.5215880699672699)I1:1.1104505168595664)I0;
Rank = 1; Size = 3; Percent = 0.3; MAP = -2437.0654296232783:((TaB:0.561805846080817)I2#H1:0.46079502961747665::0.5721872707642428,(TaA:0.8950782820984362,(I2#H1:0.3411560735694928::0.4278127292357572,TaD:0.006727870085083132)I3:0.5352165283781162)I1:0.5975616454139091)I0; Ave=-2438.660343133385; ((TaB:0.32291232768964834)I2#H1:0.4966162673971479::0.7172194611811242,(TaA:1.1187461803245535,(TaD:0.2756780415827574,I2#H1:0.2514608129776594::0.2827805388188757)I3:0.6520769835900365)I1:0.6443648892894459)I0;
Rank = 2; Size = 2; Percent = 0.2; MAP = -2439.4473793924326:((((TaA:0.17336878182196402)I1#H1:0.033229535170339664::0.3976884184622619,TaD:0.14393890216907568)I3:1.0180387358655751,TaB:0.4248091073311614)I2:0.34370948802981766,I1#H1:2.096254546618168::0.6023115815377381)I0; Ave=-2439.822939110307; ((TaA:0.7295242299369377)I1#H1:1.6167094294728663::0.8011557907688691,(TaB:0.40994585165323877,(TaD:0.17676921294169629,I1#H1:0.3700000579930729::0.19884420923113094)I3:0.7599278870428627)I2:0.44012247258275883)I0;

Rank = 0; Size = 2; Percent = 40.00; MAP = -39.23243337560144:(C:1.303229359865713,(G:1.184262389767834,(F:9.355326885355721,K:1.9913949707859038)I0:0.8785013943118355)I3:0.005027219859507291)I2; Ave=-39.25394715434493; (C:1.20916762172346,(G:2.057607023787008,(K:4.61838854181666,F:6.605842763421295)I0:0.5911795016873735)I4:0.1657841343330578)I3;

Rank = 1; Size = 1; Percent = 20.00; MAP = -47.01271365298103:((((G:0.6775006643112376)I1#H1:0.10254403746151251::0.6222138281679854,(K:0.40305290671104776,F:11.774054935191478)I3:1.0127444936379693)I4:0.11119651081773953,C:0.6245266587065907)I2:0.24534630112752273,I1#H1:0.6332472675472998::0.3777861718320146)I0; Ave=-47.01271365298103; ((G:0.6775006643112376)I1#H1:0.6332472675472998::0.3777861718320146,(C:0.6245266587065907,((F:11.774054935191478,K:0.40305290671104776)I3:1.0127444936379693,I1#H1:0.10254403746151251::0.6222138281679854)I4:0.11119651081773953)I2:0.24534630112752273)I0;

Rank = 2; Size = 1; Percent = 20.00; MAP = -39.13178296704008:(((G:1.8467353971326255,F:3.669429912707025)I4:0.72972613976057,C:0.7672463997220461)I0:0.14233512944191162,K:7.34631035390478)I3; Ave=-39.13178296704008; (K:7.34631035390478,(C:0.7672463997220461,(F:3.669429912707025,G:1.8467353971326255)I4:0.72972613976057)I0:0.14233512944191162)I3;

Rank = 3; Size = 1; Percent = 20.00; MAP = -40.2382981193348:(((F:7.823288510084807,K:6.50888387662072)I0:0.32861454580215427,C:0.8862007905628368)I4:0.1556168196177095,G:1.218111399301718)I3; Ave=-40.2382981193348; (G:1.218111399301718,(C:0.8862007905628368,(K:6.50888387662072,F:7.823288510084807)I0:0.32861454580215427)I4:0.1556168196177095)I3; 

Total elapsed time : 31.53400

Total elapsed time : 19.42900

s

Summarization

  • Topologies: the samples (samples from burn-in period are excluded) from all the files are combined. The topologies are ranked on their posterior probabilities. Only the topologies in the 95% credible set are printed out. The first topology is MPP (maximum posterior probability) topology.
  • PSRF (Potential Scale Reduction Factor): The PSRF values of posterior, likelihood and prior are calculated respectively. A PSRF value indicates good mixing when it approaches 1.0. 
  • Sojourns: a method to evaluate convergence/mixing. 'Sojourn' is a consecutive series of samples in which only the topology of interest was found. For each file, we summarize the frequency, the posterior probability, the number of sojourns, and the max and average length of sojourns for each topology in the 95% credible set. Ideally the number of sojourns is large while the length of sojourns is small -- the ability to leave and then return quickly and repeatedly to the same topology suggests good mixing with respect to topologies. 
  • SRQ (Scaled Regeneration Quantile) Plot: a method to evaluate convergence/mixing via topologies. Let Ti be the number of sampled MPP topology in the first i iteration of the stationary phase. For each file, we extract <i/n, Ti/Tn> for every i in 1...n into <x,y>. The slope of <x,y> in an SRQ plot should ideally be close to the posterior probability of MPP. Departures from this indicate that at some points the chain was on a trajectory that should have led to a different final posterior probability. 
  • Trace Plot: a method to evaluate convergence/mixing via posterior values. For each file, we extract a list of posterior values from the sampling phase. The format is compatible with Matlab and Python. 
---------------- Topologies ----------------

PosteriorProbability Topology

0.4500 ((TaB:0.2658858620952823)I2#H1:0.7341141379047177::0.8708100650901477,(TaA:1.0,(TaD:0.32466899225557677,I2#H1:1.3465736635156926::0.1291899349098523)I3:2.4002600314073748)I1:0.19747493612759992)I0;
0.2500 ((TaD:1.0,TaA:1.0):1.0,TaB:1.0);
0.1500 (((TaD:1.57737312713865)I3#H1:0.7217516903113591::0.42596342801648157,TaB:0.3702926554366514)I2:0.5822736350667996,(I3#H1:0.8251033741688848::0.5740365719835184,TaA:0.5942441726893598)I1:0.6915888106669655)I0;
0.1500 ((((TaA:0.2655477426293258)I1#H1:0.11325339702702007::0.4241273916272569,TaD:1.935302259486147)I3:0.786549353980848,TaB:0.40541038525824113)I2:0.2974313193957629,I1#H1:1.0824385015100584::0.5758726083727431)I0;
---------------- PSRF ----------------
Posterior - 1.0498673507956626
Likelihood - 1.09497860895306455
Prior - 1.0576479101618842

---------------- Sojourn ----------------
Topology Frequency Posterior #sojourns max(sjs) ave(sjs)
1 & 4 & 0.4000 & 2 & 3 & 2.00 \\
2 & 4 & 0.4000 & 1 & 4 & 4.00 \\
3 & 1 & 0.1000 & 1 & 1 & 1.00 \\
4 & 1 & 0.1000 & 1 & 1 & 1.00 \\
Topology Frequency Posterior #sojourns max(sjs) ave(sjs)
1 & 8 & 0.8000 & 1 & 8 & 8.00 \\
2 & 2 & 0.2000 & 1 & 2 & 2.00 \\
3 & 0 & 0.0000 & 0 & 0 & NaN \\
4 & 0 & 0.0000 & 0 & 0 & NaN \\
Topology Frequency Posterior #sojourns max(sjs) ave(sjs)
1 & 4 & 0.4000 & 2 & 2 & 2.00 \\
2 & 2 & 0.2000 & 1 & 2 & 2.00 \\
3 & 1 & 0.1000 & 1 & 1 & 1.00 \\
4 & 3 & 0.3000 & 2 & 2 & 1.50 \\
Topology Frequency Posterior #sojourns max(sjs) ave(sjs)
1 & 2 & 0.2000 & 2 & 1 & 1.00 \\
2 & 2 & 0.2000 & 1 & 2 & 2.00 \\
3 & 4 & 0.4000 & 3 & 2 & 1.33 \\
4 & 2 & 0.2000 & 2 & 1 & 1.00 \\

---------------- SRQ Plot ----------------
y0 = [0.25,0.5,0.75,1.0];
x0 = [0.5,0.6,0.7,1.0];
y1 = [0.125,0.25,0.375,0.5,0.625,0.75,0.875,1.0];
x1 = [0.3,0.4,0.5,0.6,0.7,0.8,0.9,1.0];
y2 = [0.25,0.5,0.75,1.0];
x2 = [0.3,0.4,0.8,0.9];
y3 = [0.5,1.0];
x3 = [0.5,0.7];
---------------- Trace Plot ----------------

y0 = [-2736.2903,-2487.17354,-2464.78381,-2465.97101,-2452.65531,-2443.28357,-2439.46916,-2441.01877,-2439.93589,-2442.0554,];

y1 = [-2736.2903,-2469.68094,-2438.08212,-2438.52812,-2439.02494,-2438.4918,-2439.33072,-2438.70721,-2438.68125,-2438.68995,];
y2 = [-2736.2903,-2474.94649,-2446.39497,-2438.87233,-2440.56426,-2442.1411,-2438.8736,-2439.18374,-2438.65952,-2439.23713,];
y3 = [-2736.2903,-2466.11338,-2451.75728,-2439.36378,-2439.58731,-2437.75625,-2439.12275,-2438.99142,-2439.20819,-2440.1315,]; 

 

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