Inference

Inference connects observed characters to parameters, ancestral assignments, and topology. The runtime distinguishes probabilistic objectives from parsimony cost models and preserves the search or sampling record needed to interpret either one.

Family	Objective	Essential review evidence
maximum likelihood	maximize data likelihood under a named model	starts, moves, convergence, fitted parameters, support method
Bayesian inference	characterize a posterior under likelihood and priors	proposals, acceptance, burn-in, ESS, chains, topology distribution
parsimony	minimize declared character-change cost	state/cost model, search trace, equal-best trees, consensus, support

Ask Three Questions Before Reading A Result

Every inferential result combines three decisions that must remain separately reviewable:

Question	Examples	Failure if omitted
what quantity is scored?	likelihood, posterior density, distance residual, character cost	the winning number has no stable scientific meaning
how was the state space explored?	optimizer starts, topology moves, Markov chains, heuristic search	the best encountered state is presented as the best supported state
how is uncertainty or stability represented?	profiles, resampling, independent chains, equal-best sets, sensitivity	one selected estimate is mistaken for certainty

The objective defines comparison under a model; exploration determines which candidate states were actually encountered; support qualifies the selected result. None can substitute for another. A high objective value cannot prove adequate exploration, and repeated discovery of one solution cannot establish that the model represents the data-generating process.

Continue by method family:

• Likelihood And Inference defines finite-state likelihood, optimization, model comparison, and the shared probabilistic layers.
• Distance-Based Inference covers distance estimation, assumption diagnostics, tree construction, residuals, influence, and resampling.
• Bayesian Inference covers native models, priors, proposals, checkpoints, chain diagnostics, posterior summaries, and the external-engine boundary.
• Parsimony covers Fitch, Wagner, Sankoff, Dollo, Camin–Sokal, topology search, reconstruction, and support.
• Search, Model Selection, And Support connects eligible candidates, exploration records, comparison admissibility, ties, and method-specific support across inference families.

Method Ownership Map

flowchart TB
    observations["Sequences · characters<br/>traits · distances"]
    distance["Distance objective<br/>and matrix assumptions"]
    likelihood["Likelihood objective<br/>and parameter search"]
    bayesian["Posterior objective<br/>priors and sampling"]
    parsimony["Character-cost objective<br/>and topology search"]
    review["Diagnostics · alternatives<br/>support and uncertainty"]

    observations --> distance --> review
    observations --> likelihood --> review
    observations --> bayesian --> review
    observations --> parsimony --> review

The families may share trees, states, and reports, but they do not share an objective or uncertainty interpretation. Preserve the method family in every result and artifact identity.

Separate Objective, Exploration, And Support

flowchart LR
    objective["Objective<br/>likelihood · posterior · cost"]
    exploration["Exploration<br/>optimization · sampling · search"]
    estimate["Estimate or<br/>selected topology"]
    support["Support and uncertainty<br/>resampling · posterior · alternatives"]
    interpretation["Bounded inference"]

    objective --> exploration --> estimate --> support --> interpretation

These layers fail independently. A correct likelihood can be paired with an inadequate topology search. A completed chain can target the wrong posterior. A best parsimony score can coexist with many equal-best trees. Support is not a generic confidence number added after selection; its producing procedure and denominator are part of the estimand.

Native And External Inference Paths

Path	Computation owner	Retained method state	Assurance boundary
native nucleotide maximum likelihood	Bijux finite-state likelihood and native search surfaces	model, objective, topology/search candidates, estimates, convergence and artifacts	supported contracts and benchmark corpora only
native Bayesian DNA inference	Bijux Bayesian model, prior, proposal and sampler surfaces	initial state, priors, proposals, samples, acceptance, burn-in and diagnostics	supported DNA entry-point/model boundary
native parsimony	Bijux scoring, reconstruction and topology-search surfaces	coding, cost matrix, moves, scores, equal-best trees and support	declared character and search contract
IQ-TREE2 or FastTree	named external executable through Bijux adapters	executable/version, command, model, native files, parsed topology/support	adapter correspondence; external algorithm ownership retained
MrBayes or BEAST	named external executable through Bayesian adapters	prepared analysis, execution identity, traces, trees, burn-in and diagnostics	parsed or live-run state must be distinguished

“Native” identifies implementation ownership, not universal superiority. “Adapter” identifies an execution and parsing contract, not weaker science. Select by the scientific model and assurance available for the intended claim.

Select The Inferential Contract

If the question is…	Required declaration	Do not omit
Which parameterized model has the strongest support?	likelihood model, candidate set, fitting policy	comparable likelihood convention and parameter counts
Which topology maximizes likelihood?	substitution model, partitions, starting trees, moves	search coverage, convergence, branch-length constraints
What posterior uncertainty remains?	likelihood, priors, proposals, chains, retention policy	burn-in, acceptance, ESS, topology diversity
Which tree minimizes character-change cost?	coding, cost model, ancestral constraints	equal-best trees, topology moves, search limits
How stable is the selected tree?	resampling or posterior support method	replicate count, support meaning, failed replicates

The same tree can be an input, a search state, a point estimate, or a sample from uncertainty. Preserve that role in result and artifact labels.

Preserve The Candidate Population

Selection changes interpretation. A chosen model, topology, parameter start, consensus, or posterior summary must remain connected to the population and rule from which it was selected.

Selected result	Candidate population to retain	Selection-aware review
best likelihood model	every eligible model, score, parameter count, failed fit, and criterion	ties, near-ties, candidate-set limits, and criterion sensitivity
best topology	starting trees, proposed/evaluated candidates, objective values, and termination	repeated-start agreement, near-optima, and unexplored search space
consensus tree	admitted trees, weights, burn-in or replicate policy, and excluded trees	split denominator, unresolved clades, and threshold sensitivity
reported posterior interval	chains, retained draws, transform, parameter key, and missing/non-finite draws	ESS, chain agreement, tail stability, and selection of the reported quantity
parsimonious reconstruction	all equal-best states or trees under the declared cost model	ambiguity, optimization rule, and alternative-history coverage

Reporting only the selected row makes selection failures and uncertainty unrecoverable. It also prevents a reviewer from distinguishing a dominant result from one that won by a negligible difference or because alternatives failed to execute.

Use Search, Model Selection, And Support for the common review packet and method-specific denominator rules.

Review The Search, Not Only The Winner

A final topology or score is insufficient when different starts, moves, or chains explored materially different regions. Retain accepted and rejected moves where supported, convergence and termination reasons, equal or near-equal solutions, support replicates, and warnings. These records distinguish a well-supported optimum from the best result found under a narrow search.

Search Evidence By Family

Family	Exploration record	Stability evidence	Warning that blocks a clean conclusion
maximum likelihood	starting topologies/parameters, evaluated moves, objective trace, termination	repeated starts, nearby solutions, parameter/profile sensitivity	non-finite objective, boundary estimate without treatment, inconsistent starts
Bayesian	chain seed/state, proposal schedule, accepted/rejected moves, retained draws	ESS, drift, independent-chain agreement, posterior topology diversity	inadequate effective size, non-stationary trace, inconsistent chains
parsimony	initial trees, move set, accepted scores, plateau/termination, equal-best set	repeated searches, consensus, resampling and move-set sensitivity	unexplored search space presented as exhaustive, discarded equal-best trees
distance	input distances, correction, matrix diagnostics, construction order	resampling, residuals, influence and alternative correction	invalid/saturated distances or a matrix that violates method assumptions

Interpret The Run State

State	Minimum retained information	Permitted interpretation
complete	objective, configuration, termination, diagnostics, result, and artifacts	bounded result under the declared model and search or sampling policy
partial	completed starts, moves, samples, replicates, outputs, and exact interruption	diagnostic evidence; no silent promotion to a complete estimate
refused	validated input identity and the violated precondition	the runtime protected the contract before computation
failed	execution context, exception or engine status, partial outputs, and denominator	failure of this execution; not automatic evidence against every method use
unavailable	named external dependency and discovery/version evidence	no external computation occurred

Completion is not a scientific verdict. It says that the declared execution contract reached its terminal state; accuracy, reference correspondence, and study evidence require their own records.

Compare Inferential Results Safely

Before comparing two fits or trees, align the data revision, taxon order, topology constraints, branch-length scale, state model, likelihood convention, parameter bounds, and search or sampling budget. Then compare structured quantities that share meaning. A better objective from a broader model, a different retained posterior, or a support value from another method is not an unqualified improvement on the original result.

Shared Limits

A reported optimum is conditional on the model and explored search space. A posterior is conditional on priors, proposals, and retained samples. A most parsimonious tree is conditional on coding, costs, and search coverage. None of these labels alone proves a historically certain topology.

Inference should refuse interpretation when the model is undefined for the input, optimization terminates without a usable solution, chains lack adequate mixing, or support generation is incomplete. A partial artifact may remain valuable for diagnosis, but its status must remain partial.