Being a guest answers the only question the statute asks about private property.
Section 767.04 covers someone bitten while “lawfully on or in a private place,” and then defines lawful presence to include being on the property “upon invitation, expressed or implied, of the owner.”
An invited guest is inside that without argument. So is someone who was told to come round, someone attending a party, and someone who was simply welcome there.
The owner’s own property is expressly included. The statute says liability applies “including the property of the owner of the dog.” Being bitten at their house is not a defence — it is the situation the statute names.
Implied invitation covers more than a spoken invite. You do not need to have been asked that day. A standing arrangement, a regular visit, a path to the door — the statute uses “expressed or implied” deliberately.
What the other side will argue instead. Not usually your presence. Expect comparative fault — that you approached the dog, reached toward it, or ignored a warning. That is a percentage argument, and above 50% it bars recovery entirely.
They may also raise the “Bad Dog” sign, which applies on the owner’s premises and can eliminate liability — with exceptions that matter, including that it never applies to a child under six.
The hard part is usually not legal. It is that the dog belongs to someone you like. In practice you are claiming against their homeowners policy, which exists for exactly this, not against them personally.